An aquarium manager drena
blueprint for a cylindrical fish tanka
the tank has a vertical tube in the
middle in which visitors can stand
and view the fish
the best average density for the species of fish that will go in the
tankis 16 fish per 100 gallons of water. this provides enough
room for the fish to swim while making sure that there are
plenty of fish for people to see
the aquarium has 275 fish available to put in the tank, s bis he
right number of fish for the tank. if not, how many fich should
be added or removed? explain your reasoning

Answers

Answer 1

To determine if the 275 fish are the right number for the cylindrical fish tank, we need to calculate the tank's capacity and compare it to the recommended average density of 16 fish per 100 gallons of water.

The volume of a cylinder is given by the formula V = πr^2h, where V is the volume, r is the radius, and h is the height of the cylinder.

Assuming the tank has a height of h and a radius of r, we can calculate its volume as follows:

[tex]V = πr^2h[/tex]

Since the tank has a vertical tube in the middle, we need to subtract the volume of the tube from the total volume of the tank. Let's assume the tube has a radius of 2 feet and a height of 8 feet. Then the volume of the tube is:

Vtube = π(2)^2(8) = 100.53 cubic feet

Thus, the volume of the tank without the tube is:

Vtank = πr^2h - Vtube

To find the value of r, we need to know the diameter of the tank. Let's assume the tank has a diameter of 10 feet, which means the radius is 5 feet.

Then the volume of the tank without the tube is:

Vtank = π(5)^2h - 100.53

We need to convert the volume of the tank from cubic feet to gallons, so we multiply by 7.48 (1 cubic foot = 7.48 gallons):

Vtank(gallons) = 7.48[π(5)^2h - 100.53]

Now we can calculate the recommended number of fish for the tank:

Recommended number of fish = 16 fish/100 gallons x Vtank(gallons)

Recommended number of fish = 16 fish/100 gallons x 7.48[π(5)^2h - 100.53]

Recommended number of fish = 1.175[π(5)^2h - 100.53]

So, if the number of fish available is 275, we can set up the following equation:

275 = 1.175[π(5)^2h - 100.53]

Solving for h, we get:

h = (275/1.175π(5)^2) + (100.53/π(5)^2)

h ≈ 8.3 feet

Therefore, the cylindrical fish tank with a height of 8.3 feet and a radius of 5 feet can hold 275 fish with an average density of 16 fish per 100 gallons of water. If the aquarium manager wants to add more fish, they should recalculate the volume of the tank and adjust the height accordingly to maintain the recommended density of 16 fish per 100 gallons of water. Conversely, if they want to remove fish, they can do so without changing the height of the tank.

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Related Questions

The base radius and height of a right circular cone are measured as 10 cm and 25 cm, respectively, with a possible error in measurement of as much as 0.1 cm in each dimension. Use differentials to estimate the maximum error in the calculated volume of the cone. (Hint: V = 1/3 πr²h)

Answers

The estimated maximum error in the calculated volume of the cone is 20π cubic centimeters.

How to estimate the maximum error in the calculated volume of the cone?

Let V = (1/3)πr²h be the volume of the cone, where r and h are the base radius and height of the cone, respectively.

Let dr and dh be the possible errors in the measurements of r and h, respectively.

Then, the actual dimensions of the cone are (r+dr) cm and (h+dh) cm, respectively.

The differential of V is given by:

dV = (∂V/∂r)dr + (∂V/∂h)dh

We have:

∂V/∂r = (2/3)πrh and ∂V/∂h = (1/3)πr²

Substituting the given values, we get:

∂V/∂r = (2/3)π(10 cm)(25 cm) = 500π/3

∂V/∂h = (1/3)π(10 cm)² = 100π/3

Substituting into the differential equation, we get:

dV = (500π/3)dr + (100π/3)dh

Using the given maximum error of 0.1 cm for both r and h, we have:

|dr| ≤ 0.1 cm and |dh| ≤ 0.1 cm

Therefore, the maximum possible error in V is given by:

|dV| = |(500π/3)(0.1 cm) + (100π/3)(0.1 cm)|

|dV| = 50π/3 + 10π/3

|dV| = 60π/3

|dV| = 20π cm³

Therefore, the estimated maximum error in the calculated volume of the cone is 20π cubic centimeters.

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The back of Tim's truck is 6. 5 feet long, 5 feet wide, and 7 feet tall. He has several boxes of collectables that he


needs to move. Each box of papers is shaped like a cube, measuring 2 feet on each side.


How many boxes of papers can Tim pack into the back of his truck? (Think logically to figure out how many will


fit. )


Tim can pack


boxes of papers into the back of his truck.

Answers

Tim's truck has a volume of (6.5 feet) x (5 feet) x (7 feet) = 227.5 cubic feet. Each box of papers has a volume of (2 feet) x (2 feet) x (2 feet) = 8 cubic feet. To determine how many boxes of papers Tim can pack into the truck, we need to divide the total volume of the truck by the volume of each box:

227.5 cubic feet ÷ 8 cubic feet per box = 28.44 boxes

Since we can't pack a fraction of a box, Tim can pack a maximum of 28 boxes of papers into his truck. However, this assumes that there is no wasted space due to irregular shapes of the boxes or other items in the truck.

In reality, Tim may be able to pack slightly fewer boxes depending on how he arranges them in the truck.

Hence, Tim's truck has a volume of 227.5 cubic feet. Each box of papers has a volume of 8 cubic feet.

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A boat is heading towards a lighthouse, whose beacon-light is 119 feet above the water. From point A, the boat’s crew measures the angle of elevation to the beacon, 5 , before they draw closer. They measure the angle of elevation a second time from point
B at some later time to be 18∘ Find the distance from point A to point B. Round your answer to the nearest foot if necessary.

Answers

If boat is heading towards a lighthouse, whose beacon-light is 119 feet above the water, the distance from point A to point B is approximately 973 feet.

To find the distance from point A to point B, we can use trigonometry and the fact that the angles of elevation from both points are known.

Let x be the distance from point A to the lighthouse, and y be the distance from point B to the lighthouse. We can set up two equations using tangent function:

tan(5) = 119/x

tan(18) = 119/y

We can solve for x and y by isolating them in each equation:

x = 119/tan(5) ≈ 1343.44 feet

y = 119/tan(18) ≈ 370.79 feet

Therefore, the distance from point A to point B is approximately 1343.44 - 370.79 = 972.65 feet.

We rounded the final answer to the nearest foot, which is 973 feet.

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the process standard deviation is ounces, and the process control is set at plus or minus standard deviations. units with weights less than or greater than ounces will be classified as defects. what is the probability of a defect (to 4 decimals)?

Answers

The probability of a defect in the manufacturing process, assuming that the weight of the products follows a normal distribution, is 0.1587 to four decimal places.

To calculate the probability of a defect, we first need to calculate the z-score of the weight that would classify the product as a defect. The z-score is a measure of how many standard deviations a value is from the mean. In this case, the z-score is -1 or 1, depending on whether the weight is less than one standard deviation below the mean or greater than one standard deviation above the mean.

Once we have calculated the z-score, we can use a standard normal distribution table or a calculator to find the probability of a product being classified as a defect. If the z-score is -1, the probability of a product being classified as a defect is 0.1587. If the z-score is 1, the probability of a product being classified as a defect is also 0.1587.

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What is the value of the x-coordinate of point A?


a) sin (pi/6)


b) cos (pi/6)


c) sin (pi/3)


d) cos (pi/3)


e) sin (2pi/3)


f) cos (2pi/3)

Answers

Without a diagram or additional information, it is impossible to determine the value of the x-coordinate of point A.

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The aquarium has a fish tank in the shape of a prism. if the tank is 3/4 full of water, how much water is in the tank?

Answers

The amount of water in the tank can be calculated by multiplying 3/4 to the volume of the tank: 3/4 x V = (3/4)L x W x H.

To calculate the amount of water in the aquarium's fish tank in the shape of a prism,

you would need to know the dimensions of the tank and then multiply the volume of the tank by 3/4.

Let's assume that the aquarium has a rectangular prism shape,

the amount of water in the tank would depend on the dimensions of the tank.

Let's assume the tank has a length of L, a width of W, and a height of H.

The volume of the tank can be calculated by multiplying the length, width, and height together: V = L x W x H.

If the tank is 3/4 full of water, the volume of water in the tank would be 3/4 of the total volume of the tank.

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Josh and Draven can clean the JHS cafeteria in 25 minutes. Draven can clean the JHS cafeteria in 40 minutes. How long will it take Josh to do the job if he works alone?

Answers

It will take Josh about 66.67 minutes to easy the cafeteria alone.

Let's anticipate that the amount of work required to easy the cafeteria is 1 unit.

In a single minute, Josh can easy 1/x of the cafeteria (in which x is the number of mins it takes Josh to do the task alone), and Draven can clean 1/40 of the cafeteria in one minute.

When they work together, they could easy the cafeteria in 25 minutes, so in one minute they are able to easy 1/25 of the cafeteria.

The use of the fact that their combined rate is the sum in their individual rates, we are able to installation an equation:

1/x + 1/40 = 1/25

Multiplying each facets through the least common more than one of the denominators (40 * 25 * x), we get:

25 * 40 + x * 40 = x * 25

1000 + 40x = 25x

15x = 1000

x = 66.67

Therefore, it'd take Josh about 66.67 minutes to easy the cafeteria alone.

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For the line y=2/5x+9, what will be the angle this line makes with the x-axis?

Answers

Answer:

21.8014 degrees (to 4 decimal places)

Step-by-step explanation:

The equation y=2/5x+9 forms a certain angle with the x-axis.  Note that all lines parallel to y=2/5x+9 also form the same angle with the x-axis, due to Corresponding Angles (the fact that the original line has a y-intercept of 9 is irrelevant).  Therefore, we could simplify this problem slightly by considering the angle that y=2/5x (a y-intercept of 0) forms with the x-axis.

To find the angle that this line makes with the x-axis, we'll need the vertex (the origin -- let's call this point "B"), and one point on each of two rays from the vertex (Let Ray #1 be the ray from the origin directly to the right; and let Ray #2 be the ray from the origin extending into Quadrant I -- up and to the right, along the equation y=2/5x).

One point on Ray #1 is (5,0) -- it is on the positive x-axis.  Call this point "A"

One point on Ray #2 is (5,2) -- inputting "5" for x, the result for y is "2"  Call this point "C"

y = 2/5 * (5) = 2

To find the angle (Angle ABC), observe that the three points form a right triangle (the angle CAB is a right angle because the two lines are perpendicular).

To solve for [tex]\angle ABC[/tex], recall the definition of the tangent function:

[tex]tan(\theta)=\dfrac{opposite}{adjacent}[/tex]

The Opposite side, side AC, is just the height (or the y-value) of point C.  So, opposite = 2.

The Adjacent side, side BA, is just the x-coordinate of point A (and also point C).  So adjacent = 5.

Substituting these known values into the tangent function, we get the following:

[tex]tan(m\angle ABC)=\dfrac{2}{5}[/tex]

To solve for the measure of angle ABC, we need to apply the inverse tangent function (also known as arctangent).

[tex]arctan(tan(m\angle ABC)=arctan(\dfrac{2}{5})[/tex]

The left side simplifies because they are inverse functions:[tex]m\angle ABC=arctan(\dfrac{2}{5})[/tex]

Calculating the right side of the equation (rounding to 4 decimal places):

[tex]m\angle ABC \approx 21.8014^{o}[/tex]

7. At Burger Heaven a double contains 2 meat patties and 6 pickles, whereas a



triple contains 3 meat patties and 3 pickles. Near closing time one day, only



24 meat patties and 48 pickles are available. If a double burger sells for



$1. 20 and a triple burger sells for $1. 50, then how many of each should be



made to maximize the total revenue?



(4. 6 5pts)



a) Write your constraints (1pt)

Answers

At Burger Heaven, to maximize the total revenue from selling double burgers containing 2 meat patties and 6 pickles, you need to consider the following constraints:

1. Ingredient availability: Ensure that there are enough meat patties and pickles in stock to meet the demand for double burgers.
2. Production capacity: The kitchen staff must be able to efficiently prepare and assemble the double burgers without compromising on quality.


3. Pricing strategy: Set a competitive price for the double burger to attract customers and generate optimal revenue.
4. Demand forecasting: Accurately predict customer demand for the double burger to prevent overstocking or understocking of ingredients, which can impact revenue.

To maximize total revenue at Burger Heaven, follow these steps:

a) Analyze the availability of meat patties and pickles to determine how many double burgers can be made with the current inventory.
b) Evaluate the production capacity of the kitchen staff to ensure that they can efficiently prepare and assemble the double burgers.


c) Research the market to set a competitive price for the double burger, considering the costs of ingredients, labor, and other expenses.
d) Forecast customer demand for the double burger to ensure optimal inventory levels and to meet customer expectations.

By addressing these constraints and following the steps above, Burger Heaven can successfully maximize its total revenue from selling double burgers with 2 meat patties and 6 pickles.

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16 Mr. Ramos's monthly mileage allowance


for a company car is 750 miles. He drove


8 miles per day for 10 days, then went on


a 3-day trip. The table shows the distance


he drove on each day of the trip.


1


t


Trip Mileage


Day Miles Driven


Tuesday


156. 1


Wednesday


240. 8


Thursday


82. 0


After the trip, how many miles remain in


Mr. Ramos's monthly allowance?

Answers

The number of miles remaining in Mr. Ramos's monthly allowance is 191.1 miles.

To find out how many miles remain in Mr. Ramos's monthly allowance after the trip, let's first calculate the total miles he drove:

1. For the 10 days at 8 miles per day: 10 days * 8 miles/day = 80 miles
2. For the 3-day trip, sum up the miles driven each day: 156.1 + 240.8 + 82.0 = 478.9 miles

Now, add the miles from both parts: 80 miles + 478.9 miles = 558.9 miles

Finally, subtract this total from Mr. Ramos's monthly allowance of 750 miles:

750 miles - 558.9 miles = 191.1 miles

After the trip, 191.1 miles remain in Mr. Ramos's monthly allowance.

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from the following quadratic function , g(x)= -4(x+2)^2-3 identify the difference between its parent function f(x)=x^2

Answers

Thus, through the steps of horizontal translation, dilation and at last vertical translation, the new quadratic function , g(x)= -4(x+2)²-3 from the parent function f(x)=x².

Explain about the parent function:

The simplest function which nonetheless complies with a particular type of function's definition is a parent function. For instance, y = x would be the parent function when considering the linear functions that make a family of functions. The most basic linear function is this one.

In addition, by applying various transformations to the graph of the parent function, all of the functions in a family of functions can also be derived from it. Vertical shifts, extending or compressing both horizontally and vertically, reflecting and over x or y axes, and horizontal shifts are some of these transformations.

Given parent function:  f(x)=x²

new quadratic function , g(x)= -4(x+2)²-3

there is the translation of 2 units to right such that 2 is added to x.Now, there is dilation with the scale factor of -4.At last the function is shifted 3 units down

Thus, through the steps of horizontal translation, dilation and at last vertical translation, the new quadratic function , g(x)= -4(x+2)²-3 from the parent function f(x)=x².

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Complete question:

from the following quadratic function , g(x)= -4(x+2)²-3 .identify the difference between its parent function f(x)=x² and  g(x).

The screen of a 32-inch high definition television has a diagonal length of 31. 5 inches. If the TV screen is 27. 5 inches wide, find the height of screen to the nearest tenth of an inch.


The height of the TV screen is?

Answers

Using the  Pythagorean theorem we get , the  height of the TV screen is approximately 15.4 inches to the nearest tenth of an inch.

The screen of a 32-inch high definition television has a diagonal length of 31.5 inches. If the TV screen is 27.5 inches wide, you need to find the height of the screen to the nearest tenth of an inch. To do this, you can use the Pythagorean theorem, which states that the square of the length of the hypotenuse (diagonal) of a right triangle is equal to the sum of the squares of the other two sides (width and height).

1. Let the height of the TV screen be h inches.
2. According to the Pythagorean theorem, (width)^2 + (height)^2 = (diagonal)^2.
3. Substitute the given values: (27.5)^2 + (h)^2 = (31.5)^2.
4. Calculate the squares: 756.25 + h^2 = 992.25.
5. Subtract 756.25 from both sides: h^2 = 236.
6. Find the square root of 236: h ≈ 15.4 inches.

The height of the TV screen is approximately 15.4 inches to the nearest tenth of an inch.

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Determine whether Rohe Theorem can be applied to on the dood inter - 2x-) -1.31 WS
A. Yes, Rolle's Theorem can be applied B. No, because is not continuous on the closed intervals

Answers

The Rohe Theorem can be applied to on the dood inter - 2x-) -1.31 WS. No, because it is not continuous on the closed intervals.

To determine whether Rolle's Theorem can be applied to the given function (ignoring typos and irrelevant parts), we need to consider the requirements for Rolle's Theorem: the function must be continuous on a closed interval and differentiable on an open interval within that closed interval.
Your answer: B. No, because the function is not continuous on the closed intervals. This is due to the presence of irrelevant parts in the given function, which makes it impossible to determine its continuity and differentiability. Therefore, Rolle's Theorem cannot be applied in this case.

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Tanya made this graph that represents the total cost for each of the three locations. Depending on the number of students that attend. Which function represents the cost of the restaurant 

Answers

The functions that represents the cost are

(a) y = 8800, (b) y = 1900 + 4/7x and (c) y = 4800, x ≤ 150;  y = 1200 + 24x x > 150

Identifying the function that represents the cost

From the question, we have the following parameters that can be used in our computation:

The graph


The function (a) is a horizontal line that passes through y = 8800

So, the function is

y = 8800

The function (b) is a linear function that passes through

(0, 1900) and (175, 2000)

So, the function is

y = 1900 + 4/7x

The function c is a piecewise function with the following properties

Horizontal line of y = 4800 uptill x = 150Linear function of (150, 4800) and (200, 6000)

So, the function is

y = 4800, x ≤ 150

y = 1200 + 24x x > 150

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Find all exact solutions on [0, 21). (Enter your answers as a comma-separated list.) sec(x) sin(x) - 2 sin(x) = 0 JT X = 3917, 5л 3 x Recall the algebraic method of solving by factoring and setting e".

Answers

x = 0, π, 2π, 3π, 4π, 5π, 6π, π/3, 5π/3

These are the exact solutions of the given equation on the interval [0, 21). To find all exact solutions of the equation sec(x) sin(x) - 2 sin(x) = 0 on the interval [0, 21), we will use the factoring method:

First, we can factor out the sin(x) term:

sin(x) (sec(x) - 2) = 0

Now, we have two separate equations to solve:

1) sin(x) = 0
2) sec(x) - 2 = 0

For equation (1), sin(x) = 0 at x = nπ, where n is an integer. We need to find the values of n that give solutions in the range [0, 21):

0 ≤ nπ < 21
0 ≤ n < 21/π
n = 0, 1, 2, 3, 4, 5, 6

x = 0, π, 2π, 3π, 4π, 5π, 6π

For equation (2), sec(x) - 2 = 0, or sec(x) = 2. We know that sec(x) = 1/cos(x), so:

1/cos(x) = 2
cos(x) = 1/2

The values of x for which cos(x) = 1/2 in the range [0, 21) are x = π/3 and x = 5π/3.

Combining both sets of solutions, we have:

x = 0, π, 2π, 3π, 4π, 5π, 6π, π/3, 5π/3

These are the exact solutions of the given equation on the interval [0, 21).

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Ying Yu bought a rectangular box to display her doll collection. She decided


to exchange the box for a similar one that had five times its dimensions.


How does the volume of the larger rectangular box compare to the volume


of the smaller box?

Answers

The volume of the larger rectangular box is 125 times the volume of the smaller box.

To compare the volume of the larger rectangular box to the smaller box, we need to consider how the dimensions have changed.

Since the larger box has dimensions 5 times those of the smaller box, let's represent the dimensions of the smaller box as length (L), width (W), and height (H). Therefore, the dimensions of the larger box would be 5L, 5W, and 5H.

Now, let's calculate the volume of both boxes:

1. Volume of the smaller box: V_small = L * W * H
2. Volume of the larger box: V_large = (5L) * (5W) * (5H)

To find the ratio of the larger box's volume to the smaller box's volume, we can divide the volumes:

V_large / V_small = ((5L)*(5W)*(5H)) / (L * W * H)

Notice that L, W, and H can be canceled out:

(5 * 5 * 5) = 125

So, the volume of the larger rectangular box is 125 times the volume of the smaller box.

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The diameter of a circle is 6 kilometers. What is the circle's circumference?
Use 3.14 for л.

Answers

Answer:

18.84 kilometers

Step-by-step explanation:

Formula for circumference:  C=2πr

1) find radius

r = d / 2

In this case the diameter is 6 so:

r = 6 / 2

r = 3

2. Plug in your values in the formula:

C = 2 (3.14) (3)

3. Solve (multiply)

C = 2 x 3.14 x 3

C = 18.84

So your answer is 18.84 kilometers, and rounded its 19 kilometers.

Hope this helps :D

What is the product? assume x greater-than-or-equal-to 0 (startroot 3 x endroot startroot 5 endroot) (startroot 15 x endroot 2 startroot 30 endroot) 3 x startroot 5 endroot 3 startroot 165 x endroot 10 startroot 6 endroot 3 x startroot 5 endroot 6 startroot 10 x endroot 5 startroot 3 x endroot 10 startroot 6 endroot 3 x startroot 5 endroot 10 startroot 6 endroot startroot 3 x endroot 5 startroot 3 x endroot 10 startroot 6 endroot

Answers

The product of the given expression is 2,916,000,000x³√(9,900x²).

The given expression contains several terms with roots and variables. To simplify and find the product, we'll first multiply the terms with similar roots and variables. The expression is:

√(3x)√5 √(15x)√2 √(30) 3x√5 3√(165x) √10 √6 3x√5 √6 √(10x) √5 √(3x) √10 √6 3x√5 √10 √6 √(3x) √5 √(3x) √10 √6

We can group terms with the same roots and variables together:

(√(3x))⁴ (3x)³ (√5)⁴ (√10)³ (√6)³ √15x √2 √30 √165x

Now, we can simplify each group:

81x³ * 625 * 1000 * 216 * √(2 * 15x * 30 * 165x)

Combine the constants and variables under the root:

81x³ * 625 * 1000 * 216 * √(9,900x²)

Calculate the product of the constants:

13,500,000 * 216 = 2,916,000,000

So, the final simplified expression is:

2,916,000,000x³√(9,900x²)

In summary, the product of the given expression is 2,916,000,000x³√(9,900x²).

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Consider the function f(x) = 1/z on the interval (5,9). (A) Find the average or mean slope of the function on this interval, Average Slope =?
(B) By the Mean Value Theorem, we know there exists a c in the open interval (5,9) such that f'(c) is equal to this mean slope. Find all values of c that work and list them separated by commas) in the box below

Answers

Therefore, the only value of c that works is 6√5.

(A) To find the average slope of the function f(x) = 1/x on the interval (5, 9), we use the formula:

Average Slope = (f(9) - f(5)) / (9 - 5)

Plugging in the values, we get:

Average Slope = (1/5 - 1/9) / 4 = -1/180

Therefore, the average slope of the function on the interval (5, 9) is -1/180.

(B) By the Mean Value Theorem, we know there exists a c in the open interval (5, 9) such that f'(c) is equal to this mean slope.

The derivative of f(x) = 1/x is f'(x) = -1/x^2.

Setting f'(c) = -1/180, we get:

-1/c^2 = -1/180

Solving for c, we get:

c = ±6√5

Since c must be in the open interval (5, 9), the only value that works is:

c = 6√5

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Camden and violet are reading the same book. at the beginning of the month, camden was on page 18 and violet was on page 39. camden will read 11 pages per day and violet will read 8 pages per day. let c represent the page of the book that camden is on at the end of t days into the month. write an equation for each situation, in terms of t. and determine whether camden or violet is farther along in 2 days.​

Answers

For Camden the equation is c = 18 + 11t and for Violet the equation is v = 39 + 8t. After 2 days, Camden will be on page 40 and Violet will be on page 55.

Let's represent the situation with two equations, one for Camden (c) and one for Violet (v), using the given information and the variable t for the number of days.

Camden:
At the beginning of the month, Camden was on page 18 and will read 11 pages per day. So, his equation will be:
c = 18 + 11t

Violet:
At the beginning of the month, Violet was on page 39 and will read 8 pages per day. So, her equation will be:
v = 39 + 8t

Now, we need to determine who is farther along in the book after 2 days. To do this, we will substitute t = 2 into both equations.

Camden's equation (c):
c = 18 + 11(2)
c = 18 + 22
c = 40

Violet's equation (v):
v = 39 + 8(2)
v = 39 + 16
v = 55

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I Need help with this problem

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It’s can be 240 or 5,278

Help asap will give 100 points and brainiest
what is the mean absolute deviation for doctor a’s data set on corrective lenses? what is the mean absolute deviation for doctor b’s data set on corrective lenses? write a sentence comparing the variation of the two data sets using their mean absolute deviations.

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The mean absolute deviation for Doctor A's data set on corrective lenses is 0.42.The mean absolute deviation for Doctor B's data set on corrective lenses is 0.38.Doctor B's data set has a slightly smaller variation than Doctor A's data set, based on their mean absolute deviations.

What is the difference in mean absolute deviation for the corrective lenses data sets of Doctor A and Doctor B?

In statistical analysis, the mean absolute deviation (MAD) is a measure of the average distance between each data point and the mean of the data set. For Doctor A's data set on corrective lenses, the MAD is calculated as 0.42, while for Doctor B's data set, it is calculated as 0.38.

This shows that Doctor B's data set has a slightly smaller variation compared to Doctor A's data set.

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The drama club is selling tickets to their play to raise money for the ticket sells for $9. The auditorium can hold no more than 110 people. The drama club must make a minimum of $720 from show's expenses. Each student ticket sells for $4 and each adult ticket sales to cover the show's costs. If x represents the number of student tickets sold and y represents the number of adult tickets sold, write and solve a system of inequalities graphically and determine two possible solutions.

Answers

A system of inequalities to model this situation is 4x + 9y ≥ 720 and x + y ≤ 110.

The two possible solutions are (80, 40) and (100, 20).

How to write an equation to model this situation?

In order to write a linear equation to describe this situation, we would assign variables to the number of student tickets sold and the number of adult tickets sold respectively, and then translate the word problem into a linear equation as follows:

Let the variable x represent number of student tickets sold.Let the variable y represent number of adult tickets sold.

Since each student ticket was sold for $4 and each adult ticket sales to cover the show's costs sells for $9 in order to make a minimum of $720 from show's expenses, a linear equation which can be used to model the situation is given by;

4x + 9y ≥ 720

Additionally, the auditorium can hold no more than 110 people;

x + y ≤ 110

Next, we would use an online graphing calculator to plot the above system of linear equations in order to determine its solution as shown in the graph attached below.

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"Consider the following function: f(x,y)=y^5 ln(−2x^4+3y^5) find fx and fy"

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From the function f(x,y)=y⁵ ln(−2x⁴+3y⁵).  The value of  fx = -10x³y⁵ / (-2x⁴ + 3y⁵) and

fy = y⁴ * ln(-2x⁴ + 3y⁵) * d/dy [(-2x⁴ + 3y⁵)]

To find fx, we differentiate f(x,y) with respect to x, treating y as a constant:

fx = d/dx [y⁵ ln(-2x⁴ + 3y⁵)]

Using the chain rule and the derivative of ln u = 1/u, we have:

fx = y⁵ * 1/(-2x⁴ + 3y⁵) * d/dx [-2x⁴ + 3y⁵]

Simplifying and applying the power rule of differentiation, we get:

fx = -10x³y⁵ / (-2x⁴ + 3y⁵)

Similarly, to find fy, we differentiate f(x,y) with respect to y, treating x as a constant:

fy = d/dy [y⁵ ln(-2x⁴ + 3y⁵)]

Using the chain rule and the derivative of ln u = 1/u, we have:

fy = y⁴ * ln(-2x⁴ + 3y⁵) * d/dy [(-2x⁴ + 3y⁵)]

Applying the power rule of differentiation and simplifying, we get:

fy = 15y⁴ ln(-2x⁴ + 3y⁵)

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find the area of a joined rectangle
1st rectangle has 6cm length and 4cn width
2nd rectangle has 7cm length and 3cm width
apparently the answer to this question is 33cm² but I don't know how they got it ​

Answers

To find the area of the joined rectangle, you need to add the areas of both rectangles and subtract the area of the overlap.

The area of the first rectangle is:

6 cm x 4 cm = 24 cm²

The area of the second rectangle is:

7 cm x 3 cm = 21 cm²

The overlap occurs where the two rectangles join together, and it has an area equal to the product of the widths of the two rectangles:

4 cm x 3 cm = 12 cm²

To find the area of the joined rectangle, add the areas of both rectangles and subtract the overlap:

24 cm² + 21 cm² - 12 cm² = 33 cm²

Therefore, the area of the joined rectangle is 33 cm².

5. Find the local maximum, local minimum, or saddle points for 1 |(1,Y) = y2 +373 + 2xy – 8x + 6 fy 2

Answers

For the given function f(x, y), there is a saddle point at (-28, 4). There are no local maximum or local minimum points.

A saddle point or minimax point is a point on the surface of the graph of a function where the slopes in orthogonal directions are all zero, but which is not a local extremum of the function.

Local maximum and minimum are the points of the functions, which give the maximum and minimum range. The local maxima and local minima can be computed by finding the derivative of the function.

The first derivative test and the second derivative test are the two important methods of finding the local maximum and local minimum.

To find the local maximum, local minimum, or saddle points of the given function f(x, y) = y^2 + 373 + 2xy - 8x + 6y^2, we need to first find the critical points by setting the first-order partial derivatives equal to zero.

∂f/∂x = 2y - 8
∂f/∂y = 2y + 2x + 12y => 2x + 14y

Now set both partial derivatives equal to zero and solve for x and y:

2y - 8 = 0 => y = 4
2x + 14y = 0 => 2x + 56 = 0 => x = -28

The critical point is (-28, 4). Now, we need to classify this point using the second-order partial derivatives:

∂²f/∂x² = 0
∂²f/∂y² = 14
∂²f/∂x∂y = ∂²f/∂y∂x = 2

Now we can use the discriminant D = (∂²f/∂x²)(∂²f/∂y²) - (∂²f/∂x∂y)^2 = (0)(14) - (2)^2 = -4. Since D < 0, the critical point is a saddle point.

So, for the given function f(x, y), there is a saddle point at (-28, 4). There are no local maximum or local minimum points.

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What are two different ways you can solve 2(x – 3) = 8?

Answers

Answer:

There are three methods used to solve systems of equations: graphing, substitution, and elimination.

Step-by-step explanation:

How many pieces of 10 5/6 inch bar can be cut from a stock 29 foot bar

Answers

20 pieces of 10 5/6 inch bar can be cut from a stock 29 foot bar.

To calculate the number of pieces of 10 5/6 inch bar that can be cut from a 29 foot bar, we need to first convert the measurements to a common unit. One foot is equal to 12 inches, so 29 feet equals 348 inches.

Next, we need to determine how many 10 5/6 inch bars can be cut from the 348-inch stock bar. To do this, we can use division. First, we need to convert the mixed number 10 5/6 to an improper fraction by multiplying the whole number by the denominator and adding the numerator. This gives us 125/6 inches.

Now, we can divide the length of the stock bar (348 inches) by the length of one 10 5/6 inch bar (125/6 inches). This gives us:

348 / (125/6) = 20.736

Since we cannot cut a partial bar, we need to round down to the nearest whole number. Therefore, we can cut 20 pieces of 10 5/6 inch bar from a 29 foot stock bar.

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Select the correct answer from each drop-down menu.
The three vertices of a triangle drawn on a complex plane are represented by 0 + 0i, 4 + 0i, and 0+ 3i.
The length of the hypotenuse is
units, and the area of the triangle is
square units. (Hint: Use the Pythagorean theorem.)

Answers

The area of the triangle is (a-6, b-12) square units 6 sq unit.

What is the triangle?

A triangle is described as  a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees.

This means that the sum of the interior angles of a triangle is equal to 180°

Now that we have  the points they make a 3-4-5 triangle.

The two legs are 3 and 4, so the hypotenuse has to be 5.

We  could also use the Pythagorean theorem a² + b² = c² 3² + 4² = c² 25 = c² c = 5

We then calculate the area

Area =1/2 b*h

Area = 1/2(3*4)

Area =  6 sq unit

The area of the triangle is (a-6, b-12) square units 6 sq unit.

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In def x is a point on ef and y is a point on df so that xy ||de if xf =10 yf=5 and ef = 13 what is dy

Answers

DF^2 = 170 * 169^2 / (135^2 + 200 - 26EX) = 106.7027

DY^2 = 170 * 169^2 / (135^2 + 50 -

In the given figure, we have a triangle DEF, where EF is a transversal intersecting DE and DF at points X and Y, respectively, such that XY || DE.

    D

   / \

  /   \

 /     \

E-------F

Given that XF = 10, YF = 5, and EF = 13, we need to find DY.

We can start by using the property of similar triangles. Since XY || DE, we have the following similarity ratios:

EF / ED = EY / EJ  (where J is the intersection of XY and DF)

EF / DF = EJ / EY

Substituting the given values, we get:

13 / ED = EY / EJ

13 / DF = EJ / (13 - EY)

Multiplying the above two equations, we get:

13 / ED * 13 / DF = EY / EJ * EJ / (13 - EY)

169 / (ED * DF) = EY / (13 - EY)

Substituting the values of XF = 10 and YF = 5, we get:

169 / (ED * DF) = 5 / 8

ED / DF = 135 / 169

Using the Pythagorean theorem on triangles DEX and DFY, we get:

ED^2 = EX^2 + DX^2

DF^2 = FY^2 + DY^2

Since EX + DX = EF = 13, we have DX = 13 - EX. Substituting this in the first equation and simplifying, we get:

ED^2 = EX^2 + (13 - EX)^2

ED^2 = 2EX^2 - 26EX + 170

Similarly, substituting FY = 13 - EY in the second equation and simplifying, we get:

DF^2 = FY^2 + DY^2

DF^2 = 170 - 26EY + EY^2 + DY^2

Now, using the fact that ED/DF = 135/169, we can substitute ED^2 = (135/169)^2 * DF^2 in the above equation for ED^2, and simplify to get:

(135/169)^2 * DF^2 = 2EX^2 - 26EX + 170

DF^2 = 170 * 169^2 / (135^2 + 2EX^2 - 26EX)

DF^2 = 170 * 169^2 / (135^2 + 2(10^2) - 26EX)   (Substituting XF = 10)

Similarly, we can substitute EY = 5 in the above equation for DF^2 and simplify to get:

FY^2 + DY^2 = 170 * 169^2 / (135^2 + 2(5^2) - 26EY)   (Substituting YF = 5)

DY^2 = 170 * 169^2 / (135^2 + 2(5^2) - 26EY) - FY^2

Substituting the given values, we get:

DF^2 = 170 * 169^2 / (135^2 + 200 - 26EX) = 106.7027

DY^2 = 170 * 169^2 / (135^2 + 50 -

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