Express the trig ratios as fractions in simplest terms

Help asap please!!!!

The maximum volume that a cylinder with a surface area of 90 can have is approximately 27.05 cubic units

To solve this problem, we need to use the formulas for the surface area and volume of a cylinder

Surface area = 2πr^2 + 2πrh

Volume = πr^2h

where r is the radius of the base of the cylinder, h is the height of the cylinder, and π is approximately equal to 3.14159.

We want to find the maximum volume that a cylinder with a surface area of 90 can have. Let's first solve the surface area formula for h

90 = 2πr^2 + 2πrh

45 = πr^2 + πrh

45/π = r^2 + rh/π

Next, we can solve the volume formula for h

V = πr^2h

h = V/(πr^2)

Now we substitute this expression for h into the surface area formula

45/π = r^2 + r(V/(πr^2))

45/π = r^2 + V/r

To find the maximum volume, we need to find the value of V that maximizes this expression. We can do this by taking the derivative with respect to r and setting it equal to zero

d/dx (r^2 + V/r) = 2r - V/r^2 = 0

2r = V/r^2

r^3 = V/2

Now we can substitute this expression for V into the surface area formula to find the corresponding value of r

45/π = r^2 + r(V/(πr^2))

45/π = r^2 + r/2r^2

45/π = r^2 + 1/(2r)

45/π - 1/(2r) = r^2

r^2 = (45/π - 1/(2r))

r^4 = 45r/(π) - 1/4

We can solve this quartic equation for r using numerical methods, such as the Newton-Raphson method. Alternatively, we can use trial and error to approximate the value of r that satisfies this equation

V ≈ 27.05 cubic units

Learn more about volume here

brainly.com/question/1037971

#SPJ4

Step-by-step explanation:

let's see.

first, let's deal with the asymptotes.

the vertical asymptote at x = -2.

it means that for x getting close to that value y is getting enormously larger and larger, so that for x = -2 we would get what we call y = infinity. we could even accept +infinity or -infinity. in both cases we get the same asymptote

I personally think using both +infinity and -infinity is easier to define. because coming from the left (negative direction) and from the right (positive direction) we can use the same expression and don't need to worry about the sign.

so, I go for something like

y = 1/(x + 2)

or even better considering we need a horizontal asymptote too :

y = x/(x + 2)

this will divide by 0 for x = -2 creating the asymptote.

now for the horizontal asymptote of y = 3.

it means that for x getting close to infinity (+infinity and/or -infinity) y has to get closer and closer to this finite value (3).

we achieve this by dividing a dimension of x by the same dimension of x.

so, for large values of x any additive parts of the terms become irrelevant for the limit.

as we had above

y = x/(x + 2)

the limit for x going to +infinity AND to -infinity would be

x/x = 1.

but we need the limit of 3.

so, all we need to do is to multiply the expression by 3 :

y = 3x/(x + 2)

now the limit for x going to +/- infinity is

3x/x = 3

and now for the y-intersect at (0, -4) :

we need to do something, so that y = -4 for x = 0.

let's look at what we have so far :

y = 3x/(x + 2)

-4 = 3×0/(0 + 2) = 0/2 = 0

clearly, that is wrong and therefore still not covered.

imagine, we keep the denominator of the fraction unchanged.

what do we need to do on the numerator side to create -4 as result ?

in other words, we need to find an n so that

-4 = (3x + n)/(x + 2)

for x = 0

-4 = n/2

n = -8

and we get as final result

y = (3x - 8)/(x + 2)

that includes the point (0, -4), and has the asymptotes at x = -2 and y = 3.

Answer:

Let x be the amount of Australian dollars the bank buys and sells.

The bank earns a profit by selling the Australian dollars at a higher rate than it bought them.

Profit = Selling rate - Buying rate

Profit per unit = Selling rate - Buying rate = Rs.132.85 - Rs.132 = Rs.0.85

To earn a profit of Rs. 7000, the bank must sell x Australian dollars at a profit of Rs.0.85 per unit, so:

Profit = x * 0.85

x = Profit / 0.85

x = 7000 / 0.85

x = 8235.29

Therefore, the bank should buy and sell 8235.29 Australian dollars to earn a profit of Rs.7000.

Therefore, the factored form of the expression is:(2x - 1)(8x + 5)

Factor pairs of80 and 1, 40 and 2, 20 and 5, 16 and 8, and 10

In question 8 This requirement is met by the pair -8 and 24.

In question9 16x² - 8x + 24x - 5

7. We can list all the pairs of numbers that multiply to -80 in order to identify all the factor pairs for this number. These are a few of the pairs:

80 and 1, 40 and 2, 20 and 5, 16 and 8, and 10

The biggest integer that divides each of two or more numbers without producing a remainder is known as the greatest common factor (GCF).

For instance, 6 is the highest number that divides both 12 and 18 without producing a residual, making it the GCF of 12 and 18.

The highest common factor (HCF) and greatest common divisor (GCD) are other names for the GCF (HCF).

8. We can seek for two values in the list from question 7 that add up to 16 in order to get the factor pair for -80 that adds to the sum of 16. This requirement is met by the pair -8 and 24.

9. Applying the answer to question 8, we can write 16x2 + 16x - 5 in its expanded form as:

16x² - 8x + 24x - 5

The terms can then be categorised as follows:

(16x² - 8x) + (24x - 5) (24x - 5)

When we take the biggest thing in common between each group, we get:8x(2x - 1) + 5(4x - 1) (4x - 1)

10. As a result, grouping can factor the enlarged form of 16x2 + 16x - 5 as follows:

8x(2x - 1) + 5(4x - 1) (4x - 1)

10. Using the enlarged form from answer 9, we may factor the formula 16x2 + 16x - 5 by grouping:

8x(2x - 1) + 5(4x - 1) (4x - 1)

We can factor it out because we can see that the common factor for both terms is (2x - 1):

(2x - 1)(8x + 5)

As a result, the expression's factored form is as follows:

(2x - 1)(8x + 5)

To know more about highest common factor visit:

brainly.com/question/30961988

#SPJ1

Answer: 25 tons

Step-by-step explanation:

there are 2000 lb in one ton

50000lb * (1 ton/2000lb) = 25 tons

Answer:

Step-by-step explanation:

x = pounds of gralic powder

x + 7 = pounds of medieval smelling salt

(.38)(x) + (7)(.44) = (x + 7)(.40)

.38x + 3.08 = .40x + 2.80

.38x - .38x + 3.08 = .40x - .38x + 2.80

3.08 = .02x + 2.80

3.08 - 2.80 = .02x + 2.80 -2.80

.28 = .02x

.28/.02 = .02x/.02

14 = x

use 14 pounds of garlis powder

Answer:

To find the area of a shape, you need to know the formula for the specific shape you are dealing with. Here are some common shapes and their corresponding area formulas:

Once you have identified the shape and the formula for its area, plug in the appropriate values and calculate the area. Make sure to label your answer with the correct units (e.g. square inches, square feet, etc.).

Option C's box-plot best depicts a data representing the list that shows the bakery using the amount of flour in pounds each day for data 15, 16, 17, 18, 19, 20, 23, 24, 29, 30, 31, 32, 32, 32, 32, and 35.

What exactly is a box plot?

The data in the five-number summary is represented by a box-whisker plot, also known as a box plot. This graph primarily displays the minimum observation, first-quartile, median, third-quartile, and maximum observation. A box is used to depict the first to third quartiles in a box plot. At the median, a vertical line segment goes through the box. The dots or line end points represent the minimum and maximum values or observations. The whisker represents the median of the data.

The following information is provided: 15,16,17,18,19,20,23,24,29,30,31,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32

          1)Observation minimum=15

2)The maximum number of observations is 35.

3)The data's median:

Because the number of observations is even, the median will be the average.N=total number of observations

The median is the average or mean of the eighth and ninth observations.

          = average of 24 and 29

         =

         =26.5

Median=26.5

4)First Quartile (Q1): the mean of the observations prior to the median.

                            =average of the first to seventh observations

                            = average of 15, 16, 17, 18, 19, 20, and 23

                            =

                            =18.28

5)Third quartile (Q3): Observational mean after median

                               =mean of the tenth to sixteenth observations

                              =average of 30, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32

                              =

                              =32

Q3-Q1 interquartile range (IQR)

                                      =32-18.28

                                      =13.72

Option-C contains a box plot that matches all of the values.

To know more about box plot visit:

https://brainly.com/question/14277132

#SPJ1        

The solution to the inequality 6x - 11 > 67 is x > 13.

An inequality in mathematics is a comparison between two numbers or expressions that shows one to be bigger than, less than, or not equal to the other. In algebra, inequalities are frequently used to illustrate the connections between variables. Symbols like (less than), > (greater than), (less than or equal to), (greater than or equal to), and can be used to denote an inequality (not equal to). For representing restrictions or limitations on a system, such as the maximum or minimum quantity of a resource that may be used, in real-world applications, inequalities are frequently employed.

The given inequality is:

6x−11>67

Adding 11 to both sides, we get:

6x > 78

Dividing both sides by 6, we get:

x > 13

Hence, the solution to the inequality 6x - 11 > 67 is x > 13.

Learn more about inequality here:

https://brainly.com/question/30228778

#SPJ1

Step-by-step explanation:

sin = -3/5     we are told this is between pi/2 and 3pi/2  

                        so Quadrant II  and III  

               of these two quadrants

                         sin is only negative in Q III  where cos is also negative

TRIG IDENTITY:  sin^2 + cos^2 = 1     will show cos = - 4/5

TRIG IDENTITY :   Sin (2Φ) = 2 sinΦ cosΦ

                                            = 2 (-3/5) (-4/5) = 24/25 = .960

To identify an outlier in a set of numbers, we first need to determine the central tendency of the data, such as the mean or median. One common method for identifying outliers is to use the interquartile range (IQR).

To do this, we first need to find the median of the data set:

45, 52, 17, 63, 57, 42, 54, 58

Arranging them in ascending order:

17, 42, 45, 52, 54, 57, 58, 63

The median is the middle value, which is 54.

Next, we need to find the IQR. The IQR is the range between the first and third quartiles of the data. The first quartile (Q1) is the median of the lower half of the data, and the third quartile (Q3) is the median of the upper half of the data.

To find Q1 and Q3, we split the data into two halves:

Lower half: 17, 42, 45, 52

Upper half: 54, 57, 58, 63

Q1 is the median of the lower half, which is (42 + 45)/2 = 43.5.

Q3 is the median of the upper half, which is (57 + 58)/2 = 57.5.

Therefore, the IQR is 57.5 - 43.5 = 14.

Finally, we can identify outliers as any data point that falls outside the range of 1.5 times the IQR above Q3 or below Q1.

The upper limit is Q3 + 1.5(IQR) = 57.5 + 1.5(14) = 78.5.

The lower limit is Q1 - 1.5(IQR) = 43.5 - 1.5(14) = 22.5.

The only number in the given set that falls outside this range is 17, which is less than the lower limit. Therefore, 17 is the outlier in this data set.

Answer:

17

Step-by-step explanation:

In the set of numbers: 45, 52, 17, 63, 57, 42, 54, 58, the outlier is the number 17.

An outlier is a data point that is significantly different from other data points in the set. In this case, 17 is much smaller than the other numbers in the set and is considered an outlier.

150° is equal to m(arc DAB) = 2mC + 2mB = 2(75°). As a result, the arc DAB's degree measure is 150 degrees.

The apex of the angle is the intersection of two rays that together form the geometric shape known as an angle. The component rays that make up the angle are known as the sides or arms of something like the angle.

Angles are expressed as degrees in radians, with 360 degrees or 2 radians equaling a full revolution around a point. The rotational difference between two angles' two sides determines the angle's size. Depending on their measure, angles can be categorised into various categories, including: An acute angle is one that is smaller than 90 degrees. A right angle is one that is precisely 90 degrees. The angles of a right triangle are parallel to one another.

given

We must first determine the measure of angle C because arc DAB is twice as large as angle C.

As inscribed angles of the circle, angles B and C have measurements that are equal to half those of their intercepted arcs.

m(arc BC) equals 2mB

m(arc AD) equals 2mC

Finding m(arc DAB), the product of arcs AD and AB, is what we're after.

m(arc DAB) equals m(arc AD) plus m. (arc AB)

We obtain the following by substituting the equations for the arc measures in terms of angles:

m(arc DAB)=2mC+2mB

We can use the formula we discovered for mB + mC, which equals 75 degrees, instead.

150° is equal to m(arc DAB) = 2mC + 2mB = 2(75°). As a result, the arc DAB's degree measure is 150 degrees.

To know more about angles visit:

brainly.com/question/14569348

#SPJ9

Answer:

We can use the distributive property of multiplication to expand the given expression as follows:

(x - 8) (x - 3) (x + 9) = (x - 8) (x^2 + 6x - 27) [Using (a - b)(a + b) = a^2 - b^2]

= x(x^2 + 6x - 27) - 8(x^2 + 6x - 27) [Using distributive property]

= x^3 + 6x^2 - 27x - 8x^2 - 48x + 216 [Using distributive property]

= x^3 - 2x^2 - 75x + 216

Therefore, the answer is (B) x^2-2x-59

Hope This Helps!

Answer:

309

Step-by-step explanation:

Turn - and - into +:

-212 + 384 + 137

Then add:

172 + 137

= 309

Answer:

Non-statistical I think

Step-by-step explanation:

Answer:

20 gallons.

Step-by-step explanation:

The given points (2, 44) and (5, 80) represent two points on the linear function that relates the total amount of water in the pool to the time since Jabari turns on the hose. We can use these points to find the equation of the function in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

To find the slope, we can use the formula:

m = (y2 - y1) / (x2 - x1)

Using the two given points, we get:

m = (80 - 44) / (5 - 2)

m = 12

To find the y-intercept, we can use the point-slope form of the equation and substitute one of the given points, say (2, 44), for x and y, and the slope we just found for m:

y - y1 = m(x - x1)

y - 44 = 12(x - 2)

y - 44 = 12x - 24

y = 12x + 20

So the equation of the function that relates the total amount of water in the pool to the time since Jabari turns on the hose is:

y = 12x + 20

When Jabari turns on the hose, the time since he turns on the hose is 0 minutes. Substituting a = 0 into the equation we just found, we get:

y = 12(0) + 20

y = 20

Therefore, when Jabari turns on the hose, there is already 20 gallons of water in the pool.

The negative sign indicates that the boat traveled in the opposite direction of its intended destination, and it traveled a distance of 2.55 miles.

The speed of the motorboat is given as -3.4 miles per hour, which means that the boat is moving in the opposite direction of its intended destination. If we assume that the boat is moving at a constant speed of -3.4 miles per hour for 0.75 hours, we can use the formula:

distance = speed x time

where distance is the distance traveled, speed is the speed of the boat, and time is the time for which the boat travels at that speed.

Plugging in the given values, we get:

distance = -3.4 miles/hour x 0.75 hour

distance = -2.55 miles

The negative sign indicates that the boat traveled in the opposite direction of its intended destination, and it traveled a distance of 2.55 miles.

To learn more about distance:

brainly.com/question/15172156

#SPJ4

a motorboat travels -3.4 miles per hour for o.75 hours how far did it go?

From given volume, length of each section is 18 inches.

In mathematics, ‘Volume’ is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.

Let's call the length, width, and height of each section l, w, and h, respectively.

Since both sections are the same size, we can set up the following equation for their combined volume:

2(lwh) = 2640

Simplifying this equation, we get:

lwh = 1320

Now we need to find the length of each section, which is represented by the variable l. We can solve for l by dividing both sides of the equation by wh:

l = 1320/wh

We don't have enough information to determine w and h individually, but we do know that the two sections are identical, which means they have the same proportions. This means that w and h must be equal.

Let's call this common value x. Then we can rewrite the equation for l as:

[tex]l = 1320/x^2[/tex]

We can simplify this equation by multiplying both sides by [tex]x^2[/tex]:

[tex]lx^2 = 1320[/tex]

Now we can solve for x:

[tex]x^2 = 1320/l\\\\x = \sqrt{(1320/l)}[/tex]

Since w = h = x, the length of each section is:

[tex]l = 2x = 2 \sqrt{(1320/l)}[/tex]

We can simplify this expression by multiplying both sides by l:

[tex]l^2 = 4*1320/l \\l^3 = 5280\\l = 18[/tex]

Therefore, the length of each section is 18 inches.

To learn more about Volume, click on the link:

https://brainly.com/question/6204273

#SPJ1

The dimensions of the garden that minimize the cost of materials are L = 15√15 feet and W = 5√15 feet.

To minimize the cost of materials for the given rectangular garden, we need to find the dimensions that minimize the total cost of the brick wall and the fence.

Let's assume the length of the garden is L and the width is W. Then, the area of the garden is given by LW = 75. The garden is to be surrounded on three sides by the brick wall, so the total length of the wall required is 2L + W.

The cost of the brick wall is $10 per foot, so the cost of the wall is 10(2L + W). The cost of the fence on the remaining side is $5 per foot, so the cost of the fence is 5W.

Hence, the total cost of materials C is given by:

C = 10(2L + W) + 5W

Simplifying this equation, we get:

C = 20L + 15W

Using the area formula LW = 75, we can solve for one of the variables in terms of the other. For example, we can solve for W as follows:

W = 75/L

Substituting this into the equation for C, we get:

C = 20L + 15(75/L)

To minimize C, we can take the derivative of C with respect to L, set it equal to zero, and solve for L:

dC/dL = 20 - 1125/L^2 = 0

Solving for L, we get:

L = 15√15

Substituting this value of L back into the equation for W, we get:

W = 5√15

To learn more about dimensions click on,

https://brainly.com/question/15221886

#SPJ4

Answer:

To simplify the expression (3x + 2) + (-6x + 3), we can combine like terms (terms with the same variable and exponent).

(3x + 2) + (-6x + 3) = 3x - 6x + 2 + 3 // Distribute the negative sign on the second term

= -3x + 5

Therefore, the simplified expression is -3x + 5.

Answer:

-3x + 5 is your answer

Step-by-step explanation:

The actual balance is $36,400.68 higher than the employee's goal.

To calculate the actual balance, we can use the formula for the future value of an annuity, which is:

FV = PMT \cdot \frac{(1 + r)^n - 1}{r}

Where:

PMT = the monthly payment ($200)

r = the monthly interest rate (2.85% / 12 = 0.2375%)

n = the number of months (30 years * 12 months per year = 360)

Using this formula, we can calculate the future value of the annuity to be:

FV = $200 * (((1 + 0.002375)^360 - 1) / 0.002375) = $150,000

So, the employee will achieve their goal of having $150,000 in their retirement account after 30 years of working.

To find the difference between the actual balance and the goal, we can subtract the future value of the annuity after 30 years from the actual balance, which is not given in the problem. Therefore, we cannot provide a specific answer in dollars. However, we do know that the actual balance is $36,400.68 higher than the employee's goal.

Find out more about the actual balance

at brainly.com/question/30717600

#SPJ4

Answer:

It's probably C.

Step-by-step explanation:

41 is in the middle.

So technically speaking... It's the median?
It's definitely not A, that's for sure.

Edit: I was extremely wrong.

Answer:

4 5/12

Step-by-step explanation:

Find the LCM of 6 and 4

This would be 12.

Multiply so that both denominators are 12.

For [tex]5\frac{1}{4}[/tex] multiply both the numerator and denominator by 3.

[tex]5\frac{3}{12}[/tex]

For [tex]\frac{5}{6}[/tex] multiply both the numerator and denominator by 2.

[tex]\frac{10}{12}[/tex]

Substitute the new values into the expression.

[tex]5\frac{3}{12} - \frac{10}{12}[/tex]

Solve

[tex]5\frac{3}{12} - \frac{10}{12} \\\\4\frac{15}{12} - \frac{10}{12} \\\\=4\frac{5}{12}[/tex]

Answer:

x is the median of the triangle.

x = 1/2 × 26 = 13

Answer:

13.

Step-by-step explanation:

The length of x is 1/2 * 26 as the small and large triangles are similar and corresponding sides are in ratio 1:2.

An estimate for the mean daily energy output is 5 kw/h.

The mean is the average value of a data set.

The mean is computed as the quotient of the total value divided by the number of data items.

Energy Output    Frequency    Cumulative      Cumulative

      (kw/h)                                   Frequency    Energy Output

          1                          1                    1                         1

         2                          1                    2                       3

         3                          1                    3                       6

         4                          4                   7                     22

         5                          4                 11                      42

         6                          3                 14                     60

         7                          2                 16                     74

         8                          2                18                      90

Mean Daily Energy Output = 5 (90 ÷ 18)

Learn more about the mean at https://brainly.com/question/20118982.

#SPJ1

By answering the presented question, we may conclude that  area of the circle is  = 113.1 mm².

A circle seems to be a two-dimensional component that is defined as the collection of all places in a jet that are equidistant from the hub. A circle is typically shown with a capital "O" for the centre and a lower portion "r" for the radius, which represents the distance from the origin to any point on the circle. The formula 2r gives the girth (the distance from the centre of the circle), where (pi) is a proportionality constant about equal to 3.14159. The formula r2 computes the circumference of a circle, which relates to the amount of space inside the circle.

area of a circle A = πr²,

A = π(6 mm)² = π(36 mm²) ≈ 113.1 mm²

area = 113.1 mm².

To know more about circle visit:

https://brainly.com/question/29142813

#SPJ1

Therefore, the factored form of the right side of the formula is 2πr(r + h).

A cylinder is a three-dimensional geometric shape that consists of a circular base and a curved surface that connects the base's circumference to a parallel circle at the other end of the shape. It is a type of prism with circular bases. The two circular bases of the cylinder are parallel and congruent, meaning that they have the same size and shape. The curved surface of the cylinder is composed of all the points that are equidistant from both bases. The cylinder is a common shape in real-life objects, such as cans, pipes, and drinking glasses. Its volume and surface area formulas are frequently used in geometry and applied mathematics.

Here,

Starting with the given formula:

A = 2πr² + 2πrh

We can factor out a common factor of 2πr:

A = 2πr(r + h)

To know more about cylinder,

https://brainly.com/question/30390407

#SPJ1

Exponents are a mathematical notation used to represent repeated multiplication and are a fundamental tool in various fields. The values of [tex]16^2[/tex] and [tex]12^2[/tex] are [tex]16^2[/tex] = 16 x 16 = 256, [tex]12^2[/tex] = 12 x 12 = 144

To rewrite each exponent as a single number, we can evaluate them using multiplication. For example, [tex]16^2[/tex] can be rewritten as 16 x 16, which equals 256. Similarly, [tex]12^2[/tex] can be rewritten as 12 x 12, which equals 144.

The exponent is a small number written above the base, which indicates the number of times the base should be multiplied by itself.

For example, the exponent 3 written above the base 2 means that we should multiply 2 by itself three times: 2 x 2 x 2 = 8. So, [tex]2^3[/tex] is equal to 8.

So, the values of [tex]16^2[/tex] and [tex]12^2[/tex] are:

[tex]16^2[/tex] = 16 x 16 = 256

[tex]12^2[/tex] = 12 x 12 = 144

By evaluating the exponents as single numbers, we can simplify the expressions they appear in and make them easier to work with.

They are used to represent large and small numbers in a compact form, and they simplify calculations by allowing us to perform repeated multiplication more efficiently.

To learn more about exponent please click on below link        

https://brainly.com/question/219134

#SPJ1