Projection of vector u onto vector v is approximately (1.33, 0.76, -0.57).
How to find the projection of vector u onto vector v?We'll use the following formula:
projection of u onto v = (u•v / ||v||²) * v
First, we need to calculate the dot product (u•v) and the magnitude squared (||v||²) of vector v.
1. Dot product (u•v):
u•v = (5 * -7) + (-9 * -4) + (-5 * 3) = -35 + 36 - 15 = -14
2. Magnitude squared (||v||²):
||v||^2 = (-7)² + (-4)² + (3)² = 49 + 16 + 9 = 74
Now, we'll plug these values into the projection formula:
projection of u onto v = (-14 / 74) * v
We'll multiply each component of vector v by the scalar (-14/74):
projection of u onto v = (-14/74) * (-7, -4, 3) = (1.33, 0.76, -0.57)
So, the projection of vector u onto vector v is approximately (1.33, 0.76, -0.57).
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Joe and Mike ran the same race. Joe finished the race 4 minutes before Mike. If Mike finished the race at 4:02 p.m., what time did Joe finish the race?
Answer:3:58 p.m.
Step-by-step explanation:
Which expression is equivalent to 1/4 (6x + 10 - 3x)?
Answer:
B
Step-by-step explanation:
3x 5
_ + _
4 2
Pls
provide correct answer. Will upvote if correct
Find the surface area of revolution about the x-axis of y 4 sin(3.c) over the interval 0
The surface area of revolution about the x-axis of y = 4 sin(3x) over the interval 0 <= x <= pi/6 is approximately 0.9402 units^2.
How to find the surface area of revolution of a curve?To find the surface area of revolution about the x-axis of the curve y = 4 sin(3x) over the interval 0 <= x <= pi/6, we can use the formula:
Surface area = 2π∫[a,b] y √(1+(dy/dx)^2) dx
where a = 0, b = pi/6, and y = 4 sin(3x).
First, we need to find dy/dx:
dy/dx = 12 cos(3x)
Next, we need to find √(1+(dy/dx)^2):
√(1+(dy/dx)^2) = √(1+144 cos^2(3x))
Now, we can substitute y and √(1+(dy/dx)^2) into the formula and integrate:
Surface area = 2π∫[0,pi/6] 4 sin(3x) √(1+144 cos^2(3x)) dx
This integral is difficult to solve analytically, so we can use a numerical method to approximate the value. One possible method is to use Simpson's rule:
Surface area ≈ (π/3)[f(0) + 4f(h) + 2f(2h) + 4f(3h) + ... + 4f(b-h) + f(b)]
where h = (pi/6)/n, n is an even integer, and f(x) = 4 sin(3x) √(1+144 cos^2(3x)).
Using n = 10, we get:
h = (pi/6)/10 = pi/60
Surface area ≈ (π/3)[f(0) + 4f(pi/60) + 2f(pi/30) + 4f(3pi/60) + ... + 4f(9pi/60) + f(pi/6)]
where f(x) = 4 sin(3x) √(1+144 cos^2(3x)).
Evaluating each term:
f(0) = 0
f(pi/60) ≈ 0.3025
f(pi/30) ≈ 0.3069
f(3pi/60) ≈ 0.3192
f(4pi/60) ≈ 0.3227
f(5pi/60) ≈ 0.3227
f(6pi/60) ≈ 0.3192
f(7pi/60) ≈ 0.3069
f(9pi/60) ≈ 0.3025
f(pi/6) ≈ 0
Therefore, the surface area of revolution about the x-axis of y = 4 sin(3x) over the interval 0 <= x <= pi/6 is approximately:
[tex]\begin{equation}\begin{aligned}& \text { Surface area } \approx(\pi / 3)[f(0)+4 f(p i / 60)+2 f(\text { pi/30) }+4 f(3 \text { pi/60) }+\ldots+ \\& 4 f(9 \text { pi/60) }+f(\text { pi/6) }] \\& \approx(\pi / 3)[0+4(0.3025)+2(0.3069)+4(0.3192)+\ldots+4(0.3025)+0] \\& \approx 0.9402 \text { units }^{\wedge} 2 \text { (rounded to four decimal places) }\end{aligned}\end{equation}[/tex]
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A rectangle is changing in such a manner that its length is increasing 5 ft/sec and its width is decreasing 2 ft/sec. at what rate is the area changing at the instant when the length equals 10 feet and the width equals 8 feet
The area of the rectangle is changing at a rate of 20 ft²/sec when the length equals 10 feet and the width equals 8 feet.
How to find the length and width?Let L and W be the length and width of the rectangle, respectively, and let A be the area of the rectangle. Then we have:
L = 10 ft (given)W = 8 ft (given)dL/dt = 5 ft/sec (length is increasing)dW/dt = -2 ft/sec (width is decreasing)We want to find dA/dt, the rate of change of the area A with respect to time t, when L = 10 ft and W = 8 ft.
We know that:
A = L*W
Taking the derivative of both sides with respect to time t, we get:
dA/dt = d/dt (L*W)
Using the product rule of differentiation, we get:
dA/dt = dL/dt * W + L * dW/dt
Substituting the given values, we get:
dA/dt = 5 ft/sec * 8 ft + 10 ft * (-2 ft/sec)
Simplifying, we get:
dA/dt = 40 - 20 = 20 ft²/sec
Therefore, the area of the rectangle is changing at a rate of 20 ft^2/sec when the length equals 10 feet and the width equals 8 feet.
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Find the minimum value of the parabola y=x^2+5/2.
Someone please help fast
The minimal value of the given parabola is y = 5/2, which occurs at x = 0.
To discover the minimum value of the given parabola & that's why we need to determine the vertex of the parabola.
The vertex of a parabola in the form of y = ax^2 + bx + c is given by means of (-b/2a, f(-b/2a)).
in the given parabola, a = 1, b = 0, and c = 5/2. consequently, the x-coordinate of the vertex is -b/2a = 0/(2*1) = 0.
To discover the y-coordinate of the vertex & we substitute x = 0 within the given equation:
y = 0^2 + 5/2 = 5/2
Therefore, the minimal value of the given parabola is y = 5/2.
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A chef uses the expression 0. 3n to represent the pounds of beef to use in a soup recipe for n people. The soup also has
7 fewer pounds of carrots than beef,
twice as many pounds of potatoes as beef, and
half as many pounds of onions as carrots.
How many pounds of ingredients will the chef use to make soup for 40 people?
Enter your answer in the box
The chef will use 43.5 pounds of ingredients to make soup for 40 people. Your answer is 43.5..
Step 1: Calculate the pounds of beef for 40 people using the expression 0.3n.
0.3 * 40 = 12 pounds of beef
Step 2: Calculate the pounds of carrots, which is 7 fewer than the pounds of beef.
12 - 7 = 5 pounds of carrots
Step 3: Calculate the pounds of potatoes, which is twice the pounds of beef.
2 * 12 = 24 pounds of potatoes
Step 4: Calculate the pounds of onions, which is half the pounds of carrots.
0.5 * 5 = 2.5 pounds of onions
Step 5: Add up the pounds of all ingredients to find the total pounds for 40 people.
12 (beef) + 5 (carrots) + 24 (potatoes) + 2.5 (onions) = 43.5 pounds
The chef will use 43.5 pounds of ingredients to make soup for 40 people. Your answer is 43.5.
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In circle O, mAD = 120 and mBC= 80. What is mBEC? :0 ;(
The measure of angle m<BEC is 80 degrees
How to determine the valueFrom the information shown, we have that;
m< AD = 120 degrees
m< BC = 80 degrees
To determine the value of m<BEC, we need to know that it is a minor arc in the circle.
Also, a minor arc is described as the shorter arc that connects two endpoints on a circle.
The measure of a minor arc is less than 180° , and is equal to the measure of the arc's central angle.
We can see than the angle measure of m<BC = m<BEC
Then,
m<BEC = 80 degrees
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the state of new jersey is divided into 21 counties. the counties population range from just over 60,000 people to almost 1,000,000 people. The median country population is 445,349 people, and the interquaritle range is 467,983 people. what is the typical population of a new jersey county?
The typical population of a New Jersey county can be described as being around 445,349 people which is also the median population of a New Jersey country.
Based on the given information, the median population of a New Jersey county is 445,349 people. This means that half of the counties in the state have a population above this number, while the other half have a population below it.
However, it is important to note that the range of county populations in New Jersey is quite large, with some counties having as little as 60,000 people and others having almost 1,000,000 people. This indicates that there is significant variability in the population size of counties across the state.
The interquartile range (IQR) of county populations is also provided, which tells us that the middle 50% of county populations fall within a range of 467,983 people. This suggests that while there is variability in county populations, there is also some level of consistency in the distribution of populations across the state.
Overall, the typical population of a New Jersey county can be described as being around 445,349 people, with some counties having significantly larger or smaller populations.
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A game has a spinner with 15 equal sectors labeled 1 through 15. what is p(multiple of 3 or multiple of 7)? 215 13 25 715
Answer: D. 7/15 or
Step-by-step explanation:
You have 15 possible outcomes
Probability= possibilities/outcomes
Possible numbers that are multiples of 3 are: 3, 6, 9, 12, 15. There are 5 possibilities.
P(multiple of 3) = 5/15
Possible numbers that are multiples of 7 are: 7, 14, . There are 2 possibilities.
P(7) = 2/15
Because of the or you add th e probabilities
P(multiple of 3 or multiple of 7) = 5/15 +2/15 =7/15
D
!!PLEASEE HELPPP!! I’m having a hard time!!
a. A customer would save $492 during the first year by switching from ElectroniSource to Intellivision. b. A customer who would save $207 in the second year. c. Intellivision's total cost of $1654.56.
Describe Algebra?Algebra is a branch of mathematics that deals with the manipulation and properties of variables, symbols, and equations. In algebra, variables represent unknown quantities, and equations represent relationships between those unknown quantities.
The fundamental operations in algebra are addition, subtraction, multiplication, and division. Algebraic equations involve variables and constants, which are combined using these operations to form algebraic expressions. These expressions can be simplified by applying algebraic rules and properties, such as the distributive property, associative property, and commutative property.
a. To calculate the savings during the first year, we need to find the total cost for each company for all three services during a year and compare them.
For ElectroniSource, the total cost for a year would be:
$42/month x 12 months = $504 for phone service
$35/month x 12 months = $420 for Internet service
$59/month x 12 months = $708 for cable TV service
Total cost for a year with ElectroniSource = $504 + $420 + $708 = $1632
For Intellivision, the flat monthly fee is $95, so the total cost for a year would be:
$95/month x 12 months = $1140
Savings during the first year = Cost with ElectroniSource - Cost with Intellivision
= $1632 - $1140
= $492
Therefore, a customer would save $492 during the first year by switching from ElectroniSource to Intellivision.
b. After the first year, Intellivision raises the rates by 25%. The new monthly fee would be:
$95 + 25% of $95 = $118.75
To calculate the savings for the second year, we need to find the total cost for each company for all three services during the second year and compare them.
For ElectroniSource, the total cost for the second year would still be:
$504 for phone service
$420 for Internet service
$708 for cable TV service
Total cost for the second year with ElectroniSource = $504 + $420 + $708 = $1632
For Intellivision, the total cost for the second year would be:
$118.75/month x 12 months = $1425
Savings during the second year = Cost with ElectroniSource - Cost with Intellivision
= $1632 - $1425
= $207
Therefore, a customer who switched from ElectroniSource to Intellivision would save $207 in the second year.
c. If Intellivision raises the rates by 16% for the third year compared to the second year, the new monthly fee would be:
$118.75 + 16% of $118.75 = $137.88
To compare the total cost for each company for the third year, we need to find the total cost for each company for all three services during the third year and compare them.
For ElectroniSource, the total cost for the third year would still be:
$504 for phone service
$420 for Internet service
$708 for cable TV service
Total cost for the third year with ElectroniSource = $504 + $420 + $708 = $1632
For Intellivision, the total cost for the third year would be:
$137.88/month x 12 months = $1654.56
Therefore, ElectroniSource is cheaper for the third year, with a total cost of $1632 compared to Intellivision's total cost of $1654.56.
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In the coordinate plane, the point X(1,4) is translated to the point X(0,6) . Under the same translation, the points Y(-1,2) and Z(-3,1) are translated to Y and Z , respectively. What are the coordinates of Y and Z ?
Help!!!!!! URGENT
Thus, the coordinates of Y and Z after the translation is obtained as :
Y'(-2,4) and Z'(-4, 3).
Define about the translation:A figure is translated when it is moved from one point to another without changing in size, form, or rotation.
A figure can be translated to move it up, down, left, or right while maintaining the same size. This is carried out using a coordinate system in order to be done properly and accurately.The pre-image is the original object that needs to be translated, and the image is the translated object.Given translation:
Point X(1,4) ---> point X'(0,6)
There is 1 unit shift to left as 1 is subtracted to x coordinate to get 0.
There is 2 unit shift to upward as 2 is added to y coordinate to get 6..
Translation:
(x,y) --->(x - 1, y + 2)
Applying same on points Y and Z,
Y(-1,2) --> Y'(-2,4)
Z(-3,1) --> Z'(-4, 3)
Thus, the coordinates of Y and Z after the translation is obtained as :
Y'(-2,4) and Z'(-4, 3).
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8. If AB and BC are tangent to circle D,
AB = 15 inches, and DB = 17 inches, find
the perimeter of ABCD.
Answer:
46 inches
Step-by-step explanation:
You want the perimeter of ABCD, where AB and BC are tangent to circle D, and AB = 15 inches, BD = 17 inches.
FigureThe attachment shows the figure. Radii DA and DC are perpendicular to the tangens, so each triangle is a right triangle. The hypotenuse BD is given as 17 inches, and the leg AB is given as 15 inches. The other leg is found from the Pythagorean theorem (or from your knowledge of Pythagorean triples). It is ...
AD = √(DB² -AB²)
AD = √(17² -15²) = √(289 -225) = √64
AD = 8
PerimeterThe perimeter is the sum of side lengths. The kite shape is symmetrical, so the perimeter is ...
P = 2(AD +AB) = 2(8 +15) = 46 . . . . inches
The perimeter of ABCD is 46 inches.
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What is the missing step in solving the inequality 4(x – 3) 4 < 10 6x? 1. the distributive property: 4x – 12 4 < 10 6x 2. combine like terms: 4x – 8 < 10 6x 3. the addition property of inequality: 4x < 18 6x 4. the subtraction property of inequality: –2x < 18 5. the division property of inequality: ________ x < –9 x > –9 x < x is less than or equal to negative startfraction 1 over 9 endfraction. x > –x is greater than or equal to negative startfraction 1 over 9 endfraction.
The missing step in solving the inequality 4(x – 3) /4 < 10/6x is to divide both sides by 2.
Apply the distributive property to get 4x - 12 /4 < 10/6x.
Combine like terms to obtain 4x - 3 < 5/3x.
Add 3/3x to both sides to get 4x < 8/3x + 3.
Subtract 8/3x from both sides to get 4/3x < 3.
Divide both sides by 4/3 to get x < -9/4.
Simplify the result by dividing both sides by 2 to get x < -9/2 or x > -4/3.
Therefore, the missing step is to divide both sides by 2, which gives x < -9/2 or x > -4/3.
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To assess the effect of piston ring type and oil type on piston ring wear, three types of piston ring and four types of oil were studied. Three replications of an experiment, in which the number of milligrams of material lost from the ring in four hours of running was measured, were carried out for each of the 12 combinations of oil type and piston ring type.
With oil type as the row effect and piston ring type as the column effect, the following sums of squares were observed: SSA = 1. 0926, SSB = 0. 9340, SSAB = 0. 2485, SSE = 1. 7034.
a) How many degrees of freedom are there for the effect of oil type?
b) How many degrees of freedom are there for the effect of piston ring type?
c) How many degrees of freedom are there for interactions?
d) How many degrees of freedom are there for error?
e) Construct an ANOVA table. You may give ranges for the P-values.
f) Is the additive model plausible? Provide the value of the test statistic and the P-value.
g) Is it plausible that the main effects of oil type are all equal to 0? Provide the value of the test statistic and the P-value.
h) Is it plausible that the main effects of piston ring type are all equal to 0? Provide the value of the test statistic and the P-value
The test statistic is large and the corresponding P-value is small, we reject the null hypothesis that the main effects of piston ring type are all equal to 0.
What is the degree of freedom for the effect?a) The degree of freedom for the effect of oil type is 3 (number of levels of oil type minus 1).
b) The degrees of freedom for the effect of piston ring type is 2 (number of levels of piston ring type minus 1).
c) The degrees of freedom for interactions is (3-1) * (2-1) = 2 (product of the degrees of freedom for oil and piston ring types).
d) The degrees of freedom for error is (3 * 2 * 4) - (3 * 2) = 18 (total number of observations minus the number of treatments).
e) The ANOVA table is as follows:
Source Sum of Squares Degrees of Freedom Mean Square F-Statistic P-value
Oil 1.0926 3 0.3642 F1 P1
Piston Ring 0.9340 2 0.4670 F2 P2
Interaction 0.2485 2 0.1243 F3 P3
Error 1.7034 18 0.0946
Total 3.9785 25
Note: The F-statistics and P-values will need to be calculated using the appropriate formulas.
f) To test the plausibility of the additive model, we can compare the residual mean square from the ANOVA table to the mean square for error. If the residual mean square is much smaller than the mean square for error, this indicates that there may be additional sources of variation in the data that are not explained by the additive model. The test statistic for this is:
F = (mean square for error) / (residual mean square)
If the test statistic is large and the corresponding P-value is small, we reject the additive model.
g) To test the plausibility that the main effects of oil type are all equal to 0, we can use the F-test:
F1 = (mean square for oil type) / (mean square for error)
If the test statistic is large and the corresponding P-value is small, we reject the null hypothesis that the main effects of oil type are all equal to 0.
h) To test the plausibility that the main effects of piston ring type are all equal to 0, we can use the F-test:
F2 = (mean square for piston ring type) / (mean square for error)
If the test statistic is large and the corresponding P-value is small, we reject the null hypothesis that the main effects of piston ring type are all equal to 0.
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Krissa exercises daily by walking. she aims to walk at a steady rate of 3.4 miles per hour.
a. if t represents time in hours and d represents distance in miles, write an equation that models the relationship between these variables.
b. use your equation to calculate the distance krissa will jog in 5/8 of an hour (round to the hundredths).
c. use your equation to calculate how long it will take for krissa to walk 5.44 miles.
When Krissa exercises daily by walking and she aims to walk at a steady rate of 3.4 miles per hour:
a) The equation is d = 3.4t;
b) Krissa will walk 2.13 miles;
c) It will take Krissa 1.6 hours to walk 5.44 miles.
What is a) the equation for Krissa's walking speed (d = 3.4t), and b) how far will she walk in 5/8 of an hour (2.13 mi), and c) how long to walk 5.44 miles (1.6 hours)?When Krissa exercises daily by walking and she aims to walk at a steady rate of 3.4 miles per hour:
a. The equation that models the relationship between time and distance is:
d = 3.4t
where d is the distance Krissa walks in miles and t is the time she spends walking in hours.
b. To calculate the distance Krissa will walk in 5/8 of an hour, we can substitute t = 5/8 into the equation from part a:
d = 3.4(5/8) = 2.125 miles
Therefore, Krissa will walk 2.125 miles in 5/8 of an hour, rounded to the hundredths.
c. To calculate how long it will take Krissa to walk 5.44 miles, we can rearrange the equation from part a to solve for t:
t = d/3.4
Substituting d = 5.44 into this equation, we get:
t = 5.44/3.4 = 1.6 hours
Therefore, it will take Krissa 1.6 hours to walk 5.44 miles.
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Mirrors kitchen sink holds up to 108.460 L of water runs amount to the nearest liter
The statement mentions that the kitchen sink has a capacity of 108.460 L of water and it is important to round up the amount to the nearest liter. When we round up the capacity of the sink, it comes out to be 108 liters. This means that the sink can hold up to 108 liters of water at maximum capacity.
It is important to have an idea of the sink’s capacity in terms of liters because it helps in managing the amount of water used while washing dishes or other household items. It is also beneficial to know the capacity of the sink while filling it with water for cleaning purposes, as it prevents the sink from overflowing.
Overall, the capacity of a sink is an important factor to consider while designing a kitchen or bathroom as it ensures proper functionality and prevents any damage to the surrounding areas due to overflowing water. So, it is always advisable to check the capacity of a sink before installing it in a household.
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Complete Question : Mirrors kitchen sink holds up to 108.460 L of water. Round this amount to the nearest liter.
A bottle holds 24 ounces of water. It has x ounces of water in it.
What does 24 - x represent in this situation?
Write a question about this situation that has 24 − x for the answers.
Answer:
24 - x would mean the air, or empty space in the bottle not being used by the water in the bottle.
Question:
"Create an equation that shows how much space is not taken up by water in a 24 once water bottle if it currently has x ounces of water."
OR
"A standing garden bed has x cubic feet in the box. It can hold 24 cubic feet, counting from the bottom to very top. How much empty space is there from the top of the dirt in the box to the very top of the box?"
A baseball pitcher records 153 strikeouts in
his first year pitching. Since then, the
number of strikeouts for this pitcher has
decreased by 31% per year. If this trend
continues, what is an upper limit on the total
of strikeouts over the pitcher's lifetime?
If a baseball pitcher records 153 strikeouts in his first year pitching with the number of strikeouts decreasing by 31% yearly, and if the trend continues, the upper limit on the total of strikeouts over the pitcher's lifetime is 153.
What is the upper limit?The upper limit refers to the maximum value possible.
The initial number of recorded strikeouts = 153
The annual decay rate = 31%
Decay factor = 0.69 (1 - 0.31)
Let the number of strikeouts in the year = y
Let the number of years of pitching = x
Equation:y = 153(0.69)^x
For instance, if x = 3, y = 153(0.69)^3
y = 50
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A store has two large vats of juice
containing a total of 28 gallons of juice.
One-eighth of container A is orange juice.
Three-fourths of container B is orange
juice. Together the two containers hold 11
gallons of orange juice. Which system of
equations can be used to determine a and
b, the total amounts of juice, in gallons, in
containers A and B?
F
H
+
b = 11
a
a + b 28
a + b = 28
320
b = 28
J
+ b = 28
4
a + b = 11
a + b = 11
The system of equations can be used to determine the gallons of juice in container A and the gallon of juice in container B is A + B = 28 and A + 6B = 88
Total amount of juice in both the vats is 28
Let the first container = A
second container = B
A + B = 28
Orange juice in A = 1/8 of A
Orange juice in B = 3/4 of B
Total orange juice in container A and B = 11
(1/8)A + (3/4)B = 11
A + 6B = 88
Hence the two equations will be A + B = 28 and A + 6B = 88
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Find the perimeter of a rectangle whose vertices are (3,2), (13,2), (13,9), and (3,9).
The perimeter of a rectangle is 34 units.
To find the perimeter of the rectangle with vertices (3,2), (13,2), (13,9), and (3,9), you need to determine the lengths of its sides.
The distance between (3,2) and (13,2) is the length of the base: 13 - 3 = 10 units.
The distance between (3,2) and (3,9) is the height: 9 - 2 = 7 units.
The perimeter of a rectangle is given by the formula P = 2*(length + width). In this case, P = 2*(10 + 7) = 2*17 = 34 units.
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The points $(1, 7), (13, 16)$ and $(5, k)$, where $k$ is an integer, are vertices of a non-degenerate triangle. what is the sum of the values of $k$ for which the area of the triangle is a minimum
The minimum value of k that satisfies this inequality is k = 9.
To find the value of k for which the area of the triangle is a minimum, we'll use the following terms: vertices, non-degenerate triangle, and area of a triangle. Here's the step-by-step explanation:
1. The vertices of the triangle are $(1, 7), (13, 16),$ and $(5, k)$.
2. A non-degenerate triangle means it has a positive area.
3. The area of a triangle can be calculated using the formula: Area = (1/2) * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
Now, let's find the area of the triangle with the given vertices:
Area = (1/2) * |1(16 - k) + 13(k - 7) + 5(7 - 16)|
We want to minimize the area, so let's simplify the expression:
Area = (1/2) * |-9 + 13k - 104|
Since we want a non-degenerate triangle, the area must be greater than 0. Therefore, the expression inside the absolute value must be positive:
-9 + 13k - 104 > 0
13k > 113
k > 113/13
k > 8.69
Since k is an integer, the minimum value of k that satisfies this inequality is k = 9.
The sum of the values of k for which the area of the triangle is a minimum is just the single value we found, which is 9.
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Find the exact length of the curve. 36y² = (x² – 4)³, 5 ≤ x ≤ 9, y ≥ 0 = 96.666
The exact length of the curve is 112/3(√3 + 1), or approximately 96.666.
To find the exact length of the curve, we can use the formula for arc length:
L = ∫a^b √(1 + [f'(x)]²) dx
where f(x) = (x² - 4)^(3/2)/6, 5 ≤ x ≤ 9.
First, we find f'(x):
f'(x) = 3x(x² - 4)^(1/2)/12 = x(x² - 4)^(1/2)/4
Then we substitute f'(x) into the formula for arc length:
L = ∫5^9 √(1 + [x(x² - 4)^(1/2)/4]²) dx
L = ∫5^9 √(1 + x²(x² - 4)/16) dx
L = ∫5^9 √(16 + 16x²(x² - 4)/16) dx
L = ∫5^9 √(16x² + x^4 - 4x²) dx
L = ∫5^9 √(x^4 + 12x²) dx
L = ∫5^9 x²√(x^2 + 12) dx
We can use the substitution u = x^2 + 12, which gives du/dx = 2x and dx = du/2x, to simplify the integral:
L = (1/2)∫37^93 √u du
L = (1/2) [(2/3)u^(3/2)]_37^93
L = (1/3)[(125 + 108√3) - (13 + 36√3)]
L = (1/3)(112√3 + 112)
L = 112/3(√3 + 1)
Therefore, the exact length of the curve is 112/3(√3 + 1), or approximately 96.666.
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Ortion of
a student is randomly chosen from the group.
what is the probability that the student likes cola b and does not like cola a?
o 0.1
0.2
0.3
o 0.4
Out of the 100 students, 20 like only cola b. Therefore, the probability that a randomly chosen student likes only cola b and does not like cola a is 0.2 or 20%, which is the answer. The answer is option B.
The probability that the student likes cola b and does not like cola a can be calculated as follows
Let's start by finding the number of students who like only cola b. We know that 50 students like cola b in total, but 30 of those students also like cola a. Therefore, the number of students who like only cola b is
50 - 30 = 20
So, out of 100 students, 20 like only cola b. Therefore, the probability that a randomly chosen student likes only cola b is
P(likes only cola b) = 20/100 = 0.2
Therefore, the probability that the student likes cola b and does not like cola a is 0.2.
The answer is option B: 0.2.
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--The given question is incomplete, the complete question is given
" In a class of 100 students, 60 students likes cola a, 50 students likes cola b and 30 students likes both.
From class a student is randomly chosen from the group.
what is the probability that the student likes cola b and does not like cola a?
0.1
0.2
0.3
0.4 "--
A third candle, in the shape of a right circular cone, has a volume of 16 cubic inches and a radius of 1. 5 inches. What is the height, in inches, of the candle? Round your answer to the nearest tenth of an inch.
The height of the right circular cone ,candle is approximately 6.8 inches.
To find the height of the third candle, which is a right circular cone with a volume of 16 cubic inches and a radius of 1.5 inches, we will use the formula for the volume of a cone: V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.
1. Substitute the given values into the formula: 16 = (1/3)π(1.5)^2h
2. Simplify the equation: 16 = (1.5^2 * π * h) / 3
3. Solve for h:
a. Multiply both sides by 3: 48 = 1.5^2 * π * h
b. Divide by π: 48/π = 1.5^2 * h
c. Divide by 1.5^2: (48/π) / 1.5^2 = h
4. Calculate the height, and round to the nearest tenth: h ≈ 6.8 inches
The height of the candle is approximately 6.8 inches.
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A bunch of flowers originally cost $32. It goes on sale at 25% off the original price.
Fill in the blanks.
Original percentage:
Percentage off:
Percentage left over:
Complete the number sentence to show how to find the sale price of the bunch of flowers:
Sale price = ----------% x $32
Original percentage: 100%
Percentage off: 25%
Percentage left over: 75%
Complete the number sentence to show how to find the sale price of the bunch of flowers:
Sale price = (100% - 25%) x $32 = 75% x $32 = $24
Anna ate 58of an orange and gave the other 38 to her brother. which equation can be used to find the difference between the amount anna ate and the amount she gave her brother?
The result of this equation will give us the numerical value representing the difference between the amounts Anna ate and the amount she gave to her brother. In this case, the difference would be 20.
To find the difference between the amount of orange Anna ate and the amount she gave to her brother, we can use the equation: 58 - 38 = x
Here, x represents the difference between the two amounts. We can solve for x by subtracting 38 from 58.
58 - 38 = 20
Therefore, the difference between the amount of orange Anna ate and the amount she gave her brother is 20. Anna ate 58 of an orange and gave 38 to her brother, so the remaining 20 must be the difference between the two amounts.
In summary, the equation that can be used to find the difference between the amount Anna ate and the amount she gave her brother is 58 - 38 = x, where x represents the difference. The answer is 20.
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Write the following as a factorial: 8x7x6x5x4x3x2x1
Answer:
A factorial is the product of all positive integers from 1 to a given number. In this case, the given number is 8, so the factorial would be:
8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
This can be simplified by recognizing that each number is one less than the previous number in the sequence, so we can rewrite it as:
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
where the exclamation mark denotes a factorial. Thus, the given expression can be written as 8!
write an expression to represent; "The sum of a number b and 24"
Answer: ?
Answer:
b+24
Step-by-step explanation:
the sum of a number represented by variable b
-- b+
and 24
-- b+24
Answer: b + 24
Step-by-step explanation:
The sum of .. and ➜ addition between two values
a number b ➜ b (represented by a variable)
24 ➜ the number 24
The sum of a number b and 24 ➜ b + 24
Susan’s weekly earnings were proportional to the number of hours she worked. this table shows
the number of hours susan worked and the amount she earned. how much money did susan
earn per hour?
hours earnings ($)
5 $47.50
7 $66.50
9 $85.50
11 $104.50
Susan earns $9.50 per hour. This is found by dividing her earnings by the number of hours worked for each corresponding row in the table.
To find how much money Susan earned per hour, we need to divide the total earnings by the total number of hours worked. For finding the Total earnings we need to add the money earned in every hour,
Total earnings = $47.50 + $66.50 + $85.50 + $104.50 = $304
Total hours worked = 5 + 7 + 9 + 11 = 32
Money earned per hour = Total earnings / Total hours worked
= $304 / 32
= $9.50
Therefore, Susan earned money of $9.50 per hour.
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Help me please I need the answer to the value of x