A sphere and a cone have the same volume. The sphere has a radius x and height y. The cone has a radius of 1/2x. Find the height of the cone in terms of y.
Answers
Answer:
h = 16x
Step-by-step explanation:
The volume of a sphere and a cone is same such that,
\(V_s=V_c\\\\\dfrac{4}{3}\pi r^3=\dfrac{1}{3}\pi R^2h\)
We have, r = x, R = (1/2)x, h= ? (height of the cone)
So,
\(\dfrac{4}{3}\pi x^3=\dfrac{1}{3}\pi (\dfrac{x}{2})^2h\\\\4x^3=\dfrac{x^2}{4}h\\\\h=\dfrac{16x^3}{x^2}\\\\h=16x\)
So, the height of the cone is equal to 16x.
Related Questions
This table represents a quadratic function with a vertex at (1, 0). What is the
average rate of change for the interval from x= 5 to x = 6?
A 9
OB. 5
C. 7
D. 25
X
-
2
3
4
5
0
4
9
16
P
Answers
Answer: 9
Step-by-step explanation:
Answer:To find the average rate of change for the interval from x = 5 to x = 6, we need to calculate the change in the function values over that interval and divide it by the change in x.
Given the points (5, 0) and (6, 4), we can calculate the change in the function values:
Change in y = 4 - 0 = 4
Change in x = 6 - 5 = 1
Average rate of change = Change in y / Change in x = 4 / 1 = 4
Therefore, the correct answer is 4. None of the given options (A, B, C, or D) match the correct answer.
Step-by-step explanation:
which of the following probability distribution types has a mean, median, and mode that are all equal? constant symmetric positively skewed negatively skewed
Answers
Answer: B symmetric
Step-by-step explanation:
Since every value in a constant-distribution has the same chance of happening, the distribution is symmetric. The mean and median are both identical to this value because there is only one value, which also makes it the mode.
The mode may or may not be equal to the mean and median for a symmetric distribution, but they are always equal. The mean is often higher than the median and the mode may be lower than the median in a positively skewed distribution. The mode may be higher than the median and the mean is often lower in a negatively skewed distribution.
A constant-probability distribution is a form of probability distribution in which the likelihood of each possible result is the same. In other words, there is an equal chance of each outcome.
Therefore , The Constant-distribution is a sort of probability distribution where the mean, median, and mode are all equal.
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if a consumer researcher compares the mean price of 25 items purchased at one store to the mean price for the same 25 items purchased at a second store, how many degrees of freedom are there?
Answers
In this case, the consumer researcher has two samples of 25 items each, so the total number of observations is 50. Therefore, the degrees of freedom for this comparison would be 49 (50-1).
The formula for degrees of freedom is df = n-1,
where n represents the number of observations in a sample.
In this case, the consumer researcher has two samples of 25 items each, so the total number of observations is 50. Therefore, the degrees of freedom for this comparison would be 49 (50-1).
If a consumer researcher compares the mean price of 25 items purchased at one store to the mean price for the same 25 items purchased at a second store, the degrees of freedom are 49.
The formula for degrees of freedom is df = n-1,
where n represents the number of observations in a sample.
In this case, the consumer researcher has two samples of 25 items each, so the total number of observations is 50.
Therefore, the degrees of freedom for this comparison would be 49 (50-1).
In general, degrees of freedom are important because they help to determine the variability and precision of statistical estimates.
When the degrees of freedom are high, the estimates tend to be more precise and reliable because there is more data available to support them.
Conversely, when the degrees of freedom are low, the estimates tend to be more uncertain and prone to error because there is less data available to support them.
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Use the binomial formula to find the coefficient of the q^4 p^17
term in the expansion of (29+p)^21
Answers
Recal the binomial theorem:
\(\displaystyle (a+b)^n = \sum_{k=0}^n \binom nk a^{n-k} b^k\)
Then
\(\displaystyle (2q+p)^{21} = \sum_{k=0}^{21} \binom{21}k (2q)^{21-k} p^k = \sum_{k=0}^{21} \binom{21}k 2^{21-k} q^{21-k} p^k\)
We get the q⁴p¹⁷ term when k = 17, and its coefficient would be
\(\dbinom{21}{17} 2^{21-17} = \dfrac{21!}{17!(21-17)!} 2^4 = \dfrac{21\cdot20\cdot19\cdot18}{4\cdot3\cdot2\cdot1}\cdot2^4 = \boxed{95,760}\)
What is the surface area of the box shown by the pattern below?
Answers
Solution:
Given the figure below:
The above figure, when closed, results into a cuboid.
This can be proven in the diagram below:
where the cuboid has
\(\begin{gathered} \text{length}=7\text{ units} \\ \text{width}=5\text{ units} \\ \text{height}=2\text{ units} \end{gathered}\)The surface area of a cuboid is expressed as
\(\begin{gathered} \text{Area = 2(L}\times W)+2(L\times H)+2(H\times W) \\ \text{where} \\ L\Rightarrow\text{length} \\ W\Rightarrow\text{width} \\ H\Rightarrow\text{height} \end{gathered}\)Thus, the surface area of the cuboid is evaluated as
\(\begin{gathered} \text{Area = 2(L}\times W)+2(L\times H)+2(H\times W) \\ =2(7\text{ units}\times5\text{ units)+2(7 units}\times2\text{ units)+2(2 units}\times5\text{ units)} \\ =2(35\text{ square units)+2(14 square units})+2(10\text{ square units)} \\ =(70+28+20)\text{ square units} \\ =118\text{ square units} \end{gathered}\)Hence, the surface area of the box is
\(118\text{ square units}\)The correct option is D.
In March, Stinson Company completes its only two jobs in process, Jobs 10 and 11. Job 10 cost $20,000 and Job 11 $30,000. On
March 31, Job 10 is sold.
Record the completion of the two jobs and the sale of Job 10. (Enter negative amounts using either a negative sign preceding the number e.g.
Answers
If in March, Stinson Company completes its only two jobs in process, Jobs 10 and 11. The entry is Dr Finished goods inventory $50,000,Cr Work in process inventory $50,000.
What is journal entry?Journal entry is used by companies to record their business transactions.
Preparation of the journal entries for the completion of the two jobs and the sale of Job 10
Mar. 31
Dr Finished goods inventory $50,000
(20,000+30,00)
Cr Work in process inventory $50,000
( To record the completion of the two jobs)
Mar. 31
Dr Cash $35,000
Cr Sales revenue $35,000
(To record the sale job 10)
Mar. 31
Dr Cost of goods sold $30,000
Cr Finished goods inventory $30,000
(To record the cost of the job sold)
Therefore the entry is Dr Finished goods inventory $50,000,Cr Work in process inventory $50,000.
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The complete question is:
In March, Stinson Company completes Jobs 10 and 11. Job 10 cost $20,000 and Job 11 $30,000. On March 31, Job 10 is sold to the customer for $35,000 in cash.Journalize the entries for the completion of the two jobs and the sale of Job 10.Date Account Titles and Explanation Debit CreditMar. 31 31 31
5. William owns 55 shirts, 40% of them are dress shirts. What number are dress shirts?
Answers
Given:
Number of shirts William own = 55 shirts
Percent that are dress shirts = 40%
Let's find the number that are dress shirts.
Given that 40% of the shirts Williams own are dress shirts, to find the number of dress shirts, apply the formula:
\(\begin{gathered} \text{Number of dress shirts = Percent that are dress shirts }\ast\text{ Number of shirts} \\ \\ \text{Number of dress shirts = 40\% }\ast\text{ 55 = }\frac{40}{100}\ast55=22 \end{gathered}\)Therefore, the number of dress shirts are 22
ANSWER:
22
WILL GIVE BRAINLIESTTY HELPP!
A 8 m ladder is placed against a wall. If the foot of
the ladder on the
ground is 5 m from the wall, find the height the ladder will reach on the
wall, accurate to two decimal places if necessary.
Answers
Answer:
try doing 8×5=40 hope it helps
How does the graph of f(x) = |x| compare with the graph of g(x) = 3|x| ?
A. The graph of g is a vertical compression of the graph of f.
B. The graph of g is a vertical stretch of the graph of f.
C. The graph of g is a vertical translation 3 units up of the graph of f.
D. The graph of g is a reflection of the graph of f over the x-axis.
Answers
Use the graph to find the following(H) The number at which of has a relative minimumE,F,G,H, I, J,K, L
Answers
Explanation:
Part (e)
f is increasing when from left to right, the function goes up. Then, the interval on which f is increasing is (5, ∞)
Part (f)
f is decreasing when from left to right the graph goes down. Then, the interval is (0, 5)
Part (g)
f is constant when the graph is a horizontal line, so the interval is (-∞, 0).
Part (h)
f has a relative minimum at point (5, -1) because it is the lowest point of the curve. So, the number at which f has a relative minimum is 5.
part (i)
Since the relative minimum is at point (5, -1), the relative minimum is -1.
Part (j)
f(-2) is the y-coordinate of the graph when x = -2. Then f(-2) = 24
Part (k)
When the y-coordinate is 3, the x-coordinate is 3 and 7, so the values of x for which f(x) = 3 are 3 and 7.
Part (l)
A graph is even if it is symmetric across the y-axis and it is odd if it is symmetric across the origin. In this case, there is no symmetry, so f is neither even nor odd
Therefore, the answers are:
e) (5, ∞)
f) (0, 5)
g) (-∞, 0)
h) 5
i) -1
j) 24
k) 3 and 7
l) neither
What is the distance between points e and g? round to the nearest tenth of a unit. Responses 11. 2 units 11. 2 units 12. 0 units 12. 0 units 14. 3 units 14. 3 units 17. 0 units.
Answers
The angle of separation between E and G is 12.0415945788 degrees.
How do coordinate points work?A set of numbers that expresses "the position of points on a coordinate plane utilising the horizontal and vertical distances from two reference axes."Both Point E's and Point G's coordinates are the first pair in an ordered sequence (1,7). (9,-2).A point or shape's location in a two-dimensional plane can be found using coordinates, which are a pair of numbers. The terms "x-coordinate" and "y-coordinate" are used to define a point's location on a 2D plane. The origin of the coordinate system is the intersection of the axes, and the first and second coordinates are known as the abscissa and the ordinate of P, respectively. The coordinates are typically expressed as two numbers enclosed in parentheses and placed in that order, separated by a comma, as in (3, 10.5).Distance formula =\($\sqrt{\left(\text { dif ferenceof } f^{\prime} x^{\prime} \text { points }\right)^2+\left(\text { Differenceof }{ }^{\prime} y^{\prime} \text { points }\right)^2} \\\)
\($& =\sqrt{(1-9)^2+(7-(-2))^2} \\\)
\(& =\sqrt{(-8)^2+(9)^2} \\\)
\(& =\sqrt{64+81} \\\)
\(& =\sqrt{145} \\\)
= 12.0415945788
As a result, the distance between E and G is 12.0415945788 miles.
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(x+4) ² remove bracket and simplify
Answers
Answer:
To expand (x + 4)², we can use the formula for squaring a binomial: (a + b)² = a² + 2ab + b². In this case, a = x and b = 4.
So,
(x + 4)² = x² + 2(x)(4) + 4²
= x² + 8x + 16
Thus, (x+4)² when expanded and simplified gives x² + 8x + 16.
Step-by-step explanation:
Answer:
x²n+ 8x + 16
Step-by-step explanation:
(x + 4)²
= (x + 4)(x + 4)
each term in the second factor is multiplied by each term in the first factor, that is
x(x + 4) + 4(x + 4) ← distribute parenthesis
= x² + 4x + 4x + 16 ← collect like terms
= x² + 8x + 16
divide 180 in three parts 1/10: 1/15: 1/20
Answers
Answer:
83,55,41
Step-by-step explanation:
1/10 : 1/15 : 1/20
180/10 : 180/15 : 180/20
18 : 12 : 9
=> 6 : 4 : 3
Sum of the ratios = 6 + 4 + 3 = 13
1st ratio: (6/13) * 180 = 83 (approximately)
2nd ratio: (4/13) * 180 = 55 (approximately)
3rd ratio: (3/13) * 180 = 41 (approximately)
∴ Three parts of 180 in the ratio 6 : 4 : 3 is 83, 55 and 41
(n + 18)
(2n)
What is the value of n
Answers
Answer: if this is what you wanted ,I think that n=0 and /or n= -18
Step-by-step explanation:
In an equation equal to 0 you can say that if it is a product like that : A x B =0 so A or / and B can be equal to 0 so you have to search when A=0 and when B=0 separately then you know when n is equal to 0 so the values of n . I’m sorry if it is not what you needed as an answer.
A theater has 1,464 seats. The seats are arranged into 62 equal-sized "regular" sections plus one "premium" front-row section. How many seats are in a regular section? How many seats are in the premium front-row section? Explain.
Answers
In the theater, that have 1,464 seats.
1426 seats are in "regular" sections
38 seats are "premium" front-row section
How to find the number of seats in the "regular" sectionsThe seat arrangement is solved by division. In this case the 62 equal spaced is the divisor while the number of seats is the in each row is the quotient
The division is as follows
1464 / 62
= 23 19/31
The number of seats in the regular section is 23 * 62 = 1426
The remainder will be arranged in premium front row
using equivalent fractions
19 / 31 = 38 / 62
the remainder is 38 and this is the seat for the premium front row section
OR 1464 - 1426 = 38 seats
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Given the equation -28cos((π/12)t)+32=28 , you determined two potential solutions: t=5.4522+24n or t=18.5478+24n. In your own words, explain why there are two potential solutions and what the variable n may represent in the solutions (use n=0 as an example).
Answers
The two potential solutions, t = 5.4522 + 24n and t = 18.5478 + 24n, arise from the periodic nature of the cosine function.
The variable n represents the number of complete periods of the cosine function that have occurred.
The given equation, -28cos((π/12)t) + 32 = 28, is a trigonometric equation involving the cosine function.
The goal is to find the values of t that satisfy the equation.
In trigonometry, the cosine function has a periodic nature.
It repeats its values over specific intervals.
In this equation, the coefficient of t inside the cosine function is (π/12), which indicates that the period of the cosine function is 2π/(π/12) = 24.
When solving trigonometric equations, it's important to consider the periodicity of the functions involved.
The solutions of a trigonometric equation will often have multiple values within a specific interval.
These equations represent the general form of solutions, where n is an integer.
let's consider n = 0. Plugging in n = 0 into the solutions, we have:
t = 5.4522 + 24(0)
= 5.4522
t = 18.5478 + 24(0)
= 18.5478
n = 0 gives us specific values of t.
As we increase the value of n (such as n = 1, 2, 3, and so on), we obtain additional solutions that satisfy the equation.
These solutions correspond to different periods of the cosine function.
It allows us to generate all possible solutions by adding multiples of the period to the initial solution.
By changing the value of n, we can find infinitely many solutions that satisfy the equation and account for the periodic behavior of the cosine function.
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a $40 packpack is on sale for $28 . what is the percent of change ?
Answers
Answer:11.2
Step-by-step explanation:
15.In AABC, AB = 3, BC = 4 and
AC = 6. Name the largest angle.
Answers
The largest angle of triangle ABC is angle B.
In this question, we have been given the side length of triangle ABC.
In ΔABC, AB = 3, BC = 4 and AC = 6.
We need to name the largest angle.
We know that the largest angle of triangle is always opposite to the longest side of the triangle.
We can observe that the longest side of ΔABC is AC = 6 units
The angle opposite to side AC is angle B.
Therefore, the largest angle of triangle ABC is angle B.
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Jim and Avery compare the number of points they scored during a game. Explain your answer mathematically
Jim notices that when he doubles his number of points, then subtracts 10 from that number, the result is the same as the number of points Avery scored. Write an expression representing the number of points
Avery scored, in terms of the number of points Jim scored, j. Enter your expression in the response box
Answers
The expression representing the number of points Avery scored in terms of the number of points Jim scored is 2j - 10.
Let's assume that Jim scored 'j' points during the game. According to the given information, when Jim doubles his number of points and subtracts 10 from that number, the result is the same as the number of points Avery scored. Therefore, we can write an equation as follows:
2j - 10 = number of points scored by Avery
To find the expression representing the number of points Avery scored in terms of the number of points Jim scored, we simply solve the above equation for Avery's points:
number of points scored by Avery = 2j - 10
Therefore, the expression representing the number of points Avery scored in terms of the number of points Jim scored is 2j - 10.
In summary, Jim scored 'j' points during the game and when he doubles his number of points and subtracts 10 from that number, he gets the same result as the number of points Avery scored.
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Find the value of C that completes the square
Answers
Answer:
Step-by-step explanation:
y^2-22y+c
complete the square ax^2+bx+c is our old formula quadratic equation
we know that to find c we will divide b/2 and square it
22/2=11
c^2=121
we have y^2-22y+121
Grey ran 3 1/3 miles Monday, 1 1/6 miles on Friday and 2 3/8 miles on Sunday. How many total miles did he run on those three days?
Answers
Answer:
7 13/24 miles
Step-by-step explanation:
First reduce 11/6 into 1 5/6
Then add them all together to get 7 13/24
Answer:
The total would be 6 7/8 miles.
Step-by-step explanation:
Hope this helps :)
Approximate the area under the function between a and b using a right-hand sum with the given number of intervals.
f(x) = 4 - x^2
a = 0, b = 2
4 Intervals.
Answers
The approximate area under the curve of f(x) from x=0 to x=2 using a right-hand sum with four intervals is 4.25.
To approximate the area under the curve of the function f(x) = 4 - x^2 from x=0 to x=2 using a right-hand sum with four intervals, we first need to divide the interval [0, 2] into four equal subintervals of length h = (b-a)/n = (2-0)/4 = 0.5. The four subintervals are [0, 0.5], [0.5, 1], [1, 1.5], and [1.5, 2].
Next, we find the height of the curve at the right endpoint of each subinterval and multiply it by the width of the subinterval to get the area of the rectangle that approximates the region under the curve. Using the right endpoints of the subintervals, we have:
f(0.5) = 4 - (0.5)^2 = 3.75
f(1) = 4 - (1)^2 = 3
f(1.5) = 4 - (1.5)^2 = 1.75
f(2) = 4 - (2)^2 = 0
area of each rectangle:
A1 = f(0.5) * h = 3.75 * 0.5 = 1.875
A2 = f(1) * h = 3 * 0.5 = 1.5
A3 = f(1.5) * h = 1.75 * 0.5 = 0.875
A4 = f(2) * h = 0 * 0.5 = 0
the approximate area under the curve of f(x) from x=0 to x=2:
A ≈ A1 + A2 + A3 + A4 = 1.875 + 1.5 + 0.875 + 0 = 4.25
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Tony pays $25 for his monthly phone service and $.07 for each minute of talk time. If his May bill cost $54.54, how many minutes did he talk on the phone for?
Answers
Answer:
im not sure but i think he talked on the phone
for 7 hours. if this isnt right im sorry. if it is
please mark brainliest
Step-by-step explanation:
which of the following represents the length of ACA. 7²- 4²B. √7²+4²C. √7²-4²D. 7²+4²
Answers
Solution
For this case we have a right triangle so then we can do this:
\(7^2=4^2+x^2\)We can solve for the value of x and we got:
\(x=\sqrt[]{7^2-4^2}\)What’s 9 divided by 3/2
Answers
Answer: 6
Step-by-step explanation:
9 divided by 2/3 = 6
Answer:
6
Step-by-step explanation:
9 divided by 3/2 is the same thing as 9*2/3. This is because 3/2 and 2/3 are reciprocals. When you are dividing by fractions I like to use the phrase: keep, change, flip. We keep the first number the same, we change the division to multiplication, and then we flip the fraction. Than you just multiply across like normal and that is your answer. Hope this helps :)
Which expression is equivalent to (sqrt3 + i)^3?
Answers
Express √3 + i in polar form:
|√3 + i| = √((√3)² + 1²) = √4 = 2
arg(√3 + i) = arctan(1/√3) = π/6
Then
√3 + i = 2 (cos(π/6) + i sin(π/6))
By DeMoivre's theorem,
(√3 + i)³ = (2 (cos(π/6) + i sin(π/6)))³
… = 2³ (cos(3 • π/6) + i sin(3 • π/6))
… = 8 (cos(π/2) + i sin(π/2))
… = 8i
Sarah had some money in her savings account. She added \$18.54 each month to her savings for half a year. Then, she donated $100 to a charity. If she had $24.20 left after her donation, how much money was in her original savings? dollar
Answers
Answer:
$12.96
Step-by-step explanation:
Start by finding how much money was added to her account by multiplying 18.54 by 6. Then subtract 100 from that amount, which will give you 11.24. Subtract 11.24 from 24.20, which is 12.96.
1. What is the slope of the line tangent to the curve defined by y2 + xy - x = 11x at the point (2, 3)? A. - 5 - 2 B. O C. 1 D. 4 7 E. 3 2
Answers
The slope of the line tangent to the curve, the correct answer is not among the options
How to find the slope of the line tangent to the curve defined by y^2 + xy - x = 11x at the point (2, 3)?To find the slope of the line tangent to the curve defined by \(y^2 + xy - x = 11x\) at the point (2, 3), we need to differentiate the equation implicitly with respect to x and evaluate it at the given point.
Differentiating both sides of the equation with respect to x:
\(d/dx(y^2) + d/dx(xy) - d/dx(x) = d/dx(11x)\)
Applying the chain rule and product rule:
2y(dy/dx) + y + x(dy/dx) + y - 1 = 11
Simplifying the equation:
(2y + x)(dy/dx) = 12 - y
Now, we substitute the coordinates of the given point (2, 3) into the equation:
(2(3) + 2)(dy/dx) = 12 - 3
(6 + 2)(dy/dx) = 9
8(dy/dx) = 9
dy/dx = 9/8
Therefore, the slope of the line tangent to the curve at the point (2, 3) is 9/8.
The correct answer is not among the options provided, so none of the given options is the correct answer.
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1. A wife works three days then a day off while his husband works five days then a day off. If the couple has a day-off together today, how many days after will they have another day off together?
2. The weight W of an object above the earth varies inversely as the square of the distance D from the center of the earth. If a man weighs 180 pound on the surface of the earth, what would his weight be at an altitude 1000 miles? Assume the radius of the earth to be 4000 miles
3. Two turtles A and B start at the same time move towards each other at a distance of 150 m. The rate of turtle A is 10 m/s while that B is 20 m/s. A fly flies from one turtle to another at the same time that the turtles start to move toward its each other. The rate of the fly is constant at 100 m/s. determine the total distance traveled by the fly until the two turtles met?
Answers
1). 15 days
2). 115.2 pounds.
3). 500 meters
1. To find out when the couple will have another day off together, we need to find the least common multiple (LCM) of their work schedules. The LCM of 3 and 5 is 15, so the couple will have another day off together after 15 days.
2. The weight W of an object above the earth varies inversely as the square of the distance D from the center of the earth.
This means that W = k/D^2, where k is a constant.
To find k, we can plug in the values given in the question: 180 = k/4000^2.
Solving for k gives us k = 180*4000^2 = 2880000000. Now we can plug in the new distance, 4000 + 1000 = 5000 miles, to
find the new weight: W = 2880000000/5000^2 = 115.2 pounds.
3. To find the total distance traveled by the fly, we need to find out how long it takes for the turtles to meet.
The combined rate of the turtles is 10 + 20 = 30 m/s, so it will take them 150/30 = 5 seconds to meet.
The fly travels at a constant rate of 100 m/s, so in 5 seconds it will have traveled 100*5 = 500 meters.
Therefore, the total distance traveled by the fly is 500 meters.
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Similar
Not Similar
Please help please
Answers
Answer:
I dont think thats similar
Step-by-step explanation: