A cone has a radius of 5 ft and a height of 15 ft. It is empty and is being filled with water at a constant rate of 15 15 ft 3 ft3 / sec sec . Find the rate of change of the radius of the surface of the water when the radius of the surface of the water is 2 2 ft. (You must also include the units)

Answers

Answer 1

Answer:

[tex]\frac{dr}{dt}=0.11062ft/sec[/tex]

Step-by-step explanation:

From the question we are told that:

Radius [tex]r=5ft[/tex]

Height [tex]H=15ft[/tex]

Rate [tex]R=15ft/3sec =5ft/s[/tex]

Surface Radius [tex]R_{surf}=2.2ft[/tex]

Generally the equation for Volume is mathematically given by

 [tex]V=\frac{1}{3}\pi*r^2h[/tex]

Since radius to height ratio gives

 [tex]\frac{r}{h}=\frac{5}{15}[/tex]

 [tex]\frac{r}{h}=\frac{1}{3}[/tex]

 [tex]h=3r[/tex]

Therefore

 [tex]V=\frac{1}{3}\pi*r^2(3r)[/tex]

 [tex]V=\pi r^3[/tex]

Generally the equation for Change of Volume is mathematically given by

 [tex]\frac{dv}{dt}=\pi \frac{d}{dt}(r^3)[/tex]

 [tex]\frac{dv}{dt}=\pi 3*r^2 \frac{dr}{dt}[/tex]

 [tex]\frac{dv}{dt}=\pi 3*(2.2)^2 \frac{dr}{dt}[/tex]

 [tex]\frac{dr}{dt}=\frac{5}{45.62}[/tex]

 [tex]\frac{dr}{dt}=0.11062ft/sec[/tex]


Related Questions

To which graph does the point (−1, 3) belong?

y ≥ 2x + 6
y ≥ 3x − 1
y ≥ −x + 4
y ≥ −2x + 5

Answers

Answer:

second option "y ≥ 3x − 1."

Step-by-step explanation:

Just solved it

For a sample size of n = 26 and a population parameter of p = 0.6, a normal
curve can be used to approximate the sampling distribution.
O A. True
O B. False

Answers

Answer:true

Step-by-step explanation:

just took the test < 3

The statement : "for a sample size of n = 26 and a population parameter of  p = 0.6, a normal curve can be used to approximate the sampling distribution" is true.

What is normal curve?

Normal curve is used to represent the class shapes in the statistical probability. Mathematically, we can describe the normal curve as -

[tex]$f(x)= {\frac{1}{\sigma\sqrt{2\pi}}}e^{- {\frac {1}{2}} (\frac {x-\mu}{\sigma})^2}[/tex]

where -

f(x) = probability density function

σ = standard deviation

μ = mean

Given is that for a sample size of n = 26 and a population parameter of

p = 0.6, a normal curve can be used to approximate the sampling

distribution.

It is asked to identify whether the given statement regarding the normal curve is true or false. The given statement is - "for a sample size of n = 26 and a population parameter of  p = 0.6, a normal curve can be used to approximate the sampling distribution". The given statement is true.

Therefore, the statement : "for a sample size of n = 26 and a population parameter of  p = 0.6, a normal curve can be used to approximate the sampling distribution" is true.

To solve more questions on normal curves, visit the link below-

https://brainly.com/question/24201610

#SPJ7

If ST≅SV and m∠SUT=w+10° and m

Answers

Answer:

Step-by-step explanation:

3w= w +10

3w-w=10

2w =10

w= 10/2

w= 5

Which of the following statements are true about solids shown above
Check all that apply
A prism a has a lateral surface are of 60 cm 2
B prism b has a total surface are of 110 cm 2
C prism b has larger surface area
D prisms A and B have different values for lateral surface area

Answers

Ans its b and c

Step-by-step explanation:

please tell me is my answer right​

Answers

Yessssssssssssssssss
Yes it’s the right answer


Chau rented a truck for one day. There was a base fee of $18.95, and there was an additional charge of 95 cents for each mile driven. Chau had to pay $198.50
when he returned the truck. For how many miles did he drive the truck?

Answers

Let's say John drove 2 miles. He had to pay the base fee of $18.99 and $.75(2) = $1.50, so he paid $20.49 total.

We are given his total, though, and asked to find the mileage.

18.99 + .75m = 199.74

-18.99 -18.99

.75m = 180.75

.75 .75

m = 241

So, John drove 241 miles.

Hope this helps!

I

If f(1)=6f(1)=6 and f(n)=nf(n-1)-4f(n)=nf(n−1)−4 then find the value of f(3)f(3).

Answers

Answer:

49

Step-by-step explanation:

Answer:6144

Step-by-step explanation:

If f(1)=6f(1)=6 and f(n)=4f(n-1)f(n)=4f(n−1) then find the value of f(6)f(6).

f(1)=

f(1)=

\,\,6

6

f(\color{darkgreen}{2})=

f(2)=

\,\,4f(\color{darkgreen}{2}-1)

4f(2−1)

=

=

\,\,4f(1)

4f(1)

=

=

\,\,4(6)

4(6)

Substitute f(1)=6

f(2)=

f(2)=

\,\,24

24

f(\color{darkgreen}{3})=

f(3)=

\,\,4f(\color{darkgreen}{3}-1)

4f(3−1)

=

=

\,\,4f(2)

4f(2)

=

=

\,\,4(24)

4(24)

Substitute f(2)=24

f(3)=

f(3)=

\,\,96

96

f(\color{darkgreen}{4})=

f(4)=

\,\,4f(\color{darkgreen}{4}-1)

4f(4−1)

=

=

\,\,4f(3)

4f(3)

=

=

\,\,4(96)

4(96)

Substitute f(3)=96

f(4)=

f(4)=

\,\,384

384

f(\color{darkgreen}{5})=

f(5)=

\,\,4f(\color{darkgreen}{5}-1)

4f(5−1)

=

=

\,\,4f(4)

4f(4)

=

=

\,\,4(384)

4(384)

Substitute f(4)=384

f(5)=

f(5)=

\,\,1536

1536

f(\color{darkgreen}{6})=

f(6)=

\,\,4f(\color{darkgreen}{6}-1)

4f(6−1)

=

=

\,\,4f(5)

4f(5)

=

=

\,\,4(1536)

4(1536)

Substitute f(5)=1536

f(6)=

f(6)=

\,\,6144

6144

\text{Geometric Sequence:}

Geometric Sequence:

Common ratio of 4

6,24,96,384,1536,6144, ...

6,24,96,384,1536,6144,...

\text{Final Answer:}

Final Answer:

6144

additive inverse of -33​

Answers

Additive Inverse of -33

༆ANSWER:

—————————————————

[tex]\purple{\boxed{\boxed{\tt\pink{➢33}}}}[/tex]

The additive inverse of -33 is 33.

Remember!

»The opposite of the given integer is called its additive inverse. The sum of a number and its additive inverse is zero. For example, the additive inverse of -4 is 4, so when you add the two integer they sum will be zero.

Solve the equation.Leave your answer as simplest form a fraction

Answers

Answer:

n = 15

Step-by-step explanation:

5/2 = n/6                 Multiply both sides by 6

6 * 5/2 = 6 n/6

30/2   = n

n = 15

Which one is it?.....

Answers

Answer:

The answer is Rotation

enjoy your day hope this helps

What is the volume of the given picture below? ( HELP PLEASE )

Answers

It's 904.78.

The formula for the volume of a sphere is 4/3(pi)r^3. The diameter is 12. Half it to get the radius, which is 6. Plug 6 into the formula. The result is 904.77868.

Please help!!! Trigonometry is so complicated to me

Answers

Answer:

x = 4

Step-by-step explanation:

Given that sin(13x) = cos(9x+2)

Since sintheta  = cos(90 - theta)

hence sin (13x) = cos (90 -13x)

Substitute into the original equation

cos (90 -13x) = cos(9x+2)

90-13x = 9x+2

-13x - 9x = 2 - 90

-22x = -88

x = 88/22

x = 4

Hence the value of x is 4

please help will mark brainliest for right answer! No links...
Let f(x)=2x^3−x . What is the average rate of change of f(x) from 2 to 8 ?

Answers

Answer:

[tex]f(x) = {2x}^{3} - x \\ \delta \: f(x) = \frac{f(8) - f(2)}{2} \\ = \frac{(2 {(8)}^{3} - 8) - (2 {(2)}^{2} - 2)}{2} \\ = \frac{(1016 - 6)}{2} \\ = \frac{1010}{2} \\ = 505[/tex]

A spinner has three unequal sections: red, yellow, and blue. The table shows the results of Nolan's spins. Find the experimental probability of landing on each color. Enter your answers as simplified fractions.


Red 12
Yellow 18
Blue 5

Answers

Answer:

red: 12/35

yellow: 18/35

blue: 1/7

Step-by-step explanation:

The experimental probability is the total number of each outcome over the total outcomes. The total outcomes would be the sum, 12 + 18 + 5, or 35.

If we are looking for the experimental probability of red, we divide the spins on red by the total:

red - [tex]\frac{12}{35}[/tex]

If we are looking for the experimental probability of yellow, we divide the spins on yellow by the total:

yellow - [tex]\frac{18}{35}[/tex]

If we are looking for the experimental probability of blue, we divide the spins on blue by the total:

blue - [tex]\frac{5}{35}[/tex] = [tex]\frac{1}{7}[/tex]

Omar, Amare, and Jack paid a total of $68.25 for dinner and tickets to a concert. The concert
tickets cost $9.75 each. If the 3 friends split the dinner bill equally, how much did each friend
spend on dinner?

Answers

Answer:

32.5

Step-by-step explanation:

I I divided ot then added it together

convert 1 2/5 x 2/3 into a mixed number

Answers

it simplifies to the proper fraction 14/15 so it cannot be a mix number

hope this helps !!

at what rate percent of interest per annum will #700 gain an interest of #84 in 3 years​

Answers

Answer:

4% per annum

Step-by-step explanation:

Recall :

Simple interest = principal * rate * time

Given that :

Time = 3 ; simple interest = 84 ; principal = 700

84 = 700 * rate * 3

84 = 2100 * rate

Rate = 84 /2100

= 0.04

= 0.04 * 100% = 4% per annum

In the 1990s the demand for personal computers in the home went up with household income. For a given community in the 1990s, the average number of computers in a home could be approximated by
q = 0.3456 ln x − 3.045 10,000 ≤ x ≤ 125,000
where x is mean household income. A certain community had a mean income of $15,000, increasing at a rate of $1,500 per year.
1. How many computers per household were there?
2. How fast was the number of computers in a home increasing?

Answers

Answer:

dvffdd

Step-by-step explanation:

How do you write 6.00 × 10–5 in standard form?

Answers

Answer:

[tex]60x-5[/tex]

Step-by-step explanation:

Multiply 10 by 6

60x - 5

At time, t greater than or equal to 0, a particle moving in the xy plane has velocity vector given by v(t)=(t^2, 5t) What is the acceleration vector of the particle at time t=3?"

Answers

Answer:

The acceleration vector of the particle at time t=3 is (6,5).

Step-by-step explanation:

Acceleration:

The acceleration is the derivative of the velocity.

Derivative of a vector:

To derivate a vector, we derive each component.

v(t)=(t^2, 5t)

So

a(t) = v'(t) = (2t, 5).

What is the acceleration vector of the particle at time t=3?

a(3) = (2*3, 5) = (6,5)

The acceleration vector of the particle at time t=3 is (6,5).

Matthew decided to bake cupcakes for the school fundraiser. He wants to make 2 dozen cupcakes--one dozen strawberry and one dozen chocolate. He needs 2 1/4 cups of flour for the strawberry cupcakes and 2 1/3 cups of flour for the chocolate cupcakes, but he only has 4 cups of flour. Which two expressions could be used to correctly determine the amount of flour, in cups, Matthew still needs to bake his two dozen cupcakes? 2 part what is the total amount of flour, in cups, Mathew still needs for his cupcakes? NO LINK

Answers

Answer:

[tex]4+c=2\frac{1}{4}+2\frac{1}{3},\\\\\frac{7}{12}\:\text{more cups of flour}[/tex]

Step-by-step explanation:

The total amount of flour, in cups, Matthew needs is equal to [tex]2\frac{1}{4}+2\frac{1}{3}=4\frac{7}{12}[/tex]. Because he only has 4 cups, we can write the following expression to determine how many additional cups of flour he needs:

[tex]4+c=2\frac{1}{4}+2\frac{1}{3},\\\\4+c=\frac{7}{12}, \\\\c=\boxed{\frac{7}{12}\:\text{more cups of flour}}[/tex]

PLEASE HELP IM BEGGING PLEASEEEE SEE ATTACHED DOCUMENT

Answers

Answer:

Step-by-step explanation:

5.

3x-1 = 4x+13

-1=x+13

12=x

3(12)-1

36-1

Answer: 35

Second 5.

I'm not completely sure what this is referring to (please tell me if there is another part for this because there isn't any numbers such as <1 shown on the picture.)

6.

90+40+x=180

130+x=180

50=x

Answer: 50

7.

x+71=90

x=19

Answer: 19

The mean life expectancy of a certain type of light bulb is 945 hours with a standard deviation of 21 hours. What is the approximate standard deviation of the sampling distribution of the mean for all samples with n

Answers

Answer:

The approximate standard deviation of the sampling distribution of the mean for all samples of size n is [tex]s = \frac{\sigma}{\sqrt{n}} = \frac{21}{\sqrt{n}}[/tex]

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean life expectancy of a certain type of light bulb is 945 hours with a standard deviation of 21 hours

This means that [tex]\mu = 945, \sigma = 21[/tex].

What is the approximate standard deviation of the sampling distribution of the mean for all samples of size n?

[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{21}{\sqrt{n}}[/tex]

The approximate standard deviation of the sampling distribution of the mean for all samples of size n is [tex]s = \frac{\sigma}{\sqrt{n}} = \frac{21}{\sqrt{n}}[/tex]

Charlotte completed 12 pages of her 18-page report. What percent has she completed thus far?

Answers

Answer:

Charlotte has 23 of her book left to read. She can read 29 of it each day.

Step-by-step explanation:

Answer:

66.6666666667%

Step-by-step explanation:

12/18 = x/100

cross product

18x = 12(100)

18x = 1200

18× = 1200

__ _____

18 18

x=66.6666666667%

I need the answer to this pls.

Answers

The answer is c

Hope this helps :D

Answer:

C

Step-by-step explanation:

If 3/4 of an inch on a map is equal to 45 miles , what does 1 inch represent?

Answers

Answer:

60 miles

Step-by-step explanation:

if 45 = 3/4

divide 45 by 3 = 15

15 * 4 = 60

1)An octagon can be divided into 8 congruent triangles with base angles that are 67.5°. This octagon has a side length that is 8 cm.

2)What is the area of each triangle?

3)What is the area of the octagon?

4) Use your work from above to derive a generic formula for any octagon with side length that is n units.

Answers

Answer:

(a) [tex]Area = 14.7824cm^2[/tex]

(b) [tex]Area = 118.2592cm^2[/tex]

(c) [tex]Area = 4nh[/tex]

Step-by-step explanation:

Given

[tex]\theta = 67.5[/tex]

[tex]b= 8cm[/tex] --- base

[tex]n = 8[/tex] --- triangles

Solving (a) The area of each triangle

First, calculate the height (h) of each triangle using:

[tex]\sin(67.5) = \frac{h}{b/2}[/tex] --- i.e. we consider half of the triangle

[tex]\sin(67.5) = \frac{h}{8/2}[/tex]

[tex]\sin(67.5) = \frac{h}{4}[/tex]

Solve for h

[tex]h =4*\sin(67.5)[/tex]

[tex]h =4*0.9239[/tex]

[tex]h =3.6956[/tex]

The area of each triangle is:

[tex]Area = \frac{1}{2} *b * h[/tex]

[tex]Area = \frac{1}{2} *3.6956 * 8[/tex]

[tex]Area = 14.7824cm^2[/tex]

Solving (b): Area of the octagon

This is calculated as:

Area = 8 * area of 1 triangle

[tex]Area = 8 * 14.7824cm^2[/tex]

[tex]Area = 118.2592cm^2[/tex]

Solving (c): Area of octagon of side length n

In (a), we have:

[tex]Area = \frac{1}{2} *b * h[/tex]

Replace b with n

[tex]Area = \frac{1}{2} *n * h[/tex]

Multiply by 8 (the sides) to get the area of the octagon

[tex]Area = 8 * \frac{1}{2} *n * h[/tex]

[tex]Area = 4nh[/tex]

What is the shape of the base of the cylinder?

Answers

Answer:

circle

Step-by-step explanation:

circle because the bottom of a cylinder is circle it’s kinda common sense lol

HELP HELPP PLEASEEEE!

Answers

the length is b 12 !

Answer:

Step-by-step explanation:

volume of pyramid with square base=a^2(h/3)

84=a^2*7/3

84*3/7=a^2

252/7=a^2

36=a^2

[tex]\sqrt{36[/tex]=a

6=a

therefore length=6

help me please I have to pass​

Answers

Answer:

Step-by-step explanation:

15% of 400

15/100*400

15*400/100

6000/100

60

therefore ur answer is 60

C. 60 ✅

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex] \frac{15}{100} \times 400 \\ =15 \times 4 \\ = 60 [/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]

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