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3 years ago

Find the surface area of a cubical planter measuring 30 inches on a side.

Mathematics

1 answer:

Snezhnost [94]3 years ago

3 0

30 x 30 = 900

This is the surface area of one side

900 x 6

Multiply by 6 to get the surface area of all 6 sides of the cube

900 x 6 = 5400

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The surface area of a melting snowball decreases at a rate of3.8cm2/min. Find the rate at which its diameter decreases when the

Scorpion4ik [409]

Answer:

Step-by-step explanation:

This is a pretty basic related rates problem. I'm going to go through this just like I do in class when I'm teaching it to my students.

We see we have a snowball, which is a sphere. We are talking about the surface area of this sphere which has a formula of

$S=4\pi r^2$

In the problem we are given diameter, not radius. What we know about the relationship between a radius and a diameter is that

d = 2r so

$\frac{d}{2}=r$ Now we can have the equation in terms of diameter instead of radius. Rewriting:

$S=4\pi(\frac{d}{2})^2$ which simplifies to

$S=4\pi(\frac{d^2}{4})$ and a bit more to

$S=\pi d^2$ (the 4's cancel out by division). Now that is a simple equation for which we have to find the derivative with respect to time.

$\frac{dS}{dt}=\pi*2d\frac{dD}{dt}$ Now let's look at the problem and see what we are given as far as information.

The rate at which the surface area changes is -3.8, and we are looking for $\frac{dD}{dt}$ , the rate at which the diameter is changing, when the diameter is 13. Filling in:

$-3.8=\pi(2)(13)\frac{dD}{dt}$ and solving for the rate at which the diameter is changing:

$-\frac{3.8}{26\pi}=\frac{dD}{dt}$ and divide to get

$\frac{dD}{dt}=-.459\frac{cm}{min}$ Obviously, the negative means that the diameter is decreasing.

7 0

3 years ago

Find the sum of the sequence. 42+43+44+45+...+107

8090 [49]

Answer:

4917

Step-by-step explanation:

Given sequence:

42, 43, 44, 45, ..., 107

This is AP with common difference of 1, the first term of 42 and the last term of 107

Number of terms:

107 - 42 + 1 = 66

Sum of the terms:

Sₙ= 1/2*n*(a₁+aₙ)

Sₙ= 1/2*66*(42+107) = 4917

Answer is: 4917

8 0

3 years ago

Write a function rule for the area of a rectangle whose length is 7

zzz [600]

Your answer should be A=98ft.

5 0

3 years ago

V 1. (-6) -(-2) is equal to: (-8 (+4 (-4) None of these

Marina CMI [18]

Answer:

I think the answer is -4

3 0

3 years ago

Read 2 more answers

What is the point slope form of a line with slope 2 that contains the point (1, -1)

mezya [45]

Point slope form is y - y1 = m(x-x1)

So,

y - (-1) = 2(x - 1)
y + 1 = 2x -2 or y + 1 = 2(x -1)

Hope this helps :)

3 0

3 years ago