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3 years ago

What is the answer to this question?

Mathematics

1 answer:

Ksenya-84 [330]3 years ago

8 0

9/12= 0.75

8.00 * 0.75 = 6.00

the 9" costs $6.00

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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

A 32 foot ladder is placed on the ground 10 ft from the base of a house. How far up the house will the ladder reach?

umka2103 [35]

Answer:

22 feet

Step-by-step explanation:

7 0

3 years ago

What is the inverse one to one function of f(x) = square root of x-2???

alexira [117]

$f(x) = \sqrt{x - 2} \\y = \sqrt{x - 2} \\y^{2} = (\sqrt{x - 2})^{2} \\y^{2} = x - 2 \\x^{2} = y - 2 \\x^{2} + 2 = y \\x^{2} + 2 = f^{-1}(x)$

6 0

3 years ago

Solve equation<br> 7+3x-12x=3x+1

inysia [295]

7+3x-12x=3x+1
We will first make all the numbers which have x in go to the left.
So 7+3x-12x-3x, we make the 3x negative since to make it move it needs to change.
Then we will make all the sevens go to the right, so 3x-12x-3x=1-7.
So now it is much easier to figure out.
-12x=-6

4 0

3 years ago

Is the given value a solution to the equation? 4(n) - 3 = -2(n) + 9 n=2

nlexa [21]

Answer:

Yes!

The solution to the equation is n = 2

Step-by-step explanation:

Given the equation

$4\left(n\right)-3=-2\left(n\right)+9$