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3 years ago

Write a real-world problem that could be represented by the following equation. 70 + 5x = 40 + 10x

1 answer:

4 0

Jack wants to paint his house. he collected quotations from two different painters. The first painter's total cost in terms of the number of hours, (x), worked was modelled as f(x) = 70 + 5x, while that of the second painter was g(x) = 40 + 10x. Jack knows that it will take about 6 hours to paint the house. He figured out that the cost quoted by the two painters is equal for 6 hour of work.

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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

Timed test

marysya [2.9K]

Answer:

The correct answer should be 5,130

Step-by-step explanation:

the 3 in 513 is in the ones place, if it were ten times greater than 3 that would be 30, or a 3 in the tens place, the 3 in the number 5,130 is in the tens place, making that the correct choice

4 0

2 years ago

Which of the following expressions are equivalent to x + 2 − x ?

Paraphin [41]

it would be 0, because in the origin equations, the d's cancel out since it's x-x, only 2 would be left, therefore the correct answer is A since 0+2=2

6 0

2 years ago

Match the correct word with it's definition

Hunter-Best [27]

Answer:

Rule by a small group : Oligarchy

Rule by Citizens : Democracy

Rule by No one Anarchy

Rule by king or Queen : Monarchy

6 0

2 years ago

For a function p(x), as |x|—> infinity then p(x)—> 3. Which of the following graphs could be p(x)?

VladimirAG [237]

Answer:

Step-by-step explanation:

A pe x the answer is d

7 0

2 years ago