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3 years ago

S = 2πrh + 2πr², for h

Mathematics

1 answer:

diamong [38]3 years ago

6 0

Answer:

Step-by-step explanation:

This is a literal equation, and for some reason, students literally freak out about solving them. We will isolate h the same way we would if we were solving an equation for x. In order to get the term with the h in it all by itself, we have to move everything else away from that term. The 2πr² is added on the left, so we will move it by subtracting it from both sides, giving us

$S-2\pi r^2=2\pi rh$

Then we need to get the h alone. Everything on the right side of the equals sign is multiplied together, so the "undoing" of multiplication is division, so that's what we'll do. Divide everything away from the h:

$\frac{S-2\pi r^2}{2\pi r}=h$

which is choice C.

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Which of the graphs below represents the equation 4x + y = 7?

cupoosta [38]

Answer:

Graph C

Step-by-step explanation:

8 0

3 years ago

A population of mice is increasing exponentially. On Monday there were 120 most. One month later there were 132 most. Ready func

djyliett [7]

Answer:

$y=120 * 1.1^x$ --- function

The monthly rate is 10%

Step-by-step explanation:

Given

Let

$x \to months$

$y \to mice$

So, we have:

$(x_1,y_1) = (0,120)$ --- Monday

$(x_2,y_2) = (1,132)$ --- One month later

Required

The function

The function is represented as:

$y=ab^x$

In $(x_1,y_1) = (0,120)$ , we have:

$120 = a * b^0$

$120 = a * 1$

$120 = a$

$a=120$

In $(x_2,y_2) = (1,132)$ , we have:

$132 = a * b^1$

$132 = a * b$

Substitute: $a=120$

$132 = 120 * b$

Solve for b

$b = \frac{132}{120}$

$b = 1.1$

So, the function is:

$y=ab^x$

$y=120 * 1.1^x$

To calculate the monthly rate (r), we have:

$y =a(1 + r)^x$

Compare to: $y =ab^x$

$1 + r = b$

Make r the subject

$r = b-1$

Substitute $b = 1.1$

$r = 1.1-1$

$r = 0.1$

Express as percentage

$r = 0.1*100\%$

$r = 10\%$

5 0

3 years ago

A skier has decided that on each trip down a slope, she will do 3 more jumps than before. On her first trip she did 5 jumps. Der

taurus [48]

Since we are already given the amount of jumps from the first trial, and how much it should be increased by on each succeeding trial, we can already solve for the amount of jumps from the first through tenth trials. Starting from 5 and adding 3 each time, we get: 5 8 (11) 14 17 20 23 26 29 32, with 11 being the third trial.

Having been provided 2 different sigma notations, which I assume are choices to the question, we can substitute the initial value to see if it does match the result of the 3rd trial which we obtained by manual adding.

Let us try it below:

Sigma notation 1:

10
 Σ (2i + 3)
i = 3

@ i = 3

2(3) + 3
12

The first sigma notation does not have the same result, so we move on to the next.

10
 Σ (3i + 2)
i = 3

When i = 3; 3(3) + 2 = 11. (OK)

Since the 3rd trial is a match, we test it with the other values for the 4th through 10th trials.

When i = 4; 3(4) + 2 = 14. (OK)
When i = 5; 3(5) + 2 = 17. (OK)
When i = 6; 3(6) + 2 = 20. (OK)
When i = 7; 3(7) + 2 = 23. (OK)
When i = 8; 3(8) + 2 = 26. (OK)
When i = 9; 3(9) + 2 = 29. (OK)
When i = 10; 3(10) + 2 = 32. (OK)

Adding the results from her 3rd through 10th trials: 11 + 14 + 17 + 20 + 23 + 26 + 29 + 32 = 172.

Therefore, the total jumps she had made from her third to tenth trips is 172.

3 0

3 years ago

PLEASE ANSWER 100 PTS AND WILL MARK BRAINLIEST.

timofeeve [1]

Answer:

Step-by-step explanation:

We have the graph of f(x).

In order to find f(0), we simply need to find the y-coordinate of the coordinate when x is 0.

From the graph, we can see that there is a point at (0,1).

In other words, when x is 0, f(x) is 1.

Therefore:

$f(0)=1$

3 0

3 years ago

Read 2 more answers

What is the standard form of this expression? (4y - 9/2y - 3)

shepuryov [24]

Answer:

-1/2y-3

Step-by-step explanation:

4y-9/2y-3

8/2y-9/2y-3

-1/2y-3

4 0

3 years ago