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3 years ago

The volume of a cylinder is 108π cm³ and its height is 12 cm.

Mathematics

1 answer:

Anna007 [38]3 years ago

4 0

The formula for the volume of a cylinder is pi * r^2 * h and it is equal to 108pi. This makes r^2 = 9 which means r=3

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If Angle 1 and Angle 2 are complementary angles and if the measure of Angle 1 is 20° more than the measure of Angle 2, determine

Ratling [72]

A) Ang 1 + Ang 2 = 90
B) Ang 1 = Ang 2 + 20
B) Ang 1 -Ang 2 = 20 then adding this to equation A produces
2 Ang1= 110
Ang 1 = 55 degrees
Ang 2 =35 degrees

8 0

3 years ago

The core melt- down and explosions at the nuclear reactor in Chernobyl in 1986 released large amounts of strontium-90, which dec

elena-14-01-66 [18.8K]

If $S(t)$ is the amount of strontium-90 present in the area in year $t$ , and it decays at a rate of 2.5% per year, then

$S(t+1)=(1-0.025)S(t)=0.975S(t)$

Let $S(0)=s$ be the starting amount immediately after the nuclear reactor explodes. Then

$S(t+1)=0.975S(t)=0.975^2S(t-1)=0.975^3S(t-2)=\cdots=0.975^{t+1}S(0)$

or simply

$S(t)=0.975^ts$

So that after 50 years, the amount of strontium-90 that remains is approximately

$S(50)=0.975^{50}s\approx0.282s$

or about 28% of the original amount.

We can confirm this another way; recall the exponential decay formula,

$S(t)=se^{kt}$

where $t$ is measured in years. We're told that 2.5% of the starting amount $s$ decays after 1 year, so that

$0.975s=se^k\implies k=\ln0.975$

Then after 50 years, we have

$S(50)=se^{50k}\approx0.282s$

5 0

3 years ago

The price of the bicycle that Rocco wants to buy is $282. How much will Rocco pay for the bicycle if the state tax rate is 4%?

olasank [31]

Answer:

Rocco payes $292.28

Step-by-step explanation:

Because it is an increase so you put 104% over 100% in fraction form and then you put 282 at the bottom of another part of a fraction then you do 100 divided by 282 and you get 2.82 so then you take that 2.82 and you multiply it by 104% and you get 292.28 you can use a calculator to check but i know i did it correctly

5 0

3 years ago

Is the answer number 1? I can't get anymore wrong sorry for lengthy problem thanks!

mezya [45]

The area of the circle shown would not be 5pi. If you look closer, the area is 25pi, therefore the answer is 3. I hope this helps!

8 0

3 years ago

Find the equation of the line with a slope of 3/4 and passes through (4-2)

Ira Lisetskai [31]

Answer:

y = 3/4x - 5

Step-by-step explanation:

An equation of a line can be written in slope-intercept form:

y = mx + b

where m is the slope and b is the y-intercept.

Let's plug in what we know.

The slope is 3/4.

y = 3/4x + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the point (4, -2). Plug in the x and y values into the x and y of the standard equation.

-2 = 3/4(4) + b

To find b, multiply the slope and the input of x(4)

-2 = 3 + b

Now, subtract 3 from both sides to isolate b.

-5 = b

Plug this into your standard equation.

y = 3/4x - 5

This is your equation. It has a slope of 3/4, and passes through (4, -2)

Hope this helps!

5 0

2 years ago