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4 years ago

How do i use the pythagorean theorem

2 answers:

7 0

You first have to find your A and B values before you can do it. From there you get the A and the B value and plug it into the formula a2+b2=c2 (2= squared). An example could be like 2(2)+6(2)=c(2). This would be 4+36=c(2). In this case c is equal to 40.

AlexFokin [52]4 years ago

4 0

A squared plus b squared = c squared. c being the hypotenuse. Can only be used in a right triangle.

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1. a. A cube’s volume is 512 cubic units. What is the length of its edge?

Vanyuwa [196]

Answer:

a) The length of its edge is 8 units.

b) The volume of the sphere is approximately 268.083 cubic units.

c) The fraction of the cube that is taken up by the sphere is 0.524, whose equivalent in percentage form is 52.4 %.

Step-by-step explanation:

a) The volume of a cube ( $V_{c}$ ), measured in cubic units, is defined by the following expression:

$V_{c} = L^{3}$ (1)

Where $L$ is the side length of the cube, measured in units.

If we know that $V_{c} = 512\,u^{3}$ , then the length of its edge is:

$L = \sqrt[3]{V_{c}}$

$L = 8\,u$

The length of its edge is 8 units.

b) The volume of a sphere ( $V_{s}$ ), measured in cubic units, that fits snugly inside this cube is defined by:

$V_{s} = \frac{\pi}{6}\cdot L^{3}$ (2)

If we know that $L = 8\,u$ , then the volume of the sphere is:

$V_{s} \approx 268.083\,u^{3}$

The volume of the sphere is approximately 268.083 cubic units.

c) The fraction of the cube taken by the sphere is the ratio of the volume of the sphere to the volume of the cube. That is to say:

$r = \frac{V_{s}}{V_{c}}$

If we know that $V_{c} = 512\,u^{3}$ and $V_{s} \approx 268.083\,u^{3}$ , then the fraction of the cube that is taken up by the sphere is:

$r = 0.524$

The result in percentage form is calculated by multiplying the result above by 100.

$\% r = 52.4\,\%$

The fraction of the cube that is taken up by the sphere is 0.524, whose equivalent in percentage form is 52.4 %.

6 0

3 years ago

Please help don’t understand

yarga [219]

Answer:

Step-by-step explanation:

7 0

3 years ago

A bacteria population is going exponentially with a growth factor of 1/6 each hour. By what growth factor does the population ch

solong [7]

Answer:

The bacteria population will change with a growth factor of 1/12 for every half an hour or 1/12 per 30 minutes. (I don't know what the options are, but anything related to the answer I gave should be right.)

Step-by-step explanation:

Simple mathematics should get you the right answer. Here we are dealing with a fraction in a fraction. The first scenario should look like this: 1/6 / 1. Basically, that looks like one-sixth over one. Obviously, if we divide 1/6 by 1, we would get 1/6 itself again and we want to know what growth factor the population changes by for every half an hour. There are 30 minutes in half an hour and 60 minutes in one hour. Let's use the simplified terms to our advantage. Now, our first scenario should look like this: 1/6 / 60. Looks better now doesn't it? (Check the linked image to see the full scenario and how I did it in this next part.) For me, I divided 60 by 30 to get the scale factor, which is 2, then I divide 2 by 1/6 to get 1/12. Finally, we have 1/12 per half an hour! If I am wrong, please let me know and I hope this helps! :D