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eduard
1 year ago
12

Find the volume and surface area of a sphere with radius 3 centimeters. Round your answer to two

Mathematics
1 answer:
Harrizon [31]1 year ago
5 0

The Volume of the sphere with radius 3 cm is 113.10 cm³  and the surface area is  113.10 cm² .

In the question ,

it is given that ,

the radius of the sphere is = 3 cm

we know that formula for Volume of sphere is

Volume = (4/3)πr³

So , Volume for radius = 3 cm is

Volume = (4/3)π(3)³

= (4/3)*3.14*27

= 113.097

≈ 113.10 cm³

And the formula for the Surface area is given as

Surface Area  = 4πr²

Surface area for  radius = 3 cm is

Surface Area = 4*3.14*9

= 113.097

≈ 113.10 cm²

Therefore , The Volume of the sphere with radius 3 cm is 113.10 cm³  and the surface area is  113.10 cm² .

Learn more about Volume here

brainly.com/question/21623450

#SPJ1

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3 years ago
PLEASE HELP ASAP! I don’t recall how to do this!
MakcuM [25]

Answer:

Step-by-step explanation:

For a. we start by dividing both sides by 200:

(1.05)^x=1.885

In order to solve for x, we have to get it out from its position of an exponent.  Do that by taking the natural log of both sides:

ln(1.05)^x=ln(1.885)

Applying the power rule for logs lets us now bring down the x in front of the ln:

x * ln(1.05) = ln(1.885)

Now we can divide both sides by ln(1.05) to solve for x:

x=\frac{ln(1.885)}{ln(1.05)}

Do this on your calculator to find that

x = 12.99294297

For b. we will first apply the rule for "undoing" the addition of logs by multipllying:

ln(x*x^2)=5

Simplifying gives you

ln(x^3)=5

Applying the power rule allows us to bring down the 3 in front of the ln:

3 * ln(x) = 5

Now we can divide both sides by 3 to get

ln(x)=\frac{5}{3}

Take the inverse ln by raising each side to e:

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The "e" and the ln on the left undo each other, leaving you with just x; and raising e to the power or 5/3 gives you that

x = 5.29449005

For c. begin by dividing both sides by 20 to get:

\frac{1}{2}=e^{.1x}

"Undo" that e by taking the ln of both sides:

ln(.5)=ln(e^{.1x})

When the ln and the e undo each other on the right you're left with just .1x; on the left we have, from our calculators:

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(2^2)^x-6(2)^x=-8

Now we will bring over the -8 by adding:

(2^2)^x-6(2)^x+8=0

We can turn this into a quadratic of sorts and factor it, but we have to use a u substitution.  Let's let u=2^x

When we do that, we can rewrite the polynomial as

u^2-6u+8=0

This factors very nicely into u = 4 and u = 2

But don't forget the substitution that we made earlier to make this easy to factor.  Now we have to put it back in:

2^x=4,2^x=2

For the first solution, we will change the base of 4 into a 2 again like we did in the beginning:

2^2=2^x

Now that the bases are the same, we can say that

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2^x=2^1

Now that the bases are the same, we can say that

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