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3 years ago

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A sphere with a radius of 6cm has the same volume as a cylinder with a height of 4.5cm. What is the radius of the cylinder

1 answer:

yawa3891 [41]3 years ago

4 0

Short answer: r = 8
Remark
The easiest way to do this is to solve the sphere's volume in terms of pi. When you do this, you can equate that to the formula for a cylinder and cancel the pi values.

Step One
Find the volume of the sphere.

<em>Givens</em>
r = 6 cm

<em>Formula</em>
V = (4/3) pi r^3

<em>Sub and Solve</em>
V = 4/3 pi * 6^3
V = 288 * pi

Step two
Find the radius of the cylinder

<em>Givens</em>
V = 288* pi cm^3
h = 4.5 cm

<em>Formula</em>
V = pi r^h

<em>Sub and solve</em>
288 pi cm^3 = pi r^2 * 4.5 Divide both sides by pi
288 cm^3 = 4.5 r^2 Divide both sides by 4.5
388 / 4.5 = r^2
64 = r^2 Take the square root of both sides.
r = square root( 64)
r = 8 <<<<< Answer

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3 years ago

Complete the general form equation of the parabola that passes through (4, -11) with vertex at : (2, -3).

fomenos

Answer:

Step-by-step explanation:

You're given a coordinate in the form of (x, y) and you're also given the vertex in the form of (h, k). We will use those in the vertex form of the equation

$y=a(x-h)^2+k$ and solve for a. Filling in:

$-11=a(4-2)^2-3$ which simplifies a bit to

$-11=a(2)^2-3$ and a bit more to

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3 years ago

Mario invests 1,500 in a savings account that earns 2% interest a year. He also plans to set aside $50 cash a month. A:2100(1.02

Sedbober [7]

Answer:

<em>1500(1.02)^x + 600x</em> is how much he has in savings at the end of x years where it be in the bank or elsewhere

Step-by-step explanation:

x is in years

Let's just think about the investment of 1500 in an account earning 2% per year.

Before the years even start, you are at 1500 ( present value).

The next year (year 1), it would be 1500*.02+1500=(1500)(1.02).

The next year (year 2), it would be 1500(1.02)(.02)+1500(1.02)=1500(1.02)(1.02).

We keep multiplying factors of (1.02) each time.

So for year x, you would have saved 1500(1.02)^x.

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So the first year you would have 600.

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3 years ago

Which equation results from taking the square root of both sides of (x 9)2 = 25? x 3 = ±5 x 3 = ±25 x 9 = ±5 x 9 = ±25.

kow [346]

The equation which is results from taking the square root of both sides of the provided equation is,

$(x+9)=\pm5\\$

<h3>What is the square root?</h3>

A square root of a number is the value which is when multiplicand by itself gives the same value as the number posses.

Let a number is <em>a. </em>Then this number in the form of square root can be written as,

$a=\sqrt{a}\times \sqrt{a}$

The given algebraic equation in the problem is,

$(x+ 9)^2 = 25$

Take the square root, in both sides,

$\sqrt{(x+ 9)^2} = \sqrt{25}\\\sqrt{(x+ 9)^2} = \sqrt{5^2}$

Cancel out the square root with the square of the number as,

$(x+9)=\pm5\\$

Hence, the equation which is results from taking the square root of both sides of the provided equation is,

$(x+9)=\pm5\\$

Learn more about the square root of number here;

brainly.com/question/664132

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Hope this helps explain what was needed to be solved! :)

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