Challenge: x(2)+9x+c :-D

Find radiuses of circles, if OO1=20cm and 3AK=2BK

Serggg [28]

Answer:

radius of smaller circle on the left = 8 centimeters
radius of larger circle on the right = 12 centimeters

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Explanation:

The letter O looks very similar to the number zero, so I'm going to use other letters to avoid confusion. For the smaller circle on the left, it'll have center P. The circle on the right will have center Q. See the diagram below.

Based on that, we can say that PQ = 20 cm.

Let x = length of PK

PK + KQ = PQ

KQ = PQ - PK

KQ = 20 - x

We'll keep this in mind for later. I'll refer to this as "Fact 1" when it does come up later.

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We're given this equation

3AK=2BK

Let's get the numbers to one side and the letters to the other side like so:

3AK=2BK

3AK/BK = 2

AK/BK = 2/3

We'll use this later as well. I'll refer to this as "Fact 2" when it does come up later.

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Next, draw a segment from P to A to form triangle PAK (also shown in the diagram below). Do the same for points Q and B to form triangle QBK.

The segments PA and PK are radii of the smaller circle, so PA = PK which leads to triangle PAK being isosceles. Triangle QBK is also isosceles for similar reasoning.

The angles AKP and QKB are vertical angles, so they are congruent.

The facts mentioned so far boil down to the two triangles being similar triangles (use the angle angle method to prove).

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Now that we know the triangles are similar, we can use a proportion to solve for x.

PK/KQ = AK/KB

PK/KQ = 2/3 .... use fact 2

x/(20-x) = 2/3 .... use fact 1

3x = 2(20-x) .... cross multiply

3x = 40 - 2x

3x+2x = 40

5x = 40

x = 40/5

x = 8

So,

PK = x = 8
KQ = 20-x = 20-8 = 12

The radius of the smaller circle on the left is 8 cm.

The radius of the larger circle on the right is 12 cm.

4 0

2 years ago

Jackson has 2,000 baseball cards in his collection. Gave has 1/10 as many cards in his collection as Jackson. How many cards doe

melisa1 [442]

Answer: 200

Step-by-step explanation:

You have 2000 and 1/10 is the same as divide by 10 so:

2000/10 = 200

8 0

3 years ago

The formula for the volume V of a cylinder is LaTeX: V=\pi r^2hV = π r 2 h, where r is the radius of the base anThe formula for

Alekssandra [29.7K]

Answer:

$h = \frac{V}{\pi r^2}$

$h = 4 cm$

Step-by-step explanation:

Volume of cylinder is given as $V = \pi r^2 h$

V is the volume the cylinder, r is its radius at the base, while is its height.

To select the formula for h (height) let's make h the subject of the formula as follows:

$V = \pi r^2 h$

$\frac{V}{\pi r^2} = \frac{\pi r^2 h}{\pi r^2}$ (dividing both sides of the equation by $\pi r^2$ )

$\frac{V}{\pi r^2} = h$

$h = \frac{V}{\pi r^2}$

Use the formula above to find the height of the given cylinder where Volume (V) = 36π cm³, and base radius (r) = 3 cm:

$h = \frac{36 \pi}{\pi 3^2}$ (substitution)

$h = \frac{36 \pi}{\pi * 9}$

$h = \frac{36 \pi}{9 \pi}$

$h = \frac{36 \pi}{\pi * 9}$

$h = \frac{36}{9}$ ( $\pi$ cancels $\pi$ )

$h = 4 cm$

8 0

3 years ago

Jeremy put pepperoni on half of a pizza. He put olives on 1/3 of the pizza. What fraction of the pizza did not have pepperoni?

evablogger [386]

1/2

he only put pepperoni on the other 1/2

6 0

3 years ago

What is the value of z so that-9 and 9 are both solutions of x^2+z=103?

notka56 [123]

If the sol'ns are -9 and 9, then we can use this to form our eq'n:
(x - 9)(x + 9) = 0
x^2 - 81 = 0
so...
x^2 + z - 103 = x^2 -81
z - 103 = -81
z = -81 + 103
z = 22

8 0

3 years ago

Challenge: x(2)+9x+c:-D​

Challenge: x(2)+9x+c:-D