Question

need help with 11 and 12
https://ibb.co/eSxzvd

Answer 1

Let's start with Number 12. Let me see if I can put it up here. Give me a few ...

Answer 2

ok

Answer 3

So just to make this easier to explain, I color coded some of the sides. They give us that the red segment is 15.5 units. In other words, the length of the segment going from the center of the circle to a point on the circle is 15.5 units. Knowing this, what is the length of the green segment?

Answer 4

y?

Answer 5

The length of the green segment is not y. The segment y is only the segment that is part of the right triangle that we're given. Notice that the green segment is actually longer than y. BTW, the length of the segment going from the center of the circle to a point on the circle is generally called what?

Answer 6

the center

Answer 7

The length of a line segment going from the center of the circle to a point on the circle is generally called radius. So the length of the red segment (15.5 units) is the radius of the circle. Knowing this, what can we say about the green segment? Also just to clarify, the lengths of x and y are two segments that make up the green segment.

Answer 8

so we r trying to find the radius

Answer 9

We already know the radius. It's 15.5 units. That was given to us. The red segment is the radius. Knowing this, what can we say about the green segment?

Answer 10

i dont know

Answer 11

Do you know where the endpoints of the green segment are? If so, can you describe what they are?

Example: For the red segment, one of its endpoints is the center of the circle. Its other endpoint is on the circle.

Answer 12

isn't it a line that doesn't cross through the center?

Answer 13

That point connecting both the red segment and the green segment. What kind of point do you think that is?

Answer 14

diameter?

Answer 15

The diameter of a circle is the length of a segment from one point on a circle through the center point to a point on the opposite end of the circle. A diameter cannot be a single point.

Answer 16

So in other words, a diameter is a segment and not a point.

Answer 17

Anyway, I'll help you set up the problem. In case you didn't know, the point connecting the red and green segments is indeed the center of the circle which means the green and red segments are both the radius of the circle. They both have the same length which is 15.5 units. Since the lengths of x and y make up the length of the segment we can write \(x + y = 15.5\).

Furthermore, The red segment and the y segment are parts of the given right triangle. And we can use the Pythagorean Theorem to create a formula based on those segments which is \((13.4)^2 + y^2 = (15.5)^2\).

In other words we have a system of equations we can solve to find the length of \(y\) so that we can find the length of \(x\)

Answer 18

And that system is:
\(x + y = 15.5\)

\((13.4)^2 + y^2 = (15.5)^2\)

Any ideas on how to get started with solving this system?

Answer 19

no

Answer 20

I'll show you.
We will start with \((13.4)^2 + y^2 = (15.5)^2\)

First subtract \((13.4)^2\) from both sides to get:
\(y^2 = (15.5)^2 - (13.4)^2\)

Notice that \((15.5)^2 - (13.4)^2\) is the difference of squares \((a - b)^2 = (a + b)(a - b)\)

In other words we can re-write the equation as
\(y^2 = (15.5 + 13.4)(15.5 - 13.4)\)

After adding and subtracting we get:
\(y^2= (28.9)(2.1)\)

Which is the same as
\(y^2 = \left(28+\dfrac{9}{10}\right)\left(2+\dfrac{1}{10}\right)\)

Which using FOIL multiplies to get
\(y^2 = 56 + \dfrac{28}{10} + \dfrac{18}{10} + \dfrac{9}{100}\)

Which we can simplify this way:
\(y^2 = 56 + \dfrac{46}{10} + \dfrac{9}{100}\)
\(y^2 = 56 + \dfrac{460}{100} + \dfrac{9}{100}\)
\(y^2 = \dfrac{5600}{100} + \dfrac{469}{100}\)

\(y^2 = \dfrac{6069}{100}\)

We take the square root of both sides to get
\(y = \sqrt{\dfrac{6069}{100}}\)
\(y \approx 7.79\)

Answer 21

We replace the value we found for \(y\) in our original equation:
\(x + y \approx 15.5\) then solve for \(x\):
\(x + 7.79 \approx 15.5\).

Subtract 7.79 from both sides to get:
\(x \approx 15.5 - 7.79\)
\(x \approx 7.71\)

Answer 22

how would you set up problem 11 and where did the 7.79 come from

Answer 23

All the steps on how to get \(x\) I posted above.

Answer 24

And according to the instructions, we are supposed to round that to the nearest tenth so actually, \(x \approx 7.8\) units

Answer 25

oh ok

Answer 26

would u set up 11 like this
(5.3)2 + y + (10)2

Answer 27

For problem eleven you use one of the Chords of a Circle Theorems to set up:
Perpendicular bisector of a chord passes through the center of a circle.

Answer 28

is it this x+1/2(m+n)?