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3 years ago

Find the length of arc ABC. Express answer in terms of pi. PC=18in

Mathematics

2 answers:

lara31 [8.8K]3 years ago

7 0

Answer: $27\pi$

Step-by-step explanation:

In the given figure we have given a circle in with radius PC = 18 inches

Also, the central angle made by arc AC $90^{\circ}$ or $\dfrac{\pi}{2}$

Since the sum of angles at a point is $2\pi$

Then , the central angle made by arc AC :-

$\theta=2\pi-\dfrac{\pi}{2}=\dfrac{3\pi}{2}$

The formula to find the arc length is given by :-

$l=r\theta$

Then the length of arc ABC will be :-

$l=(18)(\dfrac{3\pi}{2})=27\pi$

Hence, the length of arc ABC = $27\pi$

Lapatulllka [165]3 years ago

3 0

The formula would be 2 * pi * (central angle)/360

Hence, 2 * 22/7 * 270/360 => 84.823 in.

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Find the distance between the two points in simplest radical form. (7,-1) and (9,-9)

storchak [24]

Answer:

$\sqrt{68}$

Step-by-step explanation:

(7 , -1) = (x1 , y1)

(9 , -9) = (x2 , y2)

distance formula = $\sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

= $\sqrt{(9 - 7)^2 + (-9 - (-1))^2}$

= $\sqrt{2^2 + (-9 + 1)^2}$

= $\sqrt{4 + (-8)^2}$

= $\sqrt{4 + 64}$

= $\sqrt{68}$

7 0

3 years ago

Read 2 more answers

How to solve and respond.

son4ous [18]

Step-by-step explanation:

the error:

it is stated that

$\frac{5x}{x+7} +\frac{7}{x} = \frac{5x}{x+7} +\frac{7(7)}{x+7}$

subtract (5x)/(x+7) from both sides

$\frac{7}{x} = \frac{7(7)}{x+7}$

multiply both sides by x + 7

7(x+7) = 49x

7x + 49 = 49x

subtract 7x from both sides to isolate x and its coefficient

49 = 42x

thus, this is only true when 49 = 42x. in order for these two equations to be equal, they must always be true, so this is wrong

the solution:

we want to express 7/x as (something) / (x+7). to do this, we can multiply 7/x by 1.

anything divided by itself = 1. thus, if we multiply both the numerator and the denominator by something that turns x into (x+7), we can do what we want to do.

(x+7)/x * x turns x into (x+7), so we multiply both the numerator and denominator by (x+7)/x to get

$\frac{7}{x} = \frac{7(x+7)/x}{x+7}$

substitute this for 7/x in our original problem

$\frac{5x}{x+7} +\frac{7(x+7)/x}{x+7} = \frac{5x}{x+7} +\frac{(7x+49)/x}{x+7} = \frac{5x}{x+7} +\frac{7+49/x}{x+7} = \frac{5x+7+49/x}{x+7}$

3 0

2 years ago

Triangle A'B'C' is a reflection of triangle ABC across line BC. Prove that ray BC is the angle bisector of angle ABA'.

hammer [34]

Answer is below in the picture:-

(From the problem, we know (triangle)ABC (round of equal of) (triangle)A'B'C'. So, <A'B'C' = <ABC {the properties of congruent triangles}. So, ray BC is the angle, bisector of angle ABA')

I hope it helps.

7 0

2 years ago

How can i use variables to describe real world problems? explain.

Assoli18 [71]

You can use variables such as x & y to represent what you're looking for in the problem or represent information you're given in a real world problem.

7 0

3 years ago

Jim drove 455 miles in 7 hours. At the same rate, how many miles would he drive in 5 hours?

Olin [163]

Given parameters:

Distance covered = 455 miles

Time taken = 7 hours

New time taken = 5 hours

Unknown:

New distance = ?

To solve this problem, we need to define what speed entails.

Speed is a physical quantity and it is distance divided by time.

Speed = $\frac{distance}{time }$

In this problem, we first find the rate at which Jim is driving;

Speed = $\frac{455}{7}$ = 65miles/hr

Now that we know the rate, we can simply find the new distance;

New distance = speed x new time taken

Input the parameters;

New distance = 65miles/hr x 5hrs = 325miles

4 0

3 years ago