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2 years ago

Circle E has a radius of 40 inches with = 324°. Find the exact length of

2 answers:

8 0

Let the arc is ABC with angle 324 degree, to find the length of that arc follow the steps;
The circumference of the circle E is :C = 2 r π
C = 2 * 40 π = 80 π cm.
Also 324° / 360° = 0.9m Arc (ABC ) = 0.9 * 80 π = 72 π cm
There is also formula for calculating the measure of an arc:
m Arc = r π α / 180°
m Arc = 40 π * 324 / 180
= 40π * 1.8 = 72 π
Now we have to find the exact length ( π ≈ 3.14 )
m Arc ( ABC ) = 72 * 3.14 = 226.08 cm

Maksim231197 [3]2 years ago

5 0

Answer:

72 π inches

Step-by-step explanation:

1) Set up a ratio: 324/360. Simplify it: 9/10.

2) Then do: 9/10 x 2 π r --> 9/10 x 2 π 40. You should get: 72 π.

3) So, the exact length of arc ABC = 72 π inches.

(The reason you are supposed to leave it 72 π inches is because only if the question asks you to find the approximate length of the arc, then you can use 3.14 instead of π. But if the question asks you to find the exact length of the arc, you have to leave it as said above because you would still have to round the answer (if you multiply 72 by pi), which makes it an approximate answer, not an exact answer.)

pi (π) = 3.14159265359......................

Pi is an endless number.

<em>Hope this helps! :)</em>

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Lavania is studying the growth of a population of fruit flies in her laboratory. After 6 days she had nine more than five times

MatroZZZ [7]

Answer:

Lavania observed 39 fruit flies after 6 days of observation

Step-by-step explanation:

Let x be the number of fruit flies on the first day of Lavania's study.

After 6 days she had nine more than five times as many fruit flies as when she began the study.

Five times as many fruit flies as when she began the study = 5x

Nine more than five times as many fruit flies as when she began the study=5x+9

The expression to find the population of fruit flies Lavania observed after 6 days is 5x+9

If she observes 20 fruit flies on the first day of the study, then x=6, then

$5x+9=5\cdot 6+9=30+9=39$

5 0

2 years ago

The graph of a proportional relationship passes through (12, 16)<br> and (1, y)<br> . Find y

k0ka [10]

Answer: The value of y is $\frac{4}{3}$ .

Explanation:

It is given that the graph of a proportional relationship passes through (12, 16)

and (1, y).

The graph of a proportional relationship means the x and y coordinates are in a proportion k. The equation of the graph is in the form of y=kx. Where k is the proportion factor.

It is given that the graph passing through (12,16).

$y=kx$

$16=k(12)$

$k=\frac{16}{12}$

$k =\frac{4}{3}$

So the equation of the line is,

$y=\frac{4}{3} x$

put x=1.

$y=\frac{4}{3} (1)$

$y=\frac{4}{3}$

Therefore, the value of y is $\frac{4}{3}$ .

8 0

2 years ago

Read 2 more answers

A circle fits inside a semicircle of diameter 24mm

patriot [66]

Answer:

The shaded are is $113\ mm^{2}$

Step-by-step explanation:

we know that

The shaded area is equal to the area of the semicircle minus the area of the circle inside the semicircle

step 1

Find the area of semicircle

The area of semicircle is equal to

$A=\frac{1}{2}\pi r^{2}$

where

$r=24/2=12\ mm$ ----> the radius is half the diameter

substitute

$A=\frac{1}{2}\pi(12)^{2}=72\pi\ mm^{2}$

step 2

Find the area of the circle inside the semicircle

The area of circle is equal to

$A=\pi r^{2}$

where

$r=12/2=6\ mm$ ---> the radius of circle inside is half the radius of semicircle

substitute

$A=\pi(6)^{2}=36\pi\ mm^{2}$

step 3

Find the shaded area

$72\pi\ mm^{2}-36\pi\ mm^{2}=36\pi\ mm^{2}$

assume

$\pi=3.14$

$36(3.14)=113.04\ mm^{2}$

3 significant figures is

$113\ mm^{2}$

6 0

2 years ago

A dentist wants to find out how often her patients floss their teeth. Which samples are biased? Check all that apply. all her pa

ArbitrLikvidat [17]

Answer:

all her patients patients with no cavities

patients younger than 18

every patient with braces

Step-by-step explanation:

when a sample is selected in a manner that some elements, in this case patients, of population have higher or lower probability of sampling then that sample is biased.

From given case, all the following are biased samples

all her patients patients with no cavities

patients younger than 18

every patient with braces

because they are non-random sample of a population in which all other elements were not equally likely to be chosen!

7 0

2 years ago

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The Adeeva's gross monthly income is $5600. They have 18 remaining payments of $ 360 on a new car. They are applying for a 15

olga55 [171]

Answer:

$1,467.20

Step-by-step explanation:

Adjusted monthly income is the gross income minus any payments made every month. 5600 - 360 = 5240. To get 28% of her adjusted income multiply 5240 X.28 =1467.20

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2 years ago