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Licemer1 [7]
3 years ago
11

An arc of length 8 in. is intersected by a central angle in a circle with a radius of 3 in. What is the measure of the angle? Ro

und your answer to the nearest tenth.
Mathematics
2 answers:
mina [271]3 years ago
5 0
Given:
Arc length = 8 inches
radius = 3 inches
find the measure of the central angle.

Arc length = radius * central angle
central angle = arc length / radius
central angle = 8 inches / 3 inches
central angle = 2.667 (radian)

Central angle in degrees  = 152.88°

Circumference of the circle = 2 * 3.14 * 3 inches = 18.84 inches
1 circle = 360° / 18.84 inches = 19.11° per inch
19.11° per inches * 8 inches of arc length = 152.88°

butalik [34]3 years ago
3 0

The answer is 2.7 radians. C on edgunity

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Find the distance between A (2,6) and N (5, 10). Round<br> To the nearest tenth
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Answer:

5.0 units

Step-by-step explanation:

The distance between two points can be expressed in formula of:

\displaystyle{d = \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}}

Determine:

  • \displaystyle{(x_2,y_2)} is (5,10).
  • \displaystyle{(x_1,y_1)} is (2,6).

Therefore, substitute in the formula to find distance:

\displaystyle{d = \sqrt{\left(5-2\right)^2+\left(10-6\right)^2}}\\\\\displaystyle{d = \sqrt{3^2+4^2}}\\\\\displaystyle{d = \sqrt{9+16}}\\\\\displaystyle{d = \sqrt{25}}\\\\\displaystyle{d = 5}

Therefore, the distance between two points is 5.0 units.

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A store owner bought some flower pots for $1,200. The flower pots were sold for $2,700, with a profit of $30 per pot. How many f
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The temperature at noon was -30C.By 10.P.M. on the same day the temperature decreased by 5.50. What is the temperature at 10 P.M
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Step-by-step explanation:

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Identify the constant of<br> proportionality (k)<br> 8Y = 16x<br> k=
RUDIKE [14]

Answer:

JUST WRITE THIS AS YOUR ANSWER

Step-by-step explanation:

Step 1: Put together the general equation.

Step 2: Solve for the constant of proportionality.

Step 3: Plugging the constant into the equation, solve for the unknown variable.

Let's solve a few problems to see how this works, shall we?

Example 1: Y is directly proportional to x. When x = 5, y = 8. What does y equal when x = 9?

First, we set up our general equation. Because y is directly proportional to x, we have:

y = cx

where c is the constant of proportionality. In other words, when x goes up, y goes up, and when x goes down, y goes down.

The next thing we do is plug our values for x and y into the equation so we can solve for c:

8 = (c)(5)

Solving for c, we get c = 8/5 = 1.6 and we plug this into our equation:

y = 1.6x

Now, we can plug x = 9 into the equation to find out what y equals:

y = (1.6)(9)

y = 14.4

So, our answer is 14.4

Example 2: Y is directly proportional to the square of x. When x = 2, y = 32. What does y equal when x = 5?

This time, our general equation is slightly more complicated because x is squared:

y = cx2

Like before, we solve for our constant:

32 = (c)(22)

32 = (c)(4)

We get c = 8:

y = 8x2

Solving for y when x = 5, we get y = (8)(52) = (8)(25) = 200

Example 3: Y is inversely proportional to x. When x = 2, y = 8. What does y equal when x = 24?

This time, because y is inversely proportional to x, our general equation is different:

xy = c

so when x goes up, y goes down, and vise versa. But, other than that, we solve these kinds of problems the same way as direct proportion problems. Solving for the constant, we get:

(2)(8) = c

So c = 16 and our equation is now:

xy = 16

Solving for y when x = 24 we get y = 16/24 = 2/3

Example 4: Y is inversely proportional to the square root of x. When x = 36, y = 2. What does y equal when x = 64?

As before, we set up our equation:

eq001

Since the square root of 36 is 6, it is easy to solve for c:

(6)(2) = c

We get c = 12 and our equation is now:

eq002

Solving for y when x = 64 we get 8y = 12 or y = 12/8 = 1.5 because the square root of 64 is 8.

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2 years ago
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