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What is the approximate area of a sector given O= 56 degrees with a diameter of 12m?

jeyben [28]

Area of sector is 17.584 meters

<em><u>Solution:</u></em>

Given that we have to find the approximate area of a sector given O= 56 degrees with a diameter of 12m

Diameter = 12 m

Radius = Diameter / 2 = 6 m

An angle of 56 degrees is the fraction $\frac{56}{360}$ of the whole rotation

A sector of a circle with a sector angle of 56 degrees is therefore also the fraction $\frac{56}{360}$ of the circle

The area of the sector will therefore also be $\frac{56}{360}$ of the area

$\text{ sector area } = \frac{56}{360} \times \pi r^2\\\\\text{ sector area } = \frac{56}{360} \times 3.14 \times 6^2\\\\\text{ sector area } = 17.584$

Thus area of sector is 17.584 meters

3 0

3 years ago

The store is selling lemons at $0.39 each. Each lemon yields about 2 tablespoons of juice. How much will it cost to buy enough l

I am Lyosha [343]

Answer: 6.24 tablespoons

Explanation: okay so if $.39 is 2 tablespoons, then you can multiply that by 8 because there are 8 tablespoons in half a cup. After you multiply that just multiply it by 2 because they are trying to make two pies. And that’s how you your answer.

5 0

3 years ago

Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Select t

nignag [31]

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

$y = mx + b$

Where:

m: It's the slope

b: It is the cut-off point with the y axis

On the other hand we have that if two lines are perpendicular, then the product of their slopes is -1. So:

$m_ {1} * m_ {2} = - 1$

The given line is:

$5x-2y = -6\\-2y = -6-5x\\2y = 5x + 6\\y = \frac {5} {2} x + \frac {6} {2}\\y = \frac {5} {2} x + 3$

So we have:

$m_ {1} = \frac {5} {2}$

We find $m_ {2}:$ $m_ {2} = \frac {-1} {\frac {5} {2}}\\m = - \frac {2} {5}$

So, a line perpendicular to the one given is of the form:

$y = - \frac {2} {5} x + b$

We substitute the given point to find "b":

$-4 = - \frac {2} {5} (5) + b\\-4 = -2 + b\\-4 + 2 = b\\b = -2$

Finally we have:

$y = - \frac {2} {5} x-2$

In point-slope form we have:

$y - (- 4) = - \frac {2} {5} (x-5)\\y + 4 = - \frac {2} {5} (x-5)$

ANswer:

$y = - \frac {2} {5} x-2\\y + 4 = - \frac {2} {5} (x-5)$

3 0

3 years ago

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Use the table below to answer this question:

andrew11 [14]

(y_final-y_start)/(x_final-x_start) always! :) that easy

(-6-2)/(2-0) = -4

You probably know that if the interval was pretty small, between 0 and 0.0001, it would take you to the concept of slope and derivatives, but average change is just ignoring anything in between x=0, and x=2 (it could go up/down million times, and still the answer would be -4)

hope it helps

3 0

3 years ago

What is the value of x?

lorasvet [3.4K]

Answer:

x=9

Step-by-step explanation:

We can use similar triangles and ratios. Put the small triangle side over the large triangle side.

9cm 3x -20

---------- = ---------------- We need to add the sides to get to the larger triangle

72+9 cm 3x-20 + 56

We can cross multiply to solve

9 * (3x-20+56) = (72+9) * (3x-20)

Simplify

9*(3x+36) = 81*(3x-20)

Distribute

27x +324 = 243x -1620

Subtract 27x from each side

27x-27x +324 = 243x-27x -1620

324 = 216x-1620

Add 1620 to each side

324+1620 = 216x

1944 = 216x

Divide each side by 216

1944/216 = 216x/216

9=x

6 0

3 years ago

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