Mathematics, 15.08.2020 21:01, joshuaburton773

the diagram shows a sector of a circle, center O, radius 5r the length of the arc AB 4r. find the area of the sector in terms of r , giving your answer in its simplest form

the diagram shows a sector of a circle, center O,radius 5r the length of the arc AB 4r. find the ar

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answered: crystal070903

the area of the sector in terms of r is 10r^2

Given :

From the given diagram , the radius of the circle is 5r and length of arc AB is 4r

Lets find out the central angle using length of arc formula

length of arc = $\frac{central-angle}{360} \cdot 2\pi r$

r=5r and length = 4r

$4r=\frac{central-angle}{360} \cdot 2\pi (5r)\\4r \cdot 360=central-angle \cdot 2\pi (5r)\\\\\\\frac{4r \cdot 360}{10\pi r} =angle\\angle =\frac{4\cdot 36}{\pi } \\angle =\frac{144}{\pi }$

Now we replace this angle in area of sector formula

Area of sector = $\frac{angle}{360} \cdot \pi r^2\\$

$Area =\frac{angle}{360} \cdot \pi r^2\\\\Area =\frac{\frac{144}{\pi } }{360} \cdot \pi\cdot 25r^2\\\\Area =\frac{ 144 }{360\pi } \cdot \pi\cdot 25r^2\\\\Area =\frac{ 2 }{5 } \cdot 25r^2\\\\\\Area=10r^2$

So, the area of the sector in terms of r is 10r^2

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answered: nnyahtoland

10r²

Step-by-step explanation:

The following data were obtained from the question:

Radius (r) = 5r

Length of arc (L) = 4r

Area of sector (A) =?

Next, we shall determine the angle θ sustained at the centre.

Recall:

Length of arc (L) = θ/360 × 2πr

With the above formula, we shall determine the angle θ sustained at the centre as follow:

Radius (r) = 5r

Length of arc (L) = 4r

Angle at the centre θ =?

L= θ/360 × 2πr

4r = θ/360 × 2π × 5r

4r = (θ × 10πr)/360

Cross multiply

θ × 10πr = 4r × 360

Divide both side by 10πr

θ = (4r × 360) /10πr

θ = 144/π

Finally, we shall determine the area of the sector as follow:

Angle at the centre θ = 144/π

Radius (r) = 5r

Area of sector (A) =?

Area of sector (A) = θ/360 × πr²

A = (144/π)/360 × π(5r)²

A = 144/360π × π × 25r²

A = 144/360 × 25r²

A = 0.4 × 25r²

A = 10r²

Therefore, the area of the sector is 10r².

answered: Guest

i really dont know

step-by-step explanation:

answered: Guest

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

the function given is y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 = -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24