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The front wheels on DeMarius’ car are divided into sectors of equal area. The radius of each wheel is 8 inches. The area painted blue is twice the area painted green. The area painted green is half the area painted red. What is the area painted red on one of the front wheels? Round your answer to the nearest hundredth.

The rear wheels of DeMarius’ car complete of a rotation for every full rotation of a front wheel. What is the radius, in feet, of a rear wheel on the car? Write your answer as a simplified fraction. 

DeMarius’ original design for his car used rear wheels with a radius of 12 inches. What is the measure of the central angle of this rear wheel such that the arc length is equivalent to that of a full rotation of the rear wheel that is actually used on DeMarius’ car?

 Mar 31, 2020
 #1
avatar+112417 
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The front wheels on DeMarius’ car are divided into sectors of equal area. The radius of each wheel is 8 inches. The area painted blue is twice the area painted green. The area painted green is half the area painted red. What is the area painted red on one of the front wheels? Round your answer to the nearest hundredth.

 

There are  5  areas on each wheel... 1 green, 2 blue and 2 red...the red area is 2/5  of  this....so  .....the   red area(s)  =

 

(2/5) pi * 8^2  =      (64 * 2) / 5 * pi   ≈    80.42 in^2

 

 

cool cool cool

 Mar 31, 2020
edited by CPhill  Mar 31, 2020
 #3
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Thank you! for question number 2 it is supposed to say  "The rear wheels of DeMarius’ car complete 4/5  of a rotation for every full rotation of a front wheel. What is the radius, in feet, of a rear wheel on the car? Write your answer as a simplified fraction."

Guest Mar 31, 2020
 #2
avatar+112417 
+1

DeMarius’ original design for his car used rear wheels with a radius of 12 inches. What is the measure of the central angle of this rear wheel such that the arc length is equivalent to that of a full rotation of the rear wheel that is actually used on DeMarius’ car?

 

 

Circumference  with  8 in radius  =   2 * pi * 8   =   16 pi

 

16pi =  12 * theta       divide  both sides  by 12

 

(16/12) pi  =   (4/3) pi  = theta  =    240°

 

 

cool cool cool

 Mar 31, 2020
 #4
avatar+112417 
+1

Thank you! for question number 2 it is supposed to say  "The rear wheels of DeMarius’ car complete 4/5  of a rotation for every full rotation of a front wheel. What is the radius, in feet, of a rear wheel on the car? Write your answer as a simplified fraction."

 

We  have  that

 

r1*  θ1  =  r2 *  θ2

 

8 (in) (2pi)  = r2  ( 4/5) (2pi)

 

16 pi  in  =  r2 (8/5) pi  in

 

16  =  r2 ( 8/5)        multiply  both sides  by   (5/8)

 

16 (5/8)  =  r2

 

80 / 8  = r2

 

10 in  =  r2   =  10/12  ft  =  (5/6) ft

 

 

cool cool cool

 Mar 31, 2020

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