A carousel with a 40-foot diameter makes 3 revolutions per minute. (a) Find the angular speed of the carousel in radians per min
1 answer:
Answer:
A). 18.84 radians per minute
B). 376.80 feet per minute
Step-by-step explanation:
As we know carousal is moving with 3 revolutions per minute.
(a). Angular speed = 3 revolutions per minute
= 3 × (2π) per minute
= 6π per minute
= 6×(3.14)
= 18.84 radians per minute
B). Since linear speed = Radius × Angular speed
=
= 20 × 18.84
= 376.80 feet per minute
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Answer:
Length, l = 11 ft.
Width, w = 9 ft.
Step-by-step explanation:
From the given data, the area of the rectangle = 99 ft².
Area of the rectangle = Length, l X Width, w
Here, Length, l = 7 more than twice the width
⇒ Length, l = 7 + 2w
Therefore, Area, A = 99 = (7 + 2w)w
⇒ 99 = 7w + 2w²
⇒ 2w² + 7w - 99 = 0
Solve the Quadratic equation using the formula: x = for the quadratic equation ax² + bx + c = 0.
Therefore, w =
Since, we get:
This gives two values of 'w', viz., w = ,
⇒ w = , -9.
We take the integer values.
If w = -9, then l = 2(-9) + 7
⇒ l = - 18 + 7 = - 11
Therefore, the length, l of the rectangle = - 11 ft.
and the width, w of the rectangle = - 9 ft.
Hence, the answer.