A car tire with a radius of 16inches is turning at a rate of 120 revolutions per minute. Find the exact linear speed of the tire
1 answer:
Answer:
The car's tire moves at a speed of 1002.24 feet per minute.
Step-by-step explanation:
Given:
The radius of the car tire is r = 16 inches
Since 12 inches equals 1 foot,
16 inches converts to ×16 = 1.33 feet
The wheel completes 120 revolutions every minute.
Let the speed of the tire be s feet per minute.
The wheel's circumference is calculated as 2 × × radius.
Here, equals 3.14.
Thus, circumference = 2 × 3.14 × 1.33.
Therefore, Circumference = 8.352 feet.
Now, Speed = circumference of the wheel × revolutions per minute.
Thus, Speed = 8.352 feet × 120 revolutions per minute.
∴ Speed = 1002.24 feet per minute.
Thus, the car's tire speed is 1002.24 feet per minute. Answer
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Solution:
We know, g(x) = f(x) + k --------(1)
It is given that f(x) = (x+2)
and g(x) = (x+5)
Substituting f(x) and g(x) into equation (1):
→ (x+5) =
(x+2) + k
→ = k
→ k =
Thus, the value of k is 1.
Explanation:
Step-by-step clarification:
Referring to step 6
(b² — 4ac) / 4a² = (x + b/2a)²
The mistake in the question is that it should be (x + b/2a)²
According to step 7
±√(b² —4ac) /2a = x + b/2a
The error in the question is that it should be divided by 2a, not 1a.
1. The transition from step 6 to step 7 involves taking the square roots of both sides
(b² — 4ac) / 4a² = (x + b/2a)²
Taking the square of both sides
√(b²—4ac) / √4a² = √(x + b/2a)²
√(b²—4ac) / 2a = x + b/2a
This forms step 7 correctly.
Next, subtracting b/2a from both sides
√(b²—4ac) / 2a - b/2a= x + b/2a -b/2a
√(b²—4ac) / 2a — b/2a = x
(√(b²—4ac) — b)/2a = x
x = [—b ± √(b²—4ac)] / 2a
This gives the desired formula.
The discriminant is D = b²—4ac.
