Question

The blade of a windshield wiper moves through an angle of 90.0° in 0.398 s. The tip of the blade moves on the arc of a circle that has a radius of 0.352 m. What is the magnitude of the centripetal acceleration of the tip of the blade?

Answer 1

So it takes the blade .398s to move 90 degrees

a full circle is 360 degrees

360/90 = 4

So time it takes to move around whole circle:

T = .398*4 = 1.59s

Velocity = Distance / time

Distance in this case is the circumference of circle:
C=2*pi*r
where r is radius

so C = 2*pi*(.352)

C = 2.21 = distance in this case

So to calculate velocity:

v = 2.21/1.59

v= 1.38 m/s

Centripetal Acceleration formula:

a=v^2/r

So plug in those values and you should have your answer.

Answer 2

thank you!!

Answer 3

Factorize x6y12 - 1 completely.

Answer 4

Solve
x 􀀀 7
x2 􀀀 x 􀀀 2
 􀀀1. [10

Answer 5

We can write x6y12 - 1 as (x3y6)2 - 12.

Now we can use the difference of squares formula, which states that a2 - b2 = (a + b)(a - b).

Let a = x3y6 and b = 1, so we have:

x6y12 - 1 = (x3y6 + 1)(x3y6 - 1)

Now we can use the difference of squares formula again for the second term:

x6y12 - 1 = (x3y6 + 1)(x3y3 + 1)(x3y3 - 1)

And finally, we can use the difference of cubes formula for the last two terms:

x6y12 - 1 = (x3y6 + 1)(x3y3 + 1)(x3 + 1)(x3y3 - x3 + 1)

Therefore, the completely factored form of x6y12 - 1 is:

(x3y6 + 1)(x3y3 + 1)(x3 + 1)(x3y3 - x3 + 1)

Answer 6

To solve the expression:

(x - 7)/(x^2 - x - 2) - 1 = 0

First, we can simplify the denominator:

x^2 - x - 2 = (x - 2)(x + 1)

So the expression becomes:

(x - 7)/[(x - 2)(x + 1)] - 1 = 0

We can combine the two terms on the left side by getting a common denominator:

(x - 7) - (x - 2)(x + 1) = 0

Expanding the second term:

(x - 7) - (x^2 - x - 2) = 0

x - 7 - x^2 + x + 2 = 0

Simplifying:

-x^2 + 3 = 0

x^2 = 3

Taking the square root of both sides:

x = ±√3

Therefore, the solutions are x = √3 or x = -√3. However, we need to check if these values satisfy the original equation.

If we plug in x = √3:

(x - 7)/(x^2 - x - 2) - 1 = (-4 - √3)/(4 - 2√3) - 1 ≈ -0.598

This is not equal to 0, so √3 is not a solution.

If we plug in x = -√3:

(x - 7)/(x^2 - x - 2) - 1 = (-4 + √3)/(4 + 2√3) - 1 ≈ 0.158

This is also not equal to 0, so -√3 is not a solution either.

Therefore, there are no solutions to the equation.