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?
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.
thank you!!
Factorize x6y12 - 1 completely.
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)
Solve
x 7
x2 x 2
� 1. [10
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.
To find the magnitude of the centripetal acceleration of the tip of the blade, we can use the formula:
a = (v^2) / r
Where:
a = centripetal acceleration
v = linear velocity
r = radius of the circle
To find the linear velocity (v), we need to first find the angular velocity (ω) using the formula:
ω = θ / t
Where:
ω = angular velocity
θ = angle (in radians)
t = time
Since the angle is given in degrees, we need to convert it to radians:
θ (in radians) = θ (in degrees) x (π / 180)
Substituting the given values:
θ (in radians) = 90° x (π / 180) = (90π / 180) = (π / 2)
Now, we can calculate the angular velocity:
ω = θ / t = (π / 2) / 0.398s
Next, substitute the given radius:
r = 0.352m
Now, we can find the linear velocity:
v = ω * r
Finally, substitute the calculated values for v and r into the centripetal acceleration formula to find the magnitude of the centripetal acceleration (a).
I'll calculate the values for each step for you.