Suppose int_5^6 f(x)dx=6 and int_5^6 g(x)dx=2.Evaluate int_5^6 (4f(x)-2g(x))dx.

The tires of a car make 65 revolutions as the car reduces its speed uniformly from 100 km/h to 50 km/h. The tires have diameter of 0.80 m. a) What was the angular acceleration? b)If the car continues to decelerate at this rate, how much more timeis required for it to stop?
For part a, I thought my method was pretty legitimate, but myanswer didn't match the one in the back of the book. The backof the book had the answer -4.4 ${\displaystyle ra\frac{d}{s^2}}$, whereas Igot $-1.59\cdot {10}^4$ ${\displaystyle ra\frac{d}{s^2}}$

A tow truck pulls a car that is stuck in the mud, with a force of 2500 N as in Fig P5.27 The tow cable is under tension and therefor pulls downward and to the left on the pin at its upper end. The light pin is held in equilibrium by forces exerted by the two bars A and B. Each bar is a strut that is, each is a bar whose weight is small compared to the forces it exerts, and which exerts forces only through hinge pins at its ends. Each strut exerts a force directed parallel to its length. Determine the force of tension or compression in each strut. Proceed as follows Make a guess as to which way (pushing or pulling ) each force acts on the top pin Draw a free-body diagram of the pin. Use the condition for equilibrium of the pin to translate the free-body diagram into equations. From the equations calculate the forces exerted by struts A and B. If you obtain a positive answer, you correctly guessed the direction of the force. A negative answer means the direction should be reversed, but the absolute value correction should be reversed, but the absolute value correctly gives the magnitude of the force. If a strut pulls of a pin, it is in tension. If it pushes, the strut is in compression. Identify whether each strut is in tension or in compression.

Two blocks with masses 4.00 kg and 8.00 kg are connected by string and slide down a 30.0 degree inclined plane. The coefficient of kinetic friction between the 4.00-kg block and the plane is 0.25; that between the 8.00-kg block and the plane is 0.35.
a) Calculate the acceleration of each block
b) Calculate the tension in the string
c) What happens if the positions of the block are reversed, so that the 4.00-kg block is above the 8.00-kg block?

A block is on a frictionless table, on earth. The block accelerates at ${\displaystyle 5.3\frac{m}{s^2}}$ when a 10 N horizontal force is applied to it. The block and table are set up on the moon. The acceleration due to gravity at the surface of the moon is ${\displaystyle 1.62\frac{m}{s^2}}$. A horizontal force of 5N is applied to the block when it is on the moon. The acceleration imparted to the block is closest to:
a) ${\displaystyle 2.9\frac{m}{s^2}}$
b) ${\displaystyle 3.2\frac{m}{s^2}}$
c) ${\displaystyle 3.4\frac{m}{s^2}}$
d) ${\displaystyle 2.7\frac{m}{s^2}}$
e) ${\displaystyle 2.4\frac{m}{s^2}}$

Predict the sign of the entropy change of the system for each of the following reactions:
${\displaystyle N_2\left(g\right)+3H_2\left(g\right)\Rightarrow 2N{H}_3\left(g\right)}$

Determine how much farther a person can jump on the Moon ascompared to the Earth if the takeoff speed and angle are the same.The acceleration due to gravity on the Moon is one-sixth what it ison Earth.

On a clear day the electric field in the atmosphere near theearths