Find the maximum and minimum values of

slanted upward by 48 degrees above the horizontal at its end, which is 0.40 m above the ground. When she leaves the track, she follows the characteristic path of projectile motion. Ignoring friction and air resistance, find the maximum height H to which she rises above the end of the track.

g and 30 cm each, respectively. Both M1 and M2 rest on frictionless surfaces and the system starts from rest. (a) Draw the fbd for each of M1, M2 and the pulley. (b) Write the equations of motion for each of M1, M2 and the pulley. (c) Calculate the linear acceleration of the two masses, as well as the angular acceleration of the pulley. (d) Calculate the angular velocity of the pulley after M1 and M2 have been displaced linearly by 2 m. Q2) (10 points) A basketball is thrown with an initial speed v0 of 10.8 m/s at 400 above horizontal, and it enters the hoop from above. The ball is released at 2.00 m above the ground. The hoop is 3.05 m above the ground and 10.0 m away from the player. (a) Find the time at which the ball passes through the hoop. (b) Find the ball’s velocity (express in component form) just when it enters the hoop. (c) Find the ball’s maximum height. Q3) (5 Points) An object is thrown up from the top of a building of height of 400 m with an initial velocity of 20 m/s. (a) Find the position and the velocity of the object 5 s later. (b) With what velocity will it hit the ground? (c) At the same time the first object is thrown up, a second object is thrown up from the ground at 100 m/s. Will the two objects collide? If yes, calculate when and where,

block moves and compress the spring. Find the maximum compression on the spring where the block momentarily comes to stop. The spring constant is 25 N/m.

pizza is already available to you, the only cost involved is that of making the pizza, which you calculate to be $ 5 per pizza. a. What is the cost function? If 10 pizzas are available in a day, the market offers a price of $ 11 per pizza. If 50 pizzas are available in a day, the market offers a price of $ 7 per pizza. b. Assuming a linear relationship between price and quantity, find the price that the market offers as a function of the number of pizzas available. You start selling the pizzas. c. What is revenue as a function of the quantity you sell? What is the profit function? d. What quantity will maximize your profit? Call it q ∗ 1. What is the maximum profit? e. If somebody is already supplying 5 pizzas every day, What is the maximum profit that you can make?

ther three sides by 600m of fencing. Find the maximum area that can be enclosed by the fence. Kindly help!

tal-revenue and​ total-cost functions, find the total​ profit, the maximum value of the total​ profit, and the value of x at which it occurs. Upper R left parenthesis x right parenthesis equals 1300 x minus x squared​, Upper C left parenthesis x right parenthesis equals 3000 plus 30 x The total​ profit, ​P(x)equals negative x squared plus 1270 x minus 3000. ​(Simplify your answer. Do not​ factor.)

imum that we can normally produce). Now suppose that the Federal Government decides to decrease taxes. If we compare the long run price and GDP levels to the price and GDP levels that existed before the Federal Government’s action, we would find that_______? A. Production or the GDP would not increase in the long run. B. Prices would decrease in the long run. C. A decrease in unemployment would result in the long run. D. Producers would increase production in the long run as a result of the Federal Government’s actions

izontal. Its upper end is connected to a wall by a rope, and its lower end rests on a rough, horizontal sur- face. The coefficient of static friction between the beam and surface is ms. Assume the angle u is such that the static friction force is at its maximum value. (a) Draw a force diagram for the beam. (b) Using the condition of rotational equilibrium, find an expression for the tension T in the rope in terms of m, g, and u. (c) Using the condition of trans- lational equilibrium, find a second expression for T in terms of ms, m, and g. (d) Using the results from parts (a) through (c), obtain an expression for ms L u Figure P12.16 Q/C S vertical component of this force. Now solve the same problem from the force diagram from part (a) by com- puting torques around the junction between the cable and the beam at the right-hand end of the beam. Find (e) the vertical component of the force exerted by the pole on the beam, (f) the tension in the cable, and (g) the horizontal component of the force exerted by the pole on the beam. (h) Compare the solution to parts (b) through (d) with the solution to parts (e) through (g). Is either solution more accurate? 19. Sir Lost-a-Lot dons his armor and sets out from the castle on his trusty steed (Fig. P12.19). Usually, the drawbridge is lowered to a horizontal position so that the end of the bridge rests on the stone ledge. Unfor- tunately, Lost-a-Lot’s squire didn’t lower the draw- involv- ing only the angle u. (e) What happens if the ladder is lifted upward and its base is placed back on the ground slightly to the left of its position in Figure P12.16? Explain.

ups need one hour in Machine 1; whereas glasses need one hour. The company has exactly ten hours available in Machine 1. Use the method of substitution to find the maximum values of X and Y and the maximum value for the objective function. Show all the steps in the method.