Let   . Use formulas from Chapter 3 to answer the following questions.  Find . Simplify.  Find . Do not simplify. Show your work and answers on your paper.  Clearly label your answer with the problem number and the part letter and hold your page up to the camera. No answer needs to be entered in the space provided. After part 1 is complete, your answer to this problem must be scanned an uploaded to part 2. 

Find the equation of the line tangent to the graph of the  equation below at     at    

A street light is mounted at the top of a 20 ft tall pole. A woman 6 feet tall walks away from the pole with a speed of 5 ft/sec along a straight path. How fast is the tip of his shadow moving when he is 35 feet from the pole? If necessary, round your answer to two decimal places. Include units Show your work and answers on your paper.  Clearly label your answer with the problem number hold your page up to the camera. No answer needs to be entered in the space provided. After part 1 is complete, your answer to this problem must be scanned an uploaded to part 2. 

Find equation of tangent line to the curve     at  . Simplify your answer and write it in slope-intercept form. Show your work and answers on your paper.  Hold your page up to the camera. No answer needs to be entered in the space provided. After part 1 is complete, your answer to this problem must be scanned an uploaded to part 2. 

A plane flying horizontally at an altitude of 1 mile and a speed of 400 mi/hr passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 5 miles away from the station. If necessary, round your answer to two decimal places. Include units Show your work and answers on your paper.  Clearly label your answer with the problem number hold your page up to the camera. No answer needs to be entered in the space provided. After part 1 is complete, your answer to this problem must be scanned an uploaded to part 2. 

A spotlight on the ground shines on a vertical wall 10 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.5 m/s, how fast is the length of his shadow on the building decreasing when he is 6 m from the building. If necessary, round your answer to two decimal places. Include units Show your work and answers on your paper.  Clearly label your answer with the problem number hold your page up to the camera. No answer needs to be entered in the space provided. After part 1 is complete, your answer to this problem must be scanned an uploaded to part 2. 

Over the weekend before the ban on social gatherings, all of the Calculus instructors headed to the Leach Recreation Center to play basketball. Upon arrival, they noticed the only ball left was completely flat. To solve this problem, air was pumped into the spherical basketball so that its volume increased at a rate of . How fast was the radius of the ball increasing when the diameter of the basketball was ? If necessary, round your answer to two decimal places. Include units Show your work and answers on your paper.  Clearly label your answer with the problem number hold your page up to the camera. No answer needs to be entered in the space provided. After part 1 is complete, your answer to this problem must be scanned an uploaded to part 2.   

An economic model should capture

Economics is best defined as the

In which of the following situations will both market clearing price and the equilibrium quantity decrease?