Consider the graph of a velocity function v(t) given below. Assuming this velocity function represents the velocity of a car and is measure in ft/sec, stein ate the total distance traveled by the car during the first 8 seconds of its moving first using four rectangles and then using 8 rectangles.

A trough is 8 ft long and its ends have the shape of isosceles triangles that are 3 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 8 ft /min, how fast is the water level rising when the water is 9 inches deep? StekM Let h be the water's height and b be the distance across the top of the water. Using the diagram below, find the relation between b and h. 3. 3/1

A formula for the drag force is F = dv² (found to be valid for a large regime of data), where F is the drag force, d is a constant (involving the area of the object, density of the fluid, etc.), and v is the relative speed between the object and the fluid. la) Rewrite the drag force equation in the form: lb) In a plot of log F (y- log F = (...) log v + log (.…..) variable) vs log v (x- variable), what do you expect to be the slope value? lb) In a plot of log F (y- variable) vs log v (x- variable), what do you expect to be the y-intercept?

The graduated cylinder above contains p milliliters of water. More water begins flowing into the cylinder at a constant rate. Which of the following graphs best models the height h of the water in the cylinder as a function of time t after the additional water began flowing into the cylinder? A) B) C) D) t -t

The position of a runner is given by s left parenthesis t right parenthesis equals 7 t squared metres from the starting point, t minutes after they begin to run. What is the runner's velocity at t = 5 minutes?

A Ferris wheel was built for an exposition. It held 2100 people, had a diameter of 251 ft, and took 25 minutes to make one revolution. Find the linear velocity in ft/sec for a person riding this wheel. The linear velocity is ft/sec. (Type an integer or decimal rounded to the nearest tenth as needed.) ←

You will be graded on your written work as well as your answer. You and Austin start at the same place when a dinosaur attacks! At t = 0 hours, you run North at 3 miles/hour while Austin runs West at 9 miles/hour. At the bottom you will answer, "how fast is the distance between us changing at t = 0.5 hours?" In your written work: a) Draw a picture and clearly label the variables. b) What relationship should you use to help you? (some equation from geometry, using your picture and your variables.) Write the relationship using the variables from your picture. c) Use implicit differentiation to take the derivative of your relationship. You do not need to solve or simplify. d) How fast is the distance between us changing at t 0.5 hours? miles/hour

If the minute hand of a clock has length r (in centimeters), find the rate at which it sweeps out area as a function of r.

The area of a circle increases at a rate of 2 cm² /s. How fast is the radius changing when the radius is 5cm? a) Draw the picture. b) Write the given and unknown derivatives in d/dt notation. c) Label the variables. d) Proceed to solve and finish the problem. Reminder, keep solutions and answer in exact form and don't forget the units on the final answer.

A trough is 16 ft long and its ends have the shape of isosceles triangles that are 3 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 14 ft3/min, how fast is the water level rising when the water is 6 inches deep? Step 1 Let h be the water's height and b be the distance across the top of the water. Using the diagram below, find the relation between b and h. 3 h Step 2 The volume of the water is as follows. V = 16 8 (3h)(h) 24h 24h?