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.

Find the wind chill for an air temperature of 10 degrees celsius and a wind speed of 8m/sec W=

A person holding a ball is on top of a building. The person jumped at the rate of 1 ft/s while dropping the ball. After 12 seconds, the ball hit the ground. Determine the following: a. The height of the building: b. The velocity of the ball when it is about to hit the ground; Ignore the dimensions of the ball and the height of the person. Use g = -32 ft/s. Give exact answer i.e., do not round off answers.

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?

e An airplane flying on a straight flight path will be exactly above a radar tracking station, which is 5,000 km below the path. When the distance of the plane from the station is 40,000 km, this distance decreases at the rate of 8,000 km/hr. At what rate is the plane flying at that instance? novi f. A truck travelling southwards at 40 kph and a car traveling eastward at a rate of 60 kph are headed for an intersection. At what rate are the vehicles approaching each other when the truck is 1 km from the intersection while the car is 2 km from the intersection? g. Water is being poured at the rate of 5 m³/sec into an inverted conical tank of radius 10 m and altitude 20 m. How fast is the water level rising when the water level is at 8 m? (Note: Here you will be using the concepts of similar triangles in order to rewrite the radius in terms of the height.) itoun bont h. A particle is moving along the curve with equation y = 3-x. At the point (2, 1), it was observed that the x-coordinate…

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