Concept explainers
Free-Falling Object In Exercises 37 and 38, use the position function
Find the velocity of the object when
When will the object hit the ground? At what velocity will the object impact the ground?
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Calculus: Early Transcendental Functions
- An airplane is flying at a speed of 350 mi/h at an altitudeof one mile and passes directly over a radar station attime t= 0 .(a) Express the horizontal distance d (in miles) that theplane has flown as a function of t.(b) Express the distance between the plane and the radarstation as a function of d.(c) Use composition to express s as a function of t .arrow_forwardA cable hangs between two poles of equal height and 30 feet apart. Set up a coordinate system where the poles are placed at x=−15 and x=15, where x is measured in feet. The height (in feet) of the cable at position x is h(x) = 17cosh(x/17) where cosh(x) = (e^x+e^-x)/2 is the hyperbolic cosine, which is an important function in physics and engineering. The cable is ______ feet long?arrow_forwardAn airplane is flying at a speed of 450 mi/h at an altitude of one mile. The plane passes directly above a radar station at time t = 0. (a) Express the distance s (in miles) between the plane and the radar station as a function of the horizontal distance d (in miles) that the plane has flown.s(d) = (b) Express d (in miles) as a function of the time t (in hours) that the plane has flown.d(t) = (c) Use composition to express s as a function of t.s(t) =arrow_forward
- Finding the Slope of a Tangent Line InExercises 9–14, find the slope of the tangent line tothe graph of the function at the given point f (t) = 3t − t2, (0, 0)arrow_forwardCalculus - limit of the functions: Continuity How do I solve this in the image below?arrow_forwardSolve the problem.A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 13 inches by 20 inches by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a function of x.arrow_forward
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