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Check Point 5 An archer’s arrow follows a parabolic path. The height of the arrow, f(x), in feet, can be modeled by
where x is the arrow’s horizontal distance, in feet.
a. What is the maximum height of the arrow and how far from its release does this occur?
b. Find the horizontal distance the arrow travels before it hits the ground. Round to the nearest foot.
c. Graph the function that models the arrow’s parabolic path.
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Chapter 2 Solutions
EP PRECALCULUS-MYLABMATH+ETEXT ACCESS
- 3. Find the slope and the equation of the tangent line to the graph of the given function at the given value of x. -4 f(x)=x-x³;x=2arrow_forward2. Find the equation of the tangent line to the graph of the given function at the given point. f(x)=(x+3)(2x²-6) at (1,-16)arrow_forward6. Researchers who have been studying the alarming rate at which the level of the Dead Sea has been dropping have shown that the density d (x) (in g per cm³) of the Dead Sea brine during evaporation can be estimated by the function d(x)=1.66 0.90x+0.47x², where x is the fraction of the remaining brine, 0≤x≤1. a) Estimate the density of the brine when 60% of the brine remains. b) Find and interpret the instantaneous rate of change of the density when 60% of the brine remains.arrow_forward
- 5. If g'(5) 10 and h'(5)=-4, find f'(5) for f(x)=4g(x)-2h(x)+3.arrow_forward2. Find each derivative. Write answers with positive exponents. a) Dx 9x -3 [97] b) f'(3) if f(x) = x²-5x² 8arrow_forwardA ladder 27 feet long leans against a wall and the foot of the ladder is sliding away at a constant rate of 3 feet/sec. Meanwhile, a firefighter is climbing up the ladder at a rate of 2 feet/sec. When the firefighter has climbed up 6 feet of the ladder, the ladder makes an angle of л/3 with the ground. Answer the two related rates questions below. (Hint: Use two carefully labeled similar right triangles.) (a) If h is the height of the firefighter above the ground, at the instant the angle of the ladder with the ground is л/3, find dh/dt= feet/sec. (b) If w is the horizontal distance from the firefighter to the wall, at the instant the angle of the ladder with the ground is л/3, find dw/dt= feet/sec.arrow_forward
- Two cars start moving from the same point. One travels south at 60 mi/h and the other travels west at 25 mi/h. At what rate (in mi/h) is the distance between the cars increasing four hours later? Step 1 Using the diagram of a right triangle given below, the relation between x, y, and z is z² = x²+ +12 x Step 2 We must find dz/dt. Differentiating both sides and simplifying gives us the following. 2z dz dt dx 2x. +2y dt dx dy dz x +y dt dt dt 2z dy dt × dx (x+y dt dy dtarrow_forwardAn elastic rope is attached to the ground at the positions shown in the picture. The rope is being pulled up along the dotted line. Assume the units are meters. 9 ground level Assume that x is increasing at a rate of 3 meters/sec. (a) Write as a function of x: 0= (b) When x=10, the angle is changing at a rate of rad/sec. (c) Let L be the the left hand piece of rope and R the right hand piece of rope. When x=10, is the rate of change of L larger than the rate of change of R? ○ Yes ○ Noarrow_forward4.1 Basic Rules of Differentiation. 1. Find the derivative of each function. Write answers with positive exponents. Label your derivatives with appropriate derivative notation. a) y=8x-5x3 4 X b) y=-50 √x+11x -5 c) p(x)=-10x²+6x3³arrow_forward
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- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
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