Concept explainers
True or False? In Exercises 85 and 86, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.
If C is given by
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Calculus (MindTap Course List)
- Projectile Motion In Exercises 75 and 76, consider the path of an object projected horizontally with a velocity of v feet per second at a height of s feet, where the model for the path is x2=v216ys. In this model (in which air resistance is disregarded), y is the height (in feet) of the projectile and x is the horizontal distance (in feet) the projectile travels. A ball is thrown from the top of a 100-foot tower with a velocity of 28 feet per second. (a) Write an equation for the parabolic path. (b) How far does the ball travel horizontally before it strikes the ground?arrow_forwardHooke’s Law In Exercises 65-68, use Hooke’s Law, which states that the distance a spring stretches (or compresses) from its natural, or equilibrium, length varies directly as the applied force on the spring. The coiled spring of a toy supports the weight of a child. The weight of a 25-pound child compresses the spring a distance of 1.9 inches. The toy does not work properly when a weight compresses the spring more than 3 inches. What is the maximum weight for which the toy works properly?arrow_forwardCalculus 11th Edition - Ron Larson Chapter 3.9 - Differentials Find the tangent line approximationT to the graph of f at the given point. Thencomplete the table.arrow_forward
- The average amount of time that a customer waits in line for service is given by W(x, y) = 1/(x-y), y < x where y is the average arrival rate and x is the average service rate (x and y are measured in the number of customers per hour). Evaluate W at each point (a) (11, 6)(b) (10, 4) (c) (10, 8)(d) (5, 2)arrow_forwardJoint PDF: If f_X,Y (x,y) = 6e^-(2x + 3y) for x, y >=0 then what is P[Y>X] ?arrow_forwardDetermine whether the statement is true or false. Give a proof or counter example. Suppose f(x) is differentiable and has a stationary point at c. If c is a local minimum point then f''(c) > 0arrow_forward
- (c) Let F(x, y, z) = x^3i + y^3j + z^3 k i) ∇ · F(ii) ∇ × Farrow_forwardFinding a Mathematical Model In Exercises 53-60, find a mathematical model that represents the statement. (Determine the constant of proportionality.) z varies jointly as x and y.z=64whenx=4andy=8.arrow_forwardMilk Production Milk production M (in billions of pounds) in the United States from 2000 through 2014 can be modeled by M=3.00t+163.3,0t14 where t represents the year, with t = 0 corresponding to 2000. (a) According to the model, when was the annual milk production greater than 180 billion pounds, but no more than 190 billion pounds? (b) Use the model to predict when milk production will exceed 230 billion pounds.arrow_forward
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