Calculus 8th Edition solutions

Calculus 8
Mechanical Design A chute at the top of a grain elevator of a combine funnels the grain into a bin (see figure). Find the angle between two adjacent sides.

Calculus 8
Numerical Integration Estimate the surface area of the golf green using (a) the Trapezoidal Rule and (b) Simpsons Rule. x21

Calculus 8
Weight Gain A calf that weighs 60 pounds at birth gains weight at the rate where is weight in pounds and is time in years. Solve the differential equation. (a) Use a computer algebra system to solve the differential equation for and 1. Graph the three solutions. (b) If the animal is sold when its wei

Calculus 8
The outer edge of a playground slide is in the shape of a helix of radius 1.5 meters. The slide has a height of 2 meters and makes one complete revolution from top to bottom. Find a vectorvalued function for the helix. Use a computer algebra system to graph your function. (There are many correct answ

Calculus 8
In Exercises 5 26, evaluate the definite integral of the algebraic function. Use a graphing utility to verify your result. x2y

Calculus 8
Environment A conservation department releases 1200 brook trout into a lake. It is estimated that the carrying capacity of the lake for the species is 20,400. After the first year, there are 2000 brook trout in the lake. (a) Write a logistic equation that models the number of brook trout in the lake.

Calculus 8
In Exercises 1 and 2, decide whether each labeled point is an absolute maximum or minimum, a relative maximum or minimum, or neither 2x

Calculus 8
Depth The cross section of a five-meter trough is an isosceles trapezoid with a two-meter lower base, a three-meter upper base, and an altitude of 2 meters. Water is running into the trough at a rate of 1 cubic meter per minute. How fast is the water level rising when the water is 1 meter deep? x34

Calculus 8
In Exercises 16, complete the table. 2y3

Calculus 8
Explorer 18 On November 27, 1963, the United States launched Explorer 18. Its low and high points above the surface of Earth were approximately 119 miles and 123,000 miles (see figure). The center of Earth is the focus of the orbit. Find the polar equation for the orbit and find the distance between

Calculus 8
A state legislature is debating two proposals for eliminating the annual budget deficits by the year 2010. The rate of decrease of the deficits for each proposal is shown in the figure. From the viewpoint of minimizing the cumulative state deficit, which is the better proposal? Explain. x24

Calculus 8
In Exercises 5356, (a) use a graphing utility to graph the region bounded by the graphs of the equations, (b) explain why the area of the region is difficult to find by hand, and (c) use the integration capabilities of the graphing utility to approximate the area to four decimal places. x22y

Calculus 8
Projectile Motion In Exercises 2540, use the model for projectile motion, assuming there is no air resistance. A bale ejector consists of two variable-speed belts at the end of a baler. Its purpose is to toss bales into a trailing wagon. In loading the back of a wagon, a bale must be thrown to a po

Calculus 8
In Exercises 1 and 2, determine whether the problem can be solved using precalculus or if calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, explain your reasoning. Use a graphical or numerical approach to estimate the solution. F

Calculus 8
Speed The smaller the curvature in a bend of a road, the faster a car can travel. Assume that the maximum speed around a turn is inversely proportional to the square root of the curvature. A car moving on the path ( and are measured in miles) can safely go 30 miles per hour at How fast can it go at

Calculus 8
Minimum Cost An industrial tank of the shape described in Exercise 39 must have a volume of 3000 cubic feet. The hemispherical ends cost twice as much per square foot of surface area as the sides. Find the dimensions that will minimize cost. xy4y

Calculus 8
In Exercises 27 40, find all relative extrema. Use the Second Derivative Test where applicable. 4x

Calculus 8
In Exercises 18, match the equation with its graph. [The graphs are labeled (a), (b), (c), (d), (e), (f), (g), and (h).]

Calculus 8
In Exercises 16, sketch the plane curve represented by the vector-valued function, and sketch the vectors and for the given value of Position the vectors such that the initial point of is at the origin and the initial point of is at the terminal point of What is the relationship between and the curve

Calculus 8
A rancher plans to fence a rectangular pasture adjacent to a river. The rancher has 100 meters of fence, and no fencing is needed along the river (see figure). (a) Write the area of the pasture as a function of the length of the side parallel to the river. What is the domain of (b) Graph the area fun