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Chapter 5: Q. 69 (page 315)

Use a graphing utility to solve each equation. Express your answer rounded to two decimal places.

lnx=x3-1

Short Answer

Expert verified

The solutions of the given equation are 0.39 and 1.

Step by step solution

01

Step 1. Given information.

The given equation is:

lnx=x3-1

02

Step 2. Determine the solution by the graphing utility.

Plot the graphs of y1=lnx andy2=x3-1 on a coordinate plane. The x-coordinate of the intersection point is the solution of the given equation.

The graphs intersect each other at x≈0.39andx=1.

03

Step 3. Conclusion.

The solutions of the given equation are 0.39 and 1.

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Most popular questions from this chapter

the function f is one-to-one. Find its inverse and check your answer.

f(x)=-3x-4x-2

True or False. The domain of the composite functionf∘gxis the same as the domain ofg(x).

Find the inverse of the functionf(x)=r2-x20≤x≤r

Begin with the graph of y=exand use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

fx=2-e-x/2

Vehicle Stopping Distance Taking into account reaction time, the distance d(in feet) that a car requires to come to a complete stop while traveling rmiles per hour is given by the function

localid="1646198784356" d(r)=6.97r-90.39

a. Express the speed rat which the car is traveling as a function of the distance localid="1646198792401" drequired to come to a complete stop

b. Verify that localid="1646198797631" r=r(d)is the inverse of localid="1646198802104" d=d(r)by showing that localid="1646198806352" r(d(r))=rand localid="1646198811055" d(r(d))=d

c. Predict the speed that a car was traveling if the distance required to stop was localid="1646198818232" 300feet.

d(r(d))=d
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