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To answer each question, use the function t(r) = d , where t is the time in hours, d is the distance in miles, and r is the rate in miles per hour.
a. Sydney drives 10 mi at a certain rate and then drives 20 mi at a rate 5 mi/h faster than the initial rate. Write expressions for the time along each part of the trip. Add these times to write an equation for the total time in terms of the initial rate, ttotal (r) .
b. Determine the reasonable domain and range and describe any discontinuities of ttotal (r) . Graph ttotal (r) on your graphing calculator.
c. At what rate, to the nearest mi/h, must Sydney drive if the entire 30 mi must be covered in about 45 min? Find the answer using the graph and using algebraic methods.
d. How long will Sydney take to drive the entire 30 mi if the car's initial rate varies between 10 mi/h and 20 mi/h? Use the graph and algebraic methods to find the answer.
a circle is circumscribed about an equilateral triangle whose side is 3 cm. find the area of the circle.
Keith wants to know the surface area of a basketball. Which formula will he use? The surface area of a sphere is four times π times the radius squared.
You have just renegotiated the interest rate of your home mortgage loan. (This is called rate modification.) The original loan of $400,000 carries an interest rate is 6% has an or
Testing the hypothesis equality of two variances The test for equality of two population variances is based upon the variances in two independently chosen random samples drawn
If the areas of the circular bases of a frustum of a cone are 4cm 2 and 9cm 2 respectively and the height of the frustum is 12cm. What is the volume of the frustum. (Ans:44cm 2 )
1. Consider the following differential equation with initial conditions: t 2 x'' + 5 t x' + 3 x = 0, x(1) = 3, x'(1) = -13. Assume there is a solution of the form: x (t) = t
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Arc length Formula L = ∫ ds Where ds √ (1+ (dy/dx) 2 ) dx if y = f(x), a x b ds √ (1+ (dx/dy) 2 ) dy
The area of Mr. Smith's rectangular classroom is x 2 - 25. Which of the following binomials could represent the length and the width of the room? Since area of a rectangle is
A sell a watch to B at gain of 20% and B sell to C at loss of 10%. if C pays @ 432, how much did A pays for it.
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