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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.
Properties 1. The domain of the logarithm function is (0, ∞ ) . In other terms, we can just plug positive numbers into a logarithm! We can't plug in zero or a negative numbe
There is one final topic that we need to address as far as solution sets go before leaving this section. Consider the following equation and inequality.
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Example Write down the equation of a circle alongwith radius 8 & center ( -4, 7 ) . Solution Okay, in this case we have r =8 , h = -4 and k = 7 thus all we have to do i
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Kevin ran 6.8 miles yesterday and 10.4 miles presently. How many more miles did he run today? To ?nd out how many more miles he ran today, subtract yesterday's miles from today
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