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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.
Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.
Sketch (draw) the parametric curve for the subsequent set of parametric equations. x = t 2 + t y = 2t -1 Solution At this point our simply option for sketching a par
Two circles touch externally. The sum of their areas is 58 π cm 2 and the distance between their centres is 10 cm. Find the radii of the two circles. (Ans:7cm, 3cm) Ans:
0.25+25
Proof of: lim q →0 (cos q -1) / q = 0 We will begin by doing the following, lim q →0 (cosq -1)/q = lim q →0 ((cosq - 1)(cosq + 1))/(q (cosq + 1)) = lim q
find the area of this figure in square millimeter measure each segment to the nearest millmeter
Before going to solving differential equations we must see one more function. Without Laplace transforms this would be much more hard to solve differential equations which involve
Q . Mrs. Cooper asked her math class to keep track of their own grade. Michael, one of the students, lost his assignments, but he remembered the grades of 6 out of 8 assignments:
If Var(x) = 4, find Var (3x+8), where X is a random variable. Var (ax+b) = a 2 Var x Var (3x+8) = 3 2 Var x = 36
a ,b,c are complex numbers such that a/1-b=b/1-c=c-1-a=k.find the value of k
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