For Exercises 1-2, for parts (a) and (b), graph the equation. For part (c), solve the system of equations. For parts (d) and (e) graph the solution set to the system of inequalities. If there is no solution, indicate that the solution set is the empty set. a. y = − 3 x + 5 b. − 2 x + y = 0 c. y = − 3 x + 5 − 2 x + y = 0 d. y > − 3 x + 5 − 2 x + y < 0 e. y < − 3 x + 5 − 2 x + y > 0
For Exercises 1-2, for parts (a) and (b), graph the equation. For part (c), solve the system of equations. For parts (d) and (e) graph the solution set to the system of inequalities. If there is no solution, indicate that the solution set is the empty set. a. y = − 3 x + 5 b. − 2 x + y = 0 c. y = − 3 x + 5 − 2 x + y = 0 d. y > − 3 x + 5 − 2 x + y < 0 e. y < − 3 x + 5 − 2 x + y > 0
Solution Summary: The graph for the line y=-3x+5 is: ly = 3(0)+0 0+y
For Exercises 1-2, for parts (a) and (b), graph the equation. For part (c), solve the system of equations. For parts (d) and (e) graph the solution set to the system of inequalities. If there is no solution, indicate that the solution set is the empty set.
Suppose an oil spill covers a circular area and the radius, r, increases according to the graph shown below where t
represents the number of minutes since the spill was first observed.
Radius (feet)
80
70
60
50
40
30
20
10
0
r
0 10 20 30 40 50 60 70 80 90
Time (minutes)
(a) How large is the circular area of the spill 30 minutes after it was first observed? Give your answer in terms of π.
square feet
(b) If the cost to clean the oil spill is proportional to the square of the diameter of the spill, express the cost, C, as a
function of the radius of the spill, r. Use a lower case k as the proportionality constant.
C(r) =
(c) Which of the following expressions could be used to represent the amount of time it took for the radius of the spill to
increase from 20 feet to 60 feet?
r(60) - r(20)
Or¹(80-30)
r(80) - r(30)
r-1(80) - r−1(30)
r-1(60) - r¹(20)
6. Graph the function f(x)=log3x. Label three points on the graph (one should be the intercept) with
corresponding ordered pairs and label the asymptote with its equation. Write the domain and range of the function
in interval notation. Make your graph big enough to see all important features.
Find the average value gave of the function g on the given interval.
gave =
g(x) = 8√√x, [8,64]
Need Help?
Read It
Watch It
Elementary Statistics: Picturing the World (7th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Introduction: MARKOV PROCESS And MARKOV CHAINS // Short Lecture // Linear Algebra; Author: AfterMath;https://www.youtube.com/watch?v=qK-PUTuUSpw;License: Standard Youtube License
Stochastic process and Markov Chain Model | Transition Probability Matrix (TPM); Author: Dr. Harish Garg;https://www.youtube.com/watch?v=sb4jo4P4ZLI;License: Standard YouTube License, CC-BY