Discrete Mathematics With Applications
5th Edition
ISBN: 9781337694193
Author: EPP, Susanna S.
Publisher: Cengage Learning,
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Chapter 1.3, Problem 1TY
Given sets
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A communications tower is located at the top
of a steep hill, as shown. The angle of
inclination of the hill is 77°. A guy wire is to be
attached to the top of the tower and to the
ground, 102 ft downhill from the base of the
tower. The angle formed by the guy wire is 9°.
Find the length of the cable required for the
guy wire.
9°
102 ft
77°
NOTE: The picture is NOT drawn to scale.
length of guy-wire =
ft
Enter your answer as a number; your answer
should be accurate to 2 decimal places.
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Under certain conditions, the number of diseased cells N(t) at time t increases at a rate N'(t) = Aekt, where A is the rate of increase at time 0 (in cells per day) and k is a constant.
(a) Suppose A = 60, and at 3 days, the cells are growing at a rate of 180 per day. Find a formula for the number of cells after t days, given that 200 cells are present at t = 0.
(b) Use your answer from part (a) to find the number of cells present after 8 days.
(a) Find a formula for the number of cells, N(t), after t days.
N(t) =
(Round any numbers in exponents to five decimal places. Round all other numbers to the nearest tenth.)
Chapter 1 Solutions
Discrete Mathematics With Applications
Ch. 1.1 - A universal statement asserts that a certain...Ch. 1.1 - A conditional statement asserts that if one...Ch. 1.1 - Given a property that may or may not be true, an...Ch. 1.1 - In each of 1—6, fill in the blanks using a...Ch. 1.1 - In each of 1—6, fill in the blanks using a...Ch. 1.1 - In each of 1—6, fill in the blanks using a...Ch. 1.1 - Given any real number, there is a number that is...Ch. 1.1 - The reciprocal of any postive real number is...Ch. 1.1 - Prob. 6ESCh. 1.1 - Rewrite the following statements less formally,...
Ch. 1.1 - For every object J, if J is a square then J has...Ch. 1.1 - For every equation E, if E is quadratic then E has...Ch. 1.1 - Every nonzero real number has a reciropal. All...Ch. 1.1 - Evaery positive number has a positive square root....Ch. 1.1 - There is a real number whose product with every...Ch. 1.1 - There is a real number whose product with ever...Ch. 1.2 - When the elements of a set are given using the...Ch. 1.2 - The symbol R denotes ____.Ch. 1.2 - The symbol Z denotes ______Ch. 1.2 - The symbol Q denotes__Ch. 1.2 - The notation {xP(x)} is read _______Ch. 1.2 - Prob. 6TYCh. 1.2 - Prob. 7TYCh. 1.2 - Given sets A,B, and C, the Cartesian production...Ch. 1.2 - A string of length n over a set S is an ordered...Ch. 1.2 - Prob. 1ESCh. 1.2 - Write in words how to read each of the following...Ch. 1.2 - Is 4={4}? How many elements are in the set...Ch. 1.2 - a. Is 2{2}? b. How many elements are in the set...Ch. 1.2 - Which of the following sets are equal?...Ch. 1.2 - For each integer n, let Tn={n,n2} . How many...Ch. 1.2 - Prob. 7ESCh. 1.2 - Prob. 8ESCh. 1.2 - Is3{1,2,3}? Is 1{1}? Is {2}{1,2}? Is...Ch. 1.2 - Is ((2)2,22)=(22,( 2)2)? Is (5,5)=(5,5)? Is...Ch. 1.2 - Prob. 11ESCh. 1.2 - Prob. 12ESCh. 1.2 - Prob. 13ESCh. 1.2 - Prob. 14ESCh. 1.2 - Let S={0,1} . List all the string of length 4 over...Ch. 1.2 - Let T={x,y} . List all the strings of length 5...Ch. 1.3 - Given sets A and B , relation from A to B is ____Ch. 1.3 - A function F from B is a relation from A to B that...Ch. 1.3 - If F is a function from A to B and x is an element...Ch. 1.3 - Let A={2,3,4} and B={6,8,10} and define a relation...Ch. 1.3 - Let C=D={3,2,1,1,2,3} and define a elation S from...Ch. 1.3 - Let E={1,2,3} and F={2,1,0} and define a relation...Ch. 1.3 - Let G=-2,0,2) and H=4,6,8) and define a relation V...Ch. 1.3 - Define a relations S from R to R as follows: For...Ch. 1.3 - Define a relation R from R to R as follows: For...Ch. 1.3 - Let A={4,5,6} and B={5,6,7} and define relations...Ch. 1.3 - Let A={2,4} and B={1,3,5} and define relations U,...Ch. 1.3 - Find all function from {01,} to {1} . Find two...Ch. 1.3 - Find tour relations from {a,b} to {x,y} that are...Ch. 1.3 - Let A={0,1,2} and let S be the set of all strings...Ch. 1.3 - Let A={x,y} and let S be the set all strings over...Ch. 1.3 - Let A={1,0,1} and B={t,u,v,w} . Define a function...Ch. 1.3 - Let C = (1,2,3,4) and D={a,b,c,d}. Define a...Ch. 1.3 - Let X=2,4,5) and Y=(1,2,4,6) . Which of the...Ch. 1.3 - Let f be the squaring function defined in Example...Ch. 1.3 - Let g be the successor function defined in Example...Ch. 1.3 - Let h be the constant function defined in Example...Ch. 1.3 - Define functions f and g from R to R by the...Ch. 1.3 - Define functions H and K from R to R by the...Ch. 1.4 - A graph consists of two finite sets: ______and...Ch. 1.4 - A loop in a graph is_____Ch. 1.4 - Two distinct edges in a graph are parallel if, and...Ch. 1.4 - Two vertices are called adjacent if, and only if,...Ch. 1.4 - An edge is incident on _______Ch. 1.4 - Two edges incident on the same endpoint...Ch. 1.4 - A vertex on which no edges are incident is________Ch. 1.4 - Prob. 8TYCh. 1.4 - Prob. 9TYCh. 1.4 - In 1 and 2, graphs are represented by drawings...Ch. 1.4 - In 1 and 2, graphs are represented by drawings....Ch. 1.4 - In 3 and 4, draw pictures of the specified graphs....Ch. 1.4 - Prob. 4ESCh. 1.4 - Prob. 5ESCh. 1.4 - In 5-7, show that the two drawings represent the...Ch. 1.4 - In 5-7, show that the two drawings represent the...Ch. 1.4 - For each of the graphs in 8 and 9: (i) Find all...Ch. 1.4 - For each of the graphs in 8 and 9: (i) Find all...Ch. 1.4 - Use the graph of Example 1.4.6 to determine...Ch. 1.4 - Find three other winning sequences of moves for...Ch. 1.4 - Another famous puzzle used as an example in the...Ch. 1.4 - Solve the vegetarians-and-cannibals puzzle for the...Ch. 1.4 - Two jugs A and B have capacities of 3 quarts and 5...Ch. 1.4 - Prob. 15ESCh. 1.4 - In this exercise a graph is used to help solve a...Ch. 1.4 - A deptnn1 war to ithechik final ezans that no...
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- The marginal revenue (in thousands of dollars) from the sale of x handheld gaming devices is given by the following function. R'(x) = 4x (x² +26,000) 2 3 (a) Find the total revenue function if the revenue from 125 devices is $17,939. (b) How many devices must be sold for a revenue of at least $50,000? (a) The total revenue function is R(x) = (Round to the nearest integer as needed.) given that the revenue from 125 devices is $17,939.arrow_forwardUse substitution to find the indefinite integral. S 2u √u-4 -du Describe the most appropriate substitution case and the values of u and du. Select the correct choice below and fill in the answer boxes within your choice. A. Substitute u for the quantity in the numerator. Let v = , so that dv = ( ) du. B. Substitute u for the quantity under the root. Let v = u-4, so that dv = (1) du. C. Substitute u for the quantity in the denominator. Let v = Use the substitution to evaluate the integral. so that dv= ' ( du. 2u -du= √√u-4arrow_forwardConsider the state space model X₁ = §Xt−1 + Wt, Yt = AX+Vt, where Xt Є R4 and Y E R². Suppose we know the covariance matrices for Wt and Vt. How many unknown parameters are there in the model?arrow_forward
- Use substitution to find the indefinite integral. Зи u-8 du Describe the most appropriate substitution case and the values of u and du. Select the correct choice below and fill in the answer boxes within your choice. A. Substitute u for the quantity in the numerator. Let v = , so that dv = ( ( ) du. B. Substitute u for the quantity under the root. Let v = u-8, so that dv = (1) du. C. Substitute u for the quantity in the denominator. Let v = so that dv= ( ) du. Use the substitution to evaluate the integral. S Зи -du= u-8arrow_forwardAloha Airlines Flight 007 is flying due east but finds it necessary to detour around a group of thundershowers. The plane 1st turns at a bearing of N 73° E, flies for a while, then 2nd turns to intercept the original path and travels for 50 km at a bearing of S 41° E, back to the original path. As stated the plane traveled 50 km in the 2nd leg of the journey getting back to the path. How far did the plane travel in the 1st leg of the journey?arrow_forwardQuestion 6 Aloha Airlines Flight 007 is flying due east but finds it necessary to detour around a group of thundershowers. The plane 1st turns at a bearing of N 73° E, flies for a while, then 2nd turns to intercept the original path and travels for 50 km at a bearing of S 41° E, back to the original path. As stated the plane traveled 50 km in the 2nd leg of the journey getting back to the path. How far did the plane travel in the 1st leg of the journey? Question Help: Video Submit Question Jump to Answer P3 E E T Q Search L W F1 % R R FS F € t X C V 08 7 47 * B FB Y I E 7 コ コ I Barrow_forward
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