*3. A tortoise and hare are competing in a race around a 400-meter track. The arrogant hare decides to letthe tortoise have a 225-meter head start. When the start gun is fired, the hare begins running at aconstant speed of 5.5 meters per second and the tortoise begins crawling at constant speed of 2.0meters per second. Let t represent the number of seconds since the start gun was fired. We areinterested in determining who won the race.a. Illustrate the situation with a diagram (mark off the length of the race, note the approximateposition of the tortoise from the starting line and the position of the hare, illustrate varyingquantities with vectors, etc.).b. Define a function g to represent the tortoise's distance from the finish line in terms of the numberof seconds t since the start gun was fired.420400380360c. Define a function h to represent the hare's distance from thefinish line in terms of the number of seconds t since the start340-320gun was fired.300280260240d. Evaluate g(40) and say what your answer represents.220200180160е.Solve g(t) = 80 for t and say what the solution represents.14012010080f. Solve h(t) = 0 and say what the solution represents.60402010 203040506060 10 100 110 120g. Construct a graph of g and h on the axes.-20h. Evaluate h(20) – g(20) and indicate how this quantity is represented on the graph in part (g).What does the quantity represent in the context of this situation?

Answered: Image /qna-images/answer/f8fb0054-3871-4fd7-8b73-ff0c895b4396.jpg

A tortoise and hare are competing in a race around a 400-meter track. The arrogant hare decides to let the tortoise have a 225-meter head start. When the start gun is fired, the hare begins running at a constant speed of 5.5 meters per second and the tortoise begins crawling at constant speed of 2.0 meters per second. Let t represent the number of seconds since the start gun was fired. We are interested in determining who won the race.

A tortoise and hare are competing in a race around a 400-meter track. The arrogant hare decides to let the tortoise have a 225-meter head start. When the start gun is fired, the hare begins running at a constant speed of 5.5 meters per second and the tortoise begins crawling at constant speed of 2.0 meters per second. Let t represent the number of seconds since the start gun was fired. We are interested in determining who won the race.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 94E

See similar textbooks

Related questions

Q: Relevant Relationship: There is a functional relationship between Price of an IPod Touch,p and…

A: Data is given for price and weekly demand. First We have to calculate linear model ( regression…

Q: A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of…

A: Given Information : A company produces steel rods . The lengths of the steel rods are normally…

Q: r. 34, V415

Q: Solve the problem. The following confidence interval is obtained for a population proportion, p:…

A: Given Confidence interval for a population proportion p is (0.318,0.569) Using these Confidence…

Q: The weight of an organ in adult males has a bell-shaped distribution with a mean of 300 grams and a…

A: From the provided information, Mean (µ) = 300 grams Standard deviation (σ) = 15 grams Let X be a…

Q: 2. Prove that the functions in the right-hand column below are solutions of the differential…

Q: Stating Conclusions. In Exercises 25-28, assume and use the given information for the following: a.…

A: 26) a) Given P=0.0721 and α=0.05 Decision Rule: If P is less than or equal to α=0.05, then reject…

Q: utcome is 00, 0, or 1, there is a probability of 38 of making a net profit of $60 and a 38…

A: Given playing roulette at a casino, a gambler is trying to decide whether to bet $20 on the number…

Q: X=7, Y=24 and Z=25

A: Use trigonometric ratio

Q: 8) fre-andr

Q: 1. Calculate a general solution of the ODE: dx dt (²+8) +4tx = 4 t² + 1

Q: fnd the elelope ŷ Mies 2. where 2

A: We have find Equation of Envelope.

Q: Consider the function g : Zx Z → Z × Z defined by g(x, y) = (4xy, 9x + 5y). (a) Is g injective? (b)…

Q: Exercises 1) The following values illustrate the annual incomes among a group of households in a…

Q: The figure shows the graph of y = ax²+bx+c. Suppose that the points (-h.yo). (0.0₁), and (h.y2) are…

Q: Identify which of the two variables is the independent variable x and which is the dependent…

Q: V. Determine all the relative minimum and maximum values, and saddle points of the function h…

Q: 36 – x2 – y? and S2 be t Let Si be the hemisphere with Cartesian equation z = 6 – upper nappe of the…

Q: A random sample of 35 Hollywood movies made in the last 10 years had a mean length of 125.2 minutes,…

A: Given, Sample size = 35 Sample mean = 125.2 Sample standard deviation = 20.4 Since the population…

Q: Kk.196.

A: Use the MATLAB ODE45 function to numerically solve the forced Van der Pol oscillator equation and…

Q: d) Greyhound and Trailways travel from San Francisco to Los Angeles. Trailways makes the trip in 7…

Q: Consider the ODE With the initial condition that y=1 when x = 1. Show that the particular solution…

A: The given ODE is y'+2xy=3x3+1. The initial condition is y=1 when x=1.

Q: 2.27 Use the method of characteristics to solve (y+u)ux + yuy = x-y, u(x, 1) = 1+x.

Q: 3. Find the slope of the tangent line to r²e♥ + y²e² = 2e at (1,1).

A: Please see the answer below

Q: In Wanchai Computer Centers in Hong Kong, there are dozens of computer shops selling multiple laptop…

A: Given data: (1.8, 14,500), (1.6, 12,290), (2.0, 17,500), (1.6, 16,500), (1.8, 19,650), (2.4,…

Q: A random sample of 56 students was selected, and they were asked the number of pairs of shoes they…

Question

100%

*3. A tortoise and hare are competing in a race around a 400-meter track. The arrogant hare decides to let
the tortoise have a 225-meter head start. When the start gun is fired, the hare begins running at a
constant speed of 5.5 meters per second and the tortoise begins crawling at constant speed of 2.0
meters per second. Let t represent the number of seconds since the start gun was fired. We are
interested in determining who won the race.
a. Illustrate the situation with a diagram (mark off the length of the race, note the approximate
position of the tortoise from the starting line and the position of the hare, illustrate varying
quantities with vectors, etc.).
b. Define a function g to represent the tortoise's distance from the finish line in terms of the number
of seconds t since the start gun was fired.
420
400
380
360
c. Define a function h to represent the hare's distance from the
finish line in terms of the number of seconds t since the start
340-
320
gun was fired.
300
280
260
240
d. Evaluate g(40) and say what your answer represents.
220
200
180
160
е.
Solve g(t) = 80 for t and say what the solution represents.
140
120
100
80
f. Solve h(t) = 0 and say what the solution represents.
60
40
20
10 20
30
40
50
60
60 10 100 110 120
g. Construct a graph of g and h on the axes.
-20
h. Evaluate h(20) – g(20) and indicate how this quantity is represented on the graph in part (g).
What does the quantity represent in the context of this situation?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Markov Processes and Markov chain$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions

Find the intensity of light at a depth of 12 meter if I0=14 and k=0.7. Round to two decimals.
A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.m. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 10.7 gallons. What is the average rate of flow of the gasoline into the gas tank?
Find the unknown value. 27. y varies jointly with x and the cube root of 2. If when x=2 and z=27,y=12, find y if x=5 and z=8.
The ideal diameter of a rod needed for a machine is 80 mm. The actual diameter can vary from the ideal diameter by 0.009 mm. What range of diameters will be acceptable to the customer without causing the rod to be rejected?
The kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?
A shaft is turned in a lathe at 120 revolutions per minute. The cutting tool advances 0.030 inch per revolution. How bong is the length of cut along the shaft at the end of 3.50 minutes?
A pine tree casts a shadow of 80 feet next to a 30 foot tall building which casts a 40 feet shadow. How tall is the pine tree?
A boat travels at a constant speed to an island 14 miles away. It takes 0.5 hour to travel the first 5 miles. How long does the entire trip take?
The length a spring stretches varies directly with a weight placed at the end of the spring. When Meredith placed a 6-pound cantaloupe on a hanging scale, the spring stretched 2 inches. How far would the spring stretch if the cantaloupe weighed 9 pounds?
A piece shown by the shaded portion is to be cut from a square plate 128 millimeters on a side. a. Compute the area of the piece to be cut. Round the answer to the nearest square millimeter. b. After cutting the piece, determine the percentage of the plate that will be wasted.
In a classroom designed for 30 students, the air conditioning system can move 450 cubic feet of air per minute. (a) Determine the ventilation rate per child in a full classroom. (b) Estimate the air space required per child. (c) Determine the minimum number of square feet of floor space required for the room when the ceiling height is 30 feet.