To calculate the length of the ramp.
Answer to Problem 67SGR
6 feet
Explanation of Solution
Given:
Concept used:
From the given figure,
Height of the ramp is 3 feet.
The angle that it makes with the ground is 30°.
Calculation:
Given that the height of the ramp is 3 feet and the angle that it makes with the ground is 30°.
To calculate the length of the ramp,
Calculating the value of
Conclusion:
Therefore, the length of the ramp is 6 feet.
Chapter 10 Solutions
Algebra 1
Additional Math Textbook Solutions
Thinking Mathematically (6th Edition)
Calculus: Early Transcendentals (2nd Edition)
Pre-Algebra Student Edition
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Basic Business Statistics, Student Value Edition
A First Course in Probability (10th Edition)
- 2. Part II Real World Examples. Pesticides Pesticides that kill all insect species are not only bad for the environment, they can also be inefficient at controlling the pest species and can have unintended consequences. Suppose a pest insect species in a particular field has a population x(t) at a particular time t, and suppose its primary predator is another insect species with population y(t) at time t. Suppose the population of these species are accurately modeled by the system dx = 2.4x 1.2xy dt dy = −y+0.9xy dt Also suppose that at time t = 0 a pesticide is applied to the field that reduces both the pest and predator populations to a very small but non-zero numbers. 1. Use the Slopes app (or other similar app) to investigate what happens to this system. Choose 2 sets of initial conditions, both near zero. Let x(0) = 5y(0). Whatever initial values you choose for your first set, the second set of values should be 1/100 of the first. Plot the solutions. Be sure to expand the scale if…arrow_forward1. PART I: Investigating Key Concepts Using Graphs. Although the Lotka-Volterra system can be solved analytically, the solutions are beyond the scope of our class, so we will will explore key concepts such as Cyclic Behavior, Parameter Sensitivity and Equilibrium Points and other features of the Lotka-Volterra predator-prey model graphically by using the Slopes App by Tim Lucas. You can use any other app or program to graph the solutions of the predator-prey system, but the Slopes App is really convenient. Cyclic Behavior: The model predicts that predator and prey populations can exhibit cyclic or oscillatory behavior over time. When the prey population is high, it provides abundant food for predators, causing the predator population to increase. As the predator population increases, it exerts greater predation pressure on the prey, causing the prey population to decline. This, in turn, leads to a decrease in the predator population due to reduced food availability. The cycle then…arrow_forwardEquilibrium Points: The model has equilibrium points where both populations remain constant over time. These equilibrium points can be stable or unstable, depending on the values of the model parameters. A stable equilibrium represents a situation where predator and prey popula- tions coexist in a relatively stable manner. In the Lotka-Volterra Model it is rare to find perfect equilibrium solutions, more often the solutions exhibit oscillatory behaviour around the equilibrium points rather than staying at them. To find the equilibrium points for this system we set both dx/dt and dy/dt to zero and solve dx = ax - bxy dt dy dt == -cy + dxy We find we have 2 sets of equilibrium values, (0,0) when both predator and prey populations vanish, and (c/d, a/b) when there are just enough prey to support a constant predator population but there are not too many predators. Answer the following question for the system shown below. dx dt = 2.4x-1.2xy 33 dy dt = −y + xy 11. Find the equilibrium values…arrow_forward
- 2x^3-18x^2+35x+17=0, solve for xarrow_forwardL Question 7, 4.5.85 Part 1 of 4 > 527¢er 12/06/24 11:2 HW Score: 91.84%, 6.43 of 7 points Points: 0.43 of 1 The population, P, in thousands, of a resort community is given 100- 500t by P(t) = 31 ² +9 , t≥0, where t is time, in months. a) Find the population at t = 0, 1, 3, and 8 months. 80- 60- Ay b) Find the horizontal asymptote of the graph and determine the 40- A value that P(t) approaches as t goes to co? 20- c) Explain the meaning of the answer to part (b) in terms of the application. 0- 10+ 0 10 20 30 40 50 a) At t = 0, the population is At t = 1, the population is At t = 3, the population is At t=8, the population is (Simplify your answers. Round to the nearest integer as needed.) H Vo S (1,1) More View an example Get more help - Clear all Skill builder Check answ 4 Music DEC άtv Ը Warrow_forwardrth and K L Question 5, 5.6.11 Part 2 of 7 Complete the table given below. 627¢erwin=yes 12/06/24 10:57 PM > HW Score: 83.33%, 5 of 6 points C Sav × Points: 0 of 1 (Simplify your answers. Do not round until the final answers. Then round to four decimal places as needed.) Radioactive Substance a) Polonium (Po-200) Decay Rate, k Half-Life T 6.0274 % per min 11.5 mins b) Lead (Pb-196) % per min 37.0 mins View an example Get more help - A DEC 6 M tv P Clear all Skill builder Check answe A NA Warrow_forward
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education