Concept explainers
Eight differential equations and four slope fields are given below. Determine the equation that corresponds to each slope field and state briefly how you know your choice is correct. You should do this exercise without using technology.
(i)
(v)
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Chapter 1 Solutions
Differential Equations
- Find the constant of proportionality. y is directly proportional to x. If x=30, then y=15.arrow_forwardYOUR TURN Find dy if y=300x23,x=8, and dx=0.05.arrow_forwardThe gas equation for one mole of oxygen relates its pressure, P (in atmospheres), its temperature, T (in K), and its volume, V (in cubic decimeters, dm³): dT T 16.574. = 1 V 0.52754. 1 V2 (a) Find the temperature T and differential dT if the volume is 34 dm³ and the pressure is 0.75 atmosphere. T = 0.3879 P + 12.187 V P. (b) Use your answer to part (a) to estimate how much the pressure would have to change if the volume increased by 2.5 dm³ and the temperature remained constant. change in pressure =arrow_forward
- A steady wind blows a kite due west. The kite's height above ground from horizontal position x = 0 to x = 80 ft is given by y = 150 -(x − 50)². Find the distance traveled (in ft) by the kite. (Round your answer to one decimal place.)arrow_forwardPlease answer both incorrect y(t) equationsarrow_forwardcalculate y" and y"'. y = 7 − 2xarrow_forward
- The equation of motion of a particle is = 213 - 5t2+ 31+4 where s is measured in centimeters andt in seconds. What is the acceleration after 3 seconds? dv a (t) = dt Hint: velocity v (t) = ds and acceleration dt Note: Do NOT include the unit in your answer. Round off your answer in two decimal places.arrow_forwardFind the differential of the function. u = 2x5 + 5arrow_forwardNewton's Law of Cooling says that the rate at which a body cools is proportional to the difference C in temperature between the body and the environment around it. The temperature f(t) of the body at time t in hours after being introduced into an environment having constant temperature To is f(t) = T, +Ce - kt where C and k are constants. A cup of coffee with temperature 145°F is placed in a freezer with temperature 0°F. After 10 minutes, the temperature of the coffee is 64°F. Use Newton's Law of Cooling to find the coffee's temperature after 15 minutes. After 15 minutes the coffee will have a temperature of °F. (Round to the nearest integer as needed.)arrow_forward
- Solve for Z. X= (Y-Z) 3arrow_forwardKindly solve T (tension) and a (acceleration) from eq.1 and 2arrow_forwardThe velocity of an object is v(t) = 45 - t, 0 sts 6 %D = 3. where v is measured in meters per second and t is the time in seconds. Find the velocity v(3) and acceleration a(3) of the object when t = v(3) = a(3) = What can be said about the speed of the object when the velocity and acceleration have opposite signs? The speed of the object is -Select--- v, but the rate of that --Select--- is ---Select---varrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning