min How fast is the diomeser of the b) Write an ..,eatin ma\" relate. A and r (d
ID: 2888115 • Letter: M
Question
min How fast is the diomeser of the b) Write an ..,eatin ma" relate. A and r (d) At a ce air be removed when the radis i 9 c the radios is 5c at the rate of 2's How fat is the aea nmning and increaning I6. A17h ladler is lesning apainst s wall 1f the s of the coant rate of 5 /sw fast will the top of the ladder be ing down the wall when ir i.nahme de grenner adius r, and assunne thst h and r vary 17. A 13 t ladder is leaning agsinnt a wall. If the top of the (a) How ae f,dN/d, and ds d (b) elated ladder sligs down the wall at a rate of 2 fi/s, how fant will At a certain instant, he height is 6 in and increasing at 1 in/s, while the radius is 10 in and decreasing at I in/s. How fast is the volume changing at thar instane? is the volume increasing or decreasing at he fost he moving away from the wall when the top is 5 h IS. A 10ft plank i leaning against a wall If at a certain inutant the eound the boctom of the plank is 2 ft from the wall and is being paded toward the wall at the rate of 6 in/s, how fast is the 8. Let I be the length of a diagonal of a rectangle whone acute angle that the plank makes with the ground increasing 19. A sotihall iamond is a spuare whose sides are 60 ft long. ides have lengths x and y, and assume that x and y vary Suppose that a player running from first to second base has a (a) How are di ld, ds/ds, and dy/di related speed of 25 fi/s at the instant when she is 10 ft from second (b) If x increases at a constant rate of f/s and y de- creases at a constant rate of n/s. how fast is the tune. Ai what rade is the player's distance from bome plate size of the diagonal changing when3 and y = 4 ft? Is the diagonal increasing or decreasing hanging at that instant? 20. A rocket, rising vertically, is tracked by a radar station that is on the ground 5 mi from the launchpad. How fast is the rocket rising when it is 4 mi high and its distance from the 9. Let (in radians) be an acute angle in a right triangle, and let x and y, respectively, be the lengths of the sides 21. For the camera and rocket shown in Figare 2.8.5,at what rae adjacent to and opposite . Suppose also that x and y vary with time (a) How are doldt,dxidr, and dyjdr related (b) At a certain instant,A2 units and is increasing at radar station is increasing at a rate of 2000 mi/h is 4000 ft up and rising vertically at 880 f/s? radians and increasing at a rate of 0.2 rad/s? is the camer·to.rocket distance changing when the rocket 22. For the camera and rocket shown in Figure 2.8.5, at wat rate is the rocket rising when the elevation angle is /4 1 unit/s, while y2 units and is decreasing at unit/s. How fast is o changing al that instant? Is increasing or decreasing at that instant 23. A satellite is in an elliptical orbit around the Earth. Its distance r (in miles) from the center of the Earth is given by 10. Suppose thatx where both x and y are changing with time. At a certain instant whenx1 and y 2, x is decreasing at the rate of 2 units/s, and y is increasing at the rate of 3 units/s. How fast is z changing at this instant? Is 995 1+0.12 cos where 0 is the angle measured from the point on the orbit z increasing or decreasing? nearest the Earth's sarface (see the accompanying figure on II. The minule hand of a certain clock is 4 in long. Starting from the moment when the hand is pointing straight up, how fast is the area of the sector that is swept out by the hand increasing at any instant during the next revolution of the next page). (a) Find the altitude of the satellite at perigee (the point nearest the surface of the Earth) and at apogee (the point farthest from the surface of the Earth). Use 3960 mi as the radius of the Earth. (b) At the instant when e is lar.the angle is increas. 12 A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 3 ft/s. How ing at the rate of 2.7°/min. Find the altitude of theExplanation / Answer
Solution:
12) Given dr / dt = 3 ft / s
at t = 10 sec , r = 30 ft
We know that area of circle A = r^2
=> dA / dt = 2 r * dr / dt
=> dA / dt = 2 * 3.14 * 30 * 3
=> dA / dt = 565.2 ft^2 / s
13) Given dA / dt = 6 mi^2 / h ( image is not clear)
when A = 9 mi^2
r = sqrt ( 9 / )
=> r = 1.6925 mi
=> dA / dt = 2 * * r * dr / dt
=> 6 = 2 * 3.14 * 1.6925 * dr / dt
=> dr / dt = 0.564 mi / h
please comment for Queries.
Please rate thanks.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.