write a general formula to descirbe each variation v varies directly with t; v=1
ID: 3102882 • Letter: W
Question
write a general formula to descirbe each variationv varies directly with t; v=16 when t =2
V varies directly with x^3; V = 36(pi) when x=3
y varies inversley with (square rootx); y=4 when x=9
T varies jointly with the cube of the root of x and the square of d; T=18 when x=8 and d=3
the cube of z varies directly witht the sum of the sqaures of x and y; z =2 when x=9 and y=4
the velocity v of a falling object is directly proportional tot he time t of the fall. if an object falls 16 ft in 1 sec how far wil it fall in 3 secs? how long will it take an object to fall 64ft
the volume V of a right circular cone varies jointly witht he sqaure of its radius r and its height h. the constant of proportionality is (pi)/3. write an equation for v
Explanation / Answer
V varies directly with t: V = kt. >> 16 = k(2) >> k = 8
V varies directly with x^3: V = k(x^3) >> 36*pi = k(3^3) >> k = (4/3) * pi
y varies inversely...: V = k/(x^2) >> 4 = k/(81) >> k = 324
T varies ...: T = k[(x^1/3)(d^2)] >> 18 = k(18) >> k = 1
The cube of z varies...: z^3 = k[(x^2+y^2)] >> 8 = k(97) >> k = 8/97
The velocity V of a ....: V = k(t). object falls 16ft/1sec means velocity is 16 ft/s. >>
16 ft/s= k (1sec) therefore k = 16. the equation becomes V = 16t. Integrate this equation so that you can get the position equation. X = 16(t^2)/2 >> X(t) = 8t^2 + C. lets assume zero initial conditions so that we can eliminate C, the constant of integration. The position of the object after 3 seconds can be found by plugging in 3 fot X(t), this gives X(3) = 72 ft. then plu in 64 ft for X(t) to find how many seconds it takes to fall that much >> 64ft = 8t^2 >> 22 = t
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