SOLUTION: Suppose that y varies directly as w and inversely as t.
If y=4 when w=1/4 and t=1/2, find y when w=2 and t=16
Algebra.Com
Question 835038: Suppose that y varies directly as w and inversely as t.
If y=4 when w=1/4 and t=1/2, find y when w=2 and t=16
Found 2 solutions by Theo, stanbon:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
if y varies directly as w, then the equation would be y = kw
if y varies inversely with t, then the equation would be y = k/t
since y varies directly with w and inversely with t at the same time, the equation becomes y = kw/t.
if y = 4 when w = 1/4 and t = 1/2, you can use this equation to find the value of k.
your equation becomes 4 = (k * (1/4) / (1/2)
since a division by 1/2 is the same as a multiplication by 2, the equation simplifies to:
4 = (1/4) * k * 2
simplify this to get:
4 = 2/4 * k which further simplifies to 4 = 1/2 * k
multiply both sides of this equation by 2 and you get:
8 = k
the value of k should be equal to 8.
you can test by substituting k in the original equation.
the original equation says that 4 = (1/4) * k / (1/2)
replace k with 8 in this equation to get:
4 = (1/4) * 8 / (1/2)
simplify to get:
4 = 2 / (1/2)
simplify further to get 4 = 4 confirming that k = 8 is correct.
now that you know k, you can use it to solve the second part of your problem.
that second part says:
find y when w = 2 and t = 16
the equation is still y = k * w / t
replace all variables with their known values and you get:
y = 8 * 2 / 16 which results in y = 16 / 16 which results in y = 1.
see the following link for an online explanation of the combined variation equation used in this problelm.
http://hotmath.com/hotmath_help/topics/combined-variation.html
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Suppose that y varies directly as w and inversely as t.
y = kw/t
----------------------
Solve for "k" using "y=4 when w=1/4 and t=1/2"
1/2 = k*(1/4)/4
---
k = 2/(1/4) = 8
-------
Equation: y = 8*w/t
-----------------------------
Find y when w=2 and t=16
----------
y = 8*2/16 = 1
---------------------
Cheers,
Stan H.
=====================
RELATED QUESTIONS
suppose that z varies jointly as x and t^2 and inversely as w. if z=4 when x=2, t=1 and... (answered by solver91311)
14) y varies inversely as w, and y = 9 when w = 2. Find y when w =... (answered by ewatrrr)
Find and equation of varitation for the given situation.
1) y varies inversely as the (answered by stanbon)
Suppose W varies directly as x and y and inversely as Z, and W=48 when X=2, Y=8 and Z=12. (answered by kev82)
1) If w varies directly as z and w = 9 when z = -6, find w when z = 3.
a) 0
b)... (answered by Alan3354)
given that w varies directly as the product of x and y and inversely as the square of z... (answered by Cromlix)
Suppose z varies directly as x and y and inversely as w, and z =8 when x =6, y =5 and w... (answered by Edwin McCravy,Theo)
Suppose z varies inversely as the cube of w. If z = 16 when w = 2, find when w = 4. (answered by josgarithmetic)
6. If y varies inversely with x, and y = 5 when x = 8, what is k?
7. If y varies... (answered by solver91311)