SOLUTION: For the following equations connecting x and y, if the rate of change of y is 4 units s^-1, find the rate of change of x at the given instant: y = √ 2x + 7 ; y = 3

Algebra ->  Test -> SOLUTION: For the following equations connecting x and y, if the rate of change of y is 4 units s^-1, find the rate of change of x at the given instant: y = √ 2x + 7 ; y = 3      Log On


   

Question 1191910: For the following equations connecting x and y, if the rate of change of y is 4 units s^-1, find the
rate of change of x at the given instant: y = √ 2x + 7 ; y = 3
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
For the following equations connecting x and y, if the rate of change of y is 4 units s^-1,
That says that
dy%2Fdt=4units%2Fsecond

You didn't put in any parentheses, so I can't tell whether you meant
y=sqrt%282x%2B7%29 or y=sqrt%282x%29%2B7. I'll assume

y=sqrt%282x%2B7%29

Write the square root as the 1%2F2 power:

matrix%282%2C1%2C%22%22%2Cy=%282x%2B7%29%5E%281%2F2%29%29 

Take the derivative with respect to t



Substitute 4 for dy%2Fdt and simplify



matrix%282%2C1%2C%22%22%2C4=%282x%2B7%29%5E%28-1%2F2%29%28expr%28dx%2Fdt%29%29%29

Bring the negative exponent to the denominator as a positive exponent



Change the 1%2F2 power to a square root

4=%281%2Fsqrt%282x%2B7%29%29expr%28dx%2Fdt%29

find the
rate of change of x at the given instant: y = 3

Go back to y=sqrt%282x%2B7%29

Substitute y=3 and solve for x:

3=sqrt%282x%2B7%29
Square both sides:
9=2x%2B7
Solve for x

Substitute that value of x in

4=%281%2Fsqrt%282x%2B7%29%29expr%28dx%2Fdt%29

and solve for dx%2Fdt.

Edwin