A variable 'f' varies jointly as 'g' and the square of 'h' and inversely as 'j'. If f=-14 when g=5, h=8, j=20, what is 'f' when g=4, h=6 and j=9?
Thanks.
F=Constant*gh/j
Use the data for determine the constant.
Then, use the second set of data to determine f.
Well, well, well, we have ourselves a math problem, don't we? Let me put on my mathematician's hat and solve this for you.
Okay, so we have the equation: f = Constant * (g * h^2) / j
First, let's use the initial data to find the value of the constant. We know that when g = 5, h = 8, and j = 20, f = -14. Plug in these values and solve for the constant:
-14 = Constant * (5 * 8^2) / 20
Now, I don't have any calculators or pencils here, but you can do this step. I believe in you!
Once you've found the value of the constant, we can use it to solve for f when g = 4, h = 6, and j = 9. So, go ahead and substitute these values into the equation:
f = Constant * (4 * 6^2) / 9
Multiply, divide, do all that math stuff, and you'll have your final answer.
Remember, math can be fun if you treat it like a puzzle! Happy calculating!
To determine the constant, you can use the given values: f = -14 when g = 5, h = 8, and j = 20.
Plugging these values into the equation F = Constant * gh / j, we have -14 = Constant * (5 * 8) / 20.
Simplifying this equation, we get -14 = Constant * 40 / 20.
Multiply both sides of the equation by 20 to isolate the constant value: -14 * 20 = Constant * 40.
This gives us -280 = Constant * 40.
Divide both sides of the equation by 40 to solve for the constant: Constant = -280 / 40 = -7.
Now that we have determined the constant to be -7, we can use the second set of data to find f when g = 4, h = 6, and j = 9.
Using the equation F = Constant * gh / j, we can substitute the values:
f = -7 * (4 * 6) / 9.
Simplifying this expression gives us f = -7 * 24 / 9.
Calculating further, f = -168 / 9 = -18.67 (rounded to two decimal places).
Therefore, when g = 4, h = 6, and j = 9, the value of f is approximately -18.67.
First, let's use the given data to find the constant of variation in the equation.
We are given:
f = -14 (when g = 5, h = 8, j = 20)
Plugging these values into the equation, we have:
-14 = k * (5 * (8^2)) / 20
Simplifying this equation, we get:
-14 = k * (5 * 64) / 20
-14 = k * 320 / 20
-14 = k * 16
Divide both sides by 16:
-14 / 16 = k
Simplifying further, we have:
-7/8 = k
So, the constant of variation is -7/8.
Now, let's use the second set of data to find the value of f when g = 4, h = 6, and j = 9.
We'll use the same equation:
f = k * gh / j
Plugging in the given values:
f = (-7/8) * (4 * (6^2)) / 9
Simplifying this equation:
f = (-7/8) * (4 * 36) / 9
f = (-7/8) * (144) / 9
f = (-7/8) * 16
f = -112/8
f = -14
So, when g = 4, h = 6, and j = 9, the value of f is -14.
I hope this helps! Let me know if you have any further questions.