I need help with the following problem. I do not understand how to finish working it.
-3y^4/5+72=-15
-3y^4/5=-87
y^4/5=29
y=29^5/4
What next? Round answer to two decimal places. Thanks for your help.
Ok, round the answer.
29^(1.25)=67
You're right so far, which was the hard bit.
Me, I'd just pull out the calculator at this point. I did, and got 67.2972 = 67.30 to 2 d.p.
You can do it by = 29 * sqrt(sqrt(29)) or by log tables. I can't think of an especially clever way.
To finish solving the problem, you have found that y^4/5 = 29. To isolate y, you need to undo the exponent of 4/5 by raising both sides of the equation to the reciprocal exponent, which is 5/4.
So, let's raise both sides of the equation (y^4/5 = 29) to the power of 5/4:
(y^4/5)^(5/4) = 29^(5/4)
On the left side of the equation, raising a power to a power will result in the exponent multiplication, so we have:
y^((4/5)*(5/4)) = 29^(5/4)
Simplifying further:
y^1 = 29^(5/4)
Since y^1 just becomes y, we can rewrite the equation as:
y = 29^(5/4)
Now, to evaluate 29^(5/4), you can use a calculator or follow these steps:
1. Convert the exponent from a fractional form of 5/4 to a decimal: 5/4 = 1.25.
2. Raise 29 to the power of 1.25 using a calculator.
The result is approximately 40.76059, but since you need to round to two decimal places, the final answer is:
y ≈ 40.76
Therefore, the value of y, rounded to two decimal places, is 40.76.