Answer would be C.
Why A would be incorrect: 100m^2 is 100m × 100 m. That would be as big as a football field.
Why B would be incorrect: 1cm^2 is 1cm × 1cm. You can use a regular 15 cm to measure a piece of paper with the length of 1cm each side.
Why C would be correct: 1m^2 = 1m × 1m and it is also equals to 60cm × 60 cm. A 1 meter ruler = 60 cm = 4 times of your average 15 cm ruler. So, it is reasonable that a classroom is 10m by 10m in length and breadth.
Why D would be incorrect: The same explanation applies to here as well. Things that can be measured with 1m × 1m is a square table so your classroom can't be that small to fit an average of 30 to 40 students in there.
I hope my explanations were detailed and easy to understand. :)
3 prefer pop:4 prefer rock
3/4 prefer pop
(3/4)of 14=0.75*14=10.5 people/14people
around 11 people would prefer pop out of 14
Use the power rule for differentiation:
You can use this formula if you remember that a root is just a rational exponential:
![\sqrt[4]\ln(x) = (\ln(x))^{\frac{1}{4}}](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%5Cln%28x%29%20%3D%20%28%5Cln%28x%29%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%20)
So, remembering that the derivative of the logarithm is 1/x, you have
Which you can rewrite as
![\dfrac{1}{4}(\ln(x))^{\frac{1}{4}-1}\dfrac{1}{x} =\dfrac{1}{4}(\ln(x))^{\frac{-3}{4}}\dfrac{1}{x} =\dfrac{1}{4}\dfrac{1}{\sqrt[4]{\ln(x))^3}}\dfrac{1}{x} = \dfrac{1}{4x\sqrt[4]{\ln(x))^3}}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B4%7D%28%5Cln%28x%29%29%5E%7B%5Cfrac%7B1%7D%7B4%7D-1%7D%5Cdfrac%7B1%7D%7Bx%7D%20%3D%5Cdfrac%7B1%7D%7B4%7D%28%5Cln%28x%29%29%5E%7B%5Cfrac%7B-3%7D%7B4%7D%7D%5Cdfrac%7B1%7D%7Bx%7D%20%3D%5Cdfrac%7B1%7D%7B4%7D%5Cdfrac%7B1%7D%7B%5Csqrt%5B4%5D%7B%5Cln%28x%29%29%5E3%7D%7D%5Cdfrac%7B1%7D%7Bx%7D%20%3D%20%5Cdfrac%7B1%7D%7B4x%5Csqrt%5B4%5D%7B%5Cln%28x%29%29%5E3%7D%7D%20)
Answer: x^2 +6x +2x +36 = X^2 +8x + 36
Step-by-step explanation:
