Answer:
E
Step-by-step explanation:
Answer:
6 cm by 6 cm
Step-by-step explanation:
We know that the formula for area of a square is A = s² where A = area and s is the length of one side. We know that A = 36 so:
36 = s²
√36 = s
s = ±6
Note that s = -6 is an extraneous solution because you can't have a side length of -6, therefore the answer is s = 6 so the dimensions of the square are 6 cm by 6 cm.
Answer:
Step-by-step explanation:
Given that:
![f_x = \dfrac{x^2}{a^7-x^7}](https://tex.z-dn.net/?f=f_x%20%3D%20%5Cdfrac%7Bx%5E2%7D%7Ba%5E7-x%5E7%7D)
![= \dfrac{x^2}{a^7(1-\dfrac{x^7}{a^7})}](https://tex.z-dn.net/?f=%3D%20%5Cdfrac%7Bx%5E2%7D%7Ba%5E7%281-%5Cdfrac%7Bx%5E7%7D%7Ba%5E7%7D%29%7D)
![= \dfrac{x^2}{a^7}\Big(1-\dfrac{x^7}{a^7} \Big)^{-1}](https://tex.z-dn.net/?f=%3D%20%5Cdfrac%7Bx%5E2%7D%7Ba%5E7%7D%5CBig%281-%5Cdfrac%7Bx%5E7%7D%7Ba%5E7%7D%20%5CBig%29%5E%7B-1%7D)
since ![\Big((1-x)^{-1}= 1+x+x^2+x^3+...=\sum \limits ^{\infty}_{n=0}x^n\Big)](https://tex.z-dn.net/?f=%5CBig%28%281-x%29%5E%7B-1%7D%3D%201%2Bx%2Bx%5E2%2Bx%5E3%2B...%3D%5Csum%20%5Climits%20%5E%7B%5Cinfty%7D_%7Bn%3D0%7Dx%5En%5CBig%29)
Then, it implies that:
![\implies \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\Big(\dfrac{x}{a} \Big)^{^7} \Big)^n](https://tex.z-dn.net/?f=%5Cimplies%20%20%5Cdfrac%7Bx%5E2%7D%7Ba%5E7%7D%20%5Csum%20%5Climits%20%5E%7B%5Cinfty%7D_%7Bn%3D0%7D%20%5CBig%28%5CBig%28%5Cdfrac%7Bx%7D%7Ba%7D%20%5CBig%29%5E%7B%5E7%7D%20%5CBig%29%5En)
![= \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\dfrac{x}{a} \Big)^{^{7n}}](https://tex.z-dn.net/?f=%3D%20%5Cdfrac%7Bx%5E2%7D%7Ba%5E7%7D%20%5Csum%20%5Climits%20%5E%7B%5Cinfty%7D_%7Bn%3D0%7D%20%5CBig%28%5Cdfrac%7Bx%7D%7Ba%7D%20%5CBig%29%5E%7B%5E%7B7n%7D%7D)
![= \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\dfrac{x^{7n}}{a^{7n}} \Big)}](https://tex.z-dn.net/?f=%3D%20%5Cdfrac%7Bx%5E2%7D%7Ba%5E7%7D%20%5Csum%20%5Climits%20%5E%7B%5Cinfty%7D_%7Bn%3D0%7D%20%5CBig%28%5Cdfrac%7Bx%5E%7B7n%7D%7D%7Ba%5E%7B7n%7D%7D%20%5CBig%29%7D)
![\mathbf{= \sum \limits ^{\infty}_{n=0} \dfrac{x^{7n+2}}{a^{7n+7}} }}](https://tex.z-dn.net/?f=%5Cmathbf%7B%3D%20%20%5Csum%20%5Climits%20%5E%7B%5Cinfty%7D_%7Bn%3D0%7D%20%5Cdfrac%7Bx%5E%7B7n%2B2%7D%7D%7Ba%5E%7B7n%2B7%7D%7D%20%7D%7D)
Answer:
240minutes
Step-by-step explanation:
She has 4 hours and 1 hour = 60minutes
so 4x60=240minutes
Answer:
2.84
Step-by-step explanation:
Recognize that 252 = 7*36
and so:
log base 7 of 252 = log base 7 of 36 + log base 7 of 7, or
log base 7 of 36 + 1
So the most you can simplify log base 7 of 252 is to write 1 + log base 7 of 36.
Or, if you want to use the change of base formula, you could do the following:
log 36
log base 7 of 36 = -------------- = 1.84
log 7
and so log base 7 of 252 would come out to
1 + log base 7 of 36 = 1 + 1.84 = 2.84
Check: does 7^2.84 = 252? YES. So we know that:
1 + log base 7 of 36 = 2.84