Answer:0.0
Step-by-step explanation:
Answer: w = 13 m, L = 19.5 m
<u>Step-by-step explanation:</u>
P = 3w + 2L
3w + 2L = 78
2L = 78 - 3w
![L=\dfrac{78-3w}{2}](https://tex.z-dn.net/?f=L%3D%5Cdfrac%7B78-3w%7D%7B2%7D)
A = w · L
![A=w\bigg(\dfrac{78-3w}{2}\bigg)\\\\\\A=\bigg(\dfrac{78w-3w^2}{2}\bigg)\\\\\\A=39w-\dfrac{3}{2}w^2\\\\\\0=-\dfrac{3}{2}w^2+39w-A](https://tex.z-dn.net/?f=A%3Dw%5Cbigg%28%5Cdfrac%7B78-3w%7D%7B2%7D%5Cbigg%29%5C%5C%5C%5C%5C%5CA%3D%5Cbigg%28%5Cdfrac%7B78w-3w%5E2%7D%7B2%7D%5Cbigg%29%5C%5C%5C%5C%5C%5CA%3D39w-%5Cdfrac%7B3%7D%7B2%7Dw%5E2%5C%5C%5C%5C%5C%5C0%3D-%5Cdfrac%7B3%7D%7B2%7Dw%5E2%2B39w-A)
a=-3/2 b=39
![\text{Axis of Symmetry}:w=\dfrac{-b}{2a}=\dfrac{-39}{2(-\frac{3}{2})}=\dfrac{-39}{-3}=\large\boxed{13}](https://tex.z-dn.net/?f=%5Ctext%7BAxis%20of%20Symmetry%7D%3Aw%3D%5Cdfrac%7B-b%7D%7B2a%7D%3D%5Cdfrac%7B-39%7D%7B2%28-%5Cfrac%7B3%7D%7B2%7D%29%7D%3D%5Cdfrac%7B-39%7D%7B-3%7D%3D%5Clarge%5Cboxed%7B13%7D)
![\text{Maximum}:L=\dfrac{78-3w}{2}=\dfrac{78-3(13)}{2}=\dfrac{78-39}{2}=\dfrac{39}{2}=\large\boxed{19.5}](https://tex.z-dn.net/?f=%5Ctext%7BMaximum%7D%3AL%3D%5Cdfrac%7B78-3w%7D%7B2%7D%3D%5Cdfrac%7B78-3%2813%29%7D%7B2%7D%3D%5Cdfrac%7B78-39%7D%7B2%7D%3D%5Cdfrac%7B39%7D%7B2%7D%3D%5Clarge%5Cboxed%7B19.5%7D)
Let's say that:
y=(2n-8)
y+8=2n
(y+8)/2=n
then switch the variables
(n+8)/2
Answer:
I think 9.3 but I ain't sure
Answer:
As per the statement:
Elizabeth claims that the fourth root of 2 can be expressed as 2^m
"fourth root of 2" means ![\sqrt[4]{2} = 2^{\frac{1}{4}}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B2%7D%20%3D%202%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D)
then;
![2^{\frac{1}{4}} = 2^m](https://tex.z-dn.net/?f=2%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%20%3D%202%5Em)
On comparing both sides we get;
![m = \frac{1}{4}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B1%7D%7B4%7D)
Since, it is also given:
![(2^m)^n = 2](https://tex.z-dn.net/?f=%282%5Em%29%5En%20%3D%202)
Solve for n;
![(2^{\frac{1}{4}})^n = 2^{\frac{n}{4}}](https://tex.z-dn.net/?f=%282%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%29%5En%20%3D%202%5E%7B%5Cfrac%7Bn%7D%7B4%7D%7D)
then;
![2^{\frac{n}{4}} =2^1](https://tex.z-dn.net/?f=2%5E%7B%5Cfrac%7Bn%7D%7B4%7D%7D%20%3D2%5E1)
On comparing both sides we get;
![\frac{n}{4} = 1](https://tex.z-dn.net/?f=%5Cfrac%7Bn%7D%7B4%7D%20%3D%201)
Multiply 4 both sides we get;
n = 4
Therefore, value of m and n are
and 4