To express
5
−
2
as a positive exponent we will use this rule of exponents:
x
a
=
1
x
−
a
5
−
2
=
1
5
−
−
2
=
1
5
2
A= 2 WL+ 2 LH+ 2 HW.
W= width
L= length
H= height
![4*e^{2x} -3 = 12](https://tex.z-dn.net/?f=%204%2Ae%5E%7B2x%7D%20-3%20%3D%2012%20)
Step 1:
Here we have -3 in subtraction on the left side, so when we take it to the right we apply opposite operation of subtraction that is addition.
![4*e^{2x} = 12+3](https://tex.z-dn.net/?f=%204%2Ae%5E%7B2x%7D%20%3D%2012%2B3%20)
![4*e^{2x} = 15](https://tex.z-dn.net/?f=%204%2Ae%5E%7B2x%7D%20%3D%2015%20)
Step 2:
Next we have 4 in multiplication on left side, so dividing right side by 4,
![e^{2x} = 15/4](https://tex.z-dn.net/?f=%20e%5E%7B2x%7D%20%3D%2015%2F4%20)
![e^{2x} = 3.75](https://tex.z-dn.net/?f=%20e%5E%7B2x%7D%20%3D%203.75%20)
Step 3:
taking log on both sides
![ln ( e^{2x}) = ln(3.75)](https://tex.z-dn.net/?f=%20ln%20%28%20e%5E%7B2x%7D%29%20%3D%20ln%283.75%29%20)
![{2x} =ln 3.75](https://tex.z-dn.net/?f=%20%7B2x%7D%20%3Dln%203.75%20)
Step 4:
Dividing right side by 2,
x= ln (3.75) /2 = 0.66088
Answer : x = 0.66088..
Answer:
The width of the window should be
and the height of the window should be ![3.8\ ft](https://tex.z-dn.net/?f=3.8%5C%20ft)
Step-by-step explanation:
we know that
The circumference of a semicircle (window) is equal to
![C=\pi r](https://tex.z-dn.net/?f=C%3D%5Cpi%20r)
we have that
![C=12\ ft](https://tex.z-dn.net/?f=C%3D12%5C%20ft)
![\pi=3.14](https://tex.z-dn.net/?f=%5Cpi%3D3.14)
substitute and solve for r
![12=(3.14)r](https://tex.z-dn.net/?f=12%3D%283.14%29r)
![r=12/3.14=3.8\ ft](https://tex.z-dn.net/?f=r%3D12%2F3.14%3D3.8%5C%20ft)
so
the width of the window is equal to the diameter of the semicircle
so
The width of the window should be
and the height of the window should be ![3.8\ ft](https://tex.z-dn.net/?f=3.8%5C%20ft)