Answer:
m = ![\frac{-1}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7B8%7D)
Step-by-step explanation:
3x + 24y = 24
⇔ 3x + 24y - 3x = 24 - 3x
⇔ 24y = 24 -3x
⇔
Thus,
is the slope of 3x + 24y = 24
Perimeter=2L+2W
L=W+5, substitute in place of 2L
90=2(W+5)+2W
90=2W+10+2W
90-10=4W
80=4W
80/4=W
W=20, if width is 20 than the length is 20+5=25 cm
Answer:
The result of the integral is ![-\frac{\cos^3{10x}}{30} + C](https://tex.z-dn.net/?f=-%5Cfrac%7B%5Ccos%5E3%7B10x%7D%7D%7B30%7D%20%2B%20C)
Step-by-step explanation:
We are given the following integral:
![\int \sin{(10x)}\cos^{2}{(10x)} dx](https://tex.z-dn.net/?f=%5Cint%20%5Csin%7B%2810x%29%7D%5Ccos%5E%7B2%7D%7B%2810x%29%7D%20dx)
I am going to solve by substitution, using
, so
. So, we have
![-\frac{1}{10} \int u^2 du](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B10%7D%20%5Cint%20u%5E2%20du)
Which has the following result:
![-\frac{u^3}{30} + C](https://tex.z-dn.net/?f=-%5Cfrac%7Bu%5E3%7D%7B30%7D%20%2B%20C)
Going back to x, the result of the integral is
![-\frac{\cos^3{10x}}{30} + C](https://tex.z-dn.net/?f=-%5Cfrac%7B%5Ccos%5E3%7B10x%7D%7D%7B30%7D%20%2B%20C)
271%, 2.62, 2 2/5, 2.26, 26.8