Sin(8x)cos(x) - cos(8x)sin(x)
identity being used: -cos(s)sin(t) + cos(t)sin(s) = sin(s-t)
sin(8x)cos(x) - cos(8x)sin(x) --> simplified = sin(8x-x)
sin(8x-x) is simplified to --> sin (7x)
sin(8x)cos(x) - cos(8x)sin(x) = sin(7x)
Answer: The width is 
+ 1x -4
Step-by-step explanation:
We know to find the perimeter we have to add the distance around the rectangle.The distance can also be sought as 2 times the length plus times the width.
So as a formula is like P = 2l + 2w where P is the perimeter.
We are given the perimeter so we can plot it into the formula and also plot in the length because it says the length is 3x -1
+8x - 10 = 2(3x -1) + 2w Now we have to solve for w .Break it down
( + 8x -10) = (6x -2 )+ 2w subtract 6x - 2 from both sides
( + 8x -10) - (6x -2) = 2w
( + 2x -8) = 2w now divide both sides by 2
One the left side factor the numerator
= w Now multiply both sides by 2
w =( + 1x-4 )
The width is x^2 + 1x -4
3. g(x) = (x+2)/ |x+2| the denominator cannot be 0
|x+2| cannot be 0
x cannot equal -2
Domain all real numbers but -2
g(-1) = (-1+2)/ |-1+2| = 1/|1| = 1
4. h(x) = (x-4)/(x^2+5x-36)
factor the denominator
h(x) = (x-4)/(x+9) (x-4) the denominator cannot be zero do not cancel, this is a hole
x+9 cannot equal zero so x cannot equal -9
x-4 cannot equal 0 so x cannot equal 4
Domain all real numbers but -9 and 4
h(-1) = (-1-4)/((-1)^2+5(-1)-36) = -5/(1-5-36) = -5/-40 = 1/8
Two distinct real solutions
The fence should be measured in just feet
the answer is B. ft.
