Answer:

Step-by-step explanation:
[Most of the work here comes from manipulating the trig to make the term (integrand) integrable.]
Recall that we can express the squared trig functions in terms of cos(2x). That is,

And so inverting these,
.
Multiply them together to obtain an equivalent expression for sin^2(x)cos^2(x) in terms of cos(2x).

Notice we have cos^2(2x) in the integrand now. We've made it worse! Let's try plugging back in to the first identity for cos^2(2x).

So then,

This is now integrable (phew),

Answer:
x = 1/2 x=-5
Step-by-step explanation:
(2x-1)(x+5)=0
Using the zero product property
2x-1 =0 x+5 =0
2x= 1 x = -5
x = 1/2 x=-5
Do a long division
the quotient comes to
5z^2 + 19z - 4
this factors to
(5z - 1)(z + 4)
so factors are (z+3)(z+4)(5z-1)
Answer:
a² + 16a - 612 = 0
Step-by-step explanation:
Here is the complete question :
The width of an extra large rectangle poster is 8 inches more than half its length. The area of this poster is 306 square inches
Write an equation in one variable that could be used to find the number of inches in the dimensions of this poster.
Area of a rectangle = length x width
Let length = a
width = 8 + 1/2a
Area = (8 + 1/2a) x a
306 = (8 + 1/2a) x a
multiply both sides of the equation by 2
612 = 16a + a²
a² + 16a - 612 = 0
the dimensions of the poster can be determined using quadratic formula
The most likely answer is 5/6