What will the 8th term in this pattern?:400, 385, 370, 355, 340
1 answer:
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Answer:
B.
Step-by-step explanation:
To simplify something that looks like you would multiply the top and bottom by the conjugate of the bottom. So you multiply the top and bottom for this problem I just made by:
.
If you had , then you would multiply top and bottom the conjugate of
which is
.
The conjugate of a+b is a-b.
These have a term for it because when you multiply them something special happens. The middle terms cancel so you only have to really multiply the first terms and the last terms.
Let's see:
(a+b)(a-b)
I'm going to use foil:
First: a(a)=a^2
Outer: a(-b)=-ab
Inner: b(a)=ab
Last: b(-b)=-b^2
--------------------------Adding.
a^2-b^2
See -ab+ab canceled so all you had to do was the "first" and "last" of foil.
This would get rid of square roots if a and b had them because they are being squared.
Anyways the conjugate of is
.
This is the thing we are multiplying and top and bottom.
Hi there!
To find the indefinite integral, we must integrate by parts.
Let "u" be the expression most easily differentiated, and "dv" the remaining expression. Take the derivative of "u" and the integral of "dv":
u = 4x
du = 4
dv = cos(2 - 3x)
v = 1/3sin(2 - 3x)
Write into the format:
∫udv = uv - ∫vdu
Thus, utilize the solved for expressions above:
4x · (-1/3sin(2 - 3x)) -∫ 4(1/3sin(2 - 3x))dx
Simplify:
-4x/3 sin(2 - 3x) - ∫ 4/3sin(2 - 3x)dx
Integrate the integral:
∫4/3(sin(2 - 3x)dx
u = 2 - 3x
du = -3dx ⇒ -1/3du = dx
-1/3∫ 4/3(sin(2 - 3x)dx ⇒ -4/9cos(2 - 3x) + C
Combine: