Well first, you have to know the distance formula. You plug the coordinates into it and you get the answer.
√1² + -7² = d
d = 7.1
Answer: B. same distance
There is the same distance between the point on the preimage to the center of rotation and that of the distance from the corresponding point on the image to the center of rotation. There is change in the distance of the two.
Assuming x = 1 and is not any other value. I will answer two of those and leave one of them to you.
1:
tan<span>(<span>1+540</span>)</span><span><span>
</span></span><span>0.754012
3:
</span><span><span>5<span>(<span>cos<span>(1)</span></span>)</span></span>+<span>3<span>(<span>cos<span>(<span>−1</span>)</span></span>)
</span></span></span><span><span>4.322418</span></span>
Answer:
You know that if f(x) = 1/(x²+1) then F(x)=arctan(x).
What is arctan(x) function? It is inverse function of tan(x) in tge range (-π/2, π/2).
So if tan(x) = y then x = arctan(y)
therefore arctan(-1) = -π/4 because tan(-π/4)=-1 and arctan(1)=π/4 because tan(π/4) = 1.
In conclusion:
integral (dx/(x²+1)) from -1 to 1 =
= F(1) - F(-1) = arctan(1) - arctan(-1) =
=π/4-(-π/4)=π/4+π/4 = π/2.
answer B is correct
Since we cannot divide by zero, x=0 is forbidden, and x=0 is the vertical asymptote of this function.