Answer:2/3 or .666666
Step-by-step explanation:
The dilation is a contraction
Answer:
Step-by-step explanation:
integral(x/(1+x^2)^2)dx
=(1/2)integral(2x/(1+x^2)^2)dx
=(1/2)[-1/(1+x^2)] +c
<span>(1 + cos² 3θ) / (sin² 3θ) = 2 csc² 3θ - 1
Starting with the left: Note that cos²θ + </span><span>sin²θ = 1.
In the same way: </span><span>cos²3θ + <span>sin²3θ = 1
</span></span>Therefore cos²3θ = 1 - <span>sin²3θ
</span> From the top: (1 + cos² 3θ) = 1 + 1 - sin²3θ = 2 - <span>sin²3θ
</span>
(1 + cos² 3θ) / (sin² 3θ) = (<span>2 - sin²3θ) / (sin² 3θ) = 2/</span><span>sin² 3θ - </span><span>sin²3θ/</span>sin²3θ
= 2/<span>sin² 3θ - 1; But 1/</span><span>sinθ = csc</span><span>θ, Similarly </span>1/sin3θ = csc3θ
= 2 *(1/sin<span>3θ)² - 1</span>
= 2csc²3θ - 1. Therefore LHS = RHS. QED.
<span>1/2-(5/4) = x+1/4 // - x+1/4
1/2-x-(5/4)-(1/4) = 0
1/2-x-5/4-1/4 = 0
-x-1 = 0 // + 1
-x = 1 // * -1
x = -1
x = -1
</span>
