<p>Please show how you got to the answer.</p>
<ol>
<li>What is the smallest positive value for (theta) where sin2(theta) reaches its minimum value?</li>
</ol>
<p>(a)- Pi/4
(b)- Pi/2
(c)- 3Pi/4
(d)- Pi
(e)- 3Pi/2</p>
<p>2.In the real numbers, what is the solution of the equation 8^(2x+1)=4^(1-x) ? (for this I got B even though the act booklet says its C)
(a) -1/3
(b) -1/4
(c) -1/8
(d) 0
(e) 1/7</p>
<p>Any help will be much appreciated.
Thanks</p>
<p>We know from the unit circle that the minimum value for sin(x) is -1, which occurs at 3π/2 + 2kπ (where k is any integer.) Since we want the smallest positive value of theta, we conclude 2θ=3π/2 and θ=3π/4. Are those answers choices supposed to be negative, or are you just setting off the letters? I’ll assume it’s the latter, because negative answers make no sense in the context of the question. </p>
<p>You’ll need to rewrite the equations so they have common bases:</p>
<p>2^[3^(2x+1)]=2^[2^(1-x)]</p>
<p>or</p>
<p>2^(6x+3)=2^(2-2x)</p>
<p>We can rewrite as:</p>
<p>6x+3=2-2x</p>
<p>solving for x= -1/8, c.</p>
<p>Thanks aarelle.</p>