Answer:
34.4
Step-by-step explanation:
Using Triangle Sum Theory, you see that the triangles are similar. They have the same angle measurements. That means their corresponding sides are proportional.
=
=
Cross multiply
14(27) = 11(PQ)
378 = 11(PQ)
= PQ
PQ = 34.4
Answer:
(2,√21)
Step-by-step explanation:
The circle centered at the origin has equation:
Any point that satisfies this equation lie on this circle.
When x=2, we substitute and solve for y.
Take square root to get:
Therefore (2,-√21) and (2,√21) are on this circle.
From the options, (2,√21) is the correct answer
By some properties of logarithms, rewrite the equation as
so that
(<em>a</em> - 2<em>b</em>)² = <em>ab</em>
Expand the left side:
<em>a</em> ² - 4<em>ab</em> + 4<em>b</em> ² = <em>ab</em>
Rearrange terms to get a quadratic equation in <em>a</em>/<em>b</em> :
<em>a</em> ² - 5<em>ab</em> + 4<em>b</em> ² = 0
<em>b</em> must be greater than 0, otherwise log(<em>b</em>) doesn't exist, and the same goes for <em>a</em>. So we can divide by <em>b</em> ² to get
<em>a</em> ²/<em>b</em> ² - 5<em>a</em>/<em>b</em> + 4 = 0
Factorize and solve for <em>a</em>/<em>b</em> :
(<em>a</em>/<em>b</em> - 4) (<em>a</em>/<em>b</em> - 1) = 0
==> <em>a</em>/<em>b</em> = 4 or <em>a</em>/<em>b</em> = 1
However, if <em>a</em>/<em>b</em> = 1, then <em>a</em> = <em>b</em> makes <em>a</em> - 2<em>b</em> = -<em>b</em>. But we must have <em>b</em> > 0, so we omit the second solution and end up with
<em>a</em>/<em>b</em> = 4