First take note of the domain of <em>f(x)</em> ; the square root term is defined as long as <em>x</em> - <em>x</em> ² ≥ 0, or 0 ≤ <em>x</em> ≤ 1.
Check the value of <em>f(x)</em> at these endpoints:
<em>f</em> (0) = 0
<em>f</em> (1) = 0
Take the derivative of <em>f(x)</em> :
For <em>x</em> ≠ 0, we can eliminate the √<em>x</em> term in the denominator:
<em>f(x)</em> has critical points where <em>f '(x)</em> is zero or undefined. We know about the undefined case, which occurs at the boundary of the domain of <em>f(x)</em>. Check where <em>f '(x)</em> = 0 :
√<em>x</em> (3 - 4<em>x</em>) = 0
√<em>x</em> = 0 <u>or</u> 3 - 4<em>x</em> = 0
The first case gives <em>x</em> = 0, which we ignore. The second leaves us with <em>x</em> = 3/4, at which point we get a maximum of max{<em>f(x) </em>} = 3√3 / 2.
Given:
4log1/2^w (2log1/2^u-3log1/2^v)
Req'd:
Single logarithm = ?
Sol'n:
First remove the parenthesis,
4 log 1/2 (w) + 2 log 1/2 (u) - 3 log 1/2 (v)
Simplify each term,
Simplify the 4 log 1/2 (w) by moving the constant 4 inside the logarithm;
Simplify the 2 log 1/2 (u) by moving the constant 2 inside the logarithm;
Simplify the -3 log 1/2 (v) by moving the constant -3 inside the logarithm:
log 1/2 (w^4) + 2 log 1/2 (u) - 3 log 1/2 (v)
log 1/2 (w^4) + log 1/2 (u^2) - log 1/2 (v^3)
We have to use the product property of logarithms which is log of b (x) + log of b (y) = log of b (xy):
Thus,
Log of 1/2 (w^4 u^2) - log of 1/2 (v^3)
then use the quotient property of logarithms which is log of b (x) - log of b (y) = log of b (x/y)
Therefore,
log of 1/2 (w^4 u^2 / v^3)
and for the final step and answer, reorder or rearrange w^4 and u^2:
log of 1/2 (u^2 w^4 / v^3)
Answer:
Step-by-step explanation:
When y varies directly with x
y=kx x=20 y=-8
k=y/x
k=-8/20
k=-0.4
now when x=-4 find y
y=kx
y=-0.4*-4
y=1.6
She walks 3 mph because when you divide it by 2 it will equal
3 miles in 1 hour
Sorry dude i don’t know this one