Solve for <em>x</em> when √(<em>x</em> ² - 4) = 1 :
√(<em>x</em> ² - 4) = 1
<em>x</em> ² - 4 = 1
<em>x</em> ² = 5
<em>x</em> = ±√5
We're looking at <em>x </em>≤ 0, so we take the negative square root, <em>x</em> = -√5.
This means <em>f</em> (-√5) = 1, or in terms of the inverse of <em>f</em>, we have <em>f</em> ⁻¹(1) = -√5.
Now apply the inverse function theorem:
If <em>f(a)</em> = <em>b</em>, then (<em>f</em> ⁻¹)'(<em>b</em>) = 1 / <em>f '(a)</em>.
We have
<em>f(x)</em> = √(<em>x</em> ² - 4) → <em>f '(x)</em> = <em>x</em> / √(<em>x</em> ² - 4)
So if <em>a</em> = -√5 and <em>b</em> = 1, we get
(<em>f</em> ⁻¹)'(1) = 1 / <em>f '</em> (-√5)
(<em>f</em> ⁻¹)'(1) = √((-√5)² - 4) / (-√5) = -1/√5
The sign must be negative; see the attached plot, and take note of the negatively-sloped tangent line to the inverse of <em>f</em> at <em>x</em> = 1.
Answer:
43 questions in total
Step-by-step explanation:
the original equation with the unknown (total number of questions on the test) will look like this
we know this because to work out a percentage in the 1st place you need the total ÷ number (in this case it's ÷ how many questions out of the total she did answer)
now you rearrange.
you need to move the 24 to get the total on it's own here's how you do it
what you do to one side of equation you have to do to the other. the 24 and 24 on the left will cancel because 24÷24=1 and we don't write
got mum of Q's x 1= 80 x 24
now you convert % to decimal
replace
now you take the original and + the 19
therefore there are a total of 43 questions on the exam
Answer:
D. unfavorable fixed overhead flexible minus budget variance
Step-by-step explanation:
As the cost of the equipment is increasing the fixed efficiency and idle capacity variance would be unfavorable resulting in an unfavorable fixed overhead flexible minus budget variance.
The expenses of the machinery are the fixed indirect costs which result in fixed overhead variances. Since it is related to the working of the machinery it would result in efficiency and idle capacity variances that in turn would give unfavorable fixed overhead of the flexible minus budget variance.
Answer:
Yes
408 days
Step-by-step explanation:
The LCM is 408
= 408 days
