Consider the system of inequalities

1. Plot all lines that are determined by equalities (see attached diagram)

2. Determine which bounded part of the plane you should select:
means that you should take points with y-coordinates greater than or equal to 2 (top part of the coordinate plane that was formed by the red line);
means that you should take points with x-coordinates less than or equal to 6 (left part of the coordinate plane that was formed by the blue line);- for
you can check where the origin is placed. Since
, the origin belongs to the needed part and you have to take the right part of the coordinate plane that was formed by green line. - for
you can check where the origin is placed. Since
, the origin belongs to the needed part and you have to take the bottom part of the coordinate plane that was formed by orange line.
3. According to the previous explanations, the shaded region is as in A diagram.
Answer: correct choice is A.
Rachel and her sister Fran together can paint the living room in
hours
Given that
Rachel can paint half of the living room in 1 hour
Fran can paint
th part of the living room in 1 hour
Let's assume together they paint the living room in x hours
⇒ together they can paint
th part of the living room in 1 hour
By proportions,
⇒
+
=
{using operation proportions and addition}
⇒
=
⇒x=
⇒ together they can paint
th part of the living room in 1 hour
It means, Rachel and her sister Fran together can paint the living room in
hours
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Answer:
-0.43
Step-by-step explanation:
100/-43
Replace x with π/2 - x to get the equivalent integral

but the integrand is even, so this is really just

Substitute x = 1/2 arccot(u/2), which transforms the integral to

There are lots of ways to compute this. What I did was to consider the complex contour integral

where γ is a semicircle in the complex plane with its diameter joining (-R, 0) and (R, 0) on the real axis. A bound for the integral over the arc of the circle is estimated to be

which vanishes as R goes to ∞. Then by the residue theorem, we have in the limit

and it follows that

T - ( - 10) = 9
t + 10 = 9
t = 9 - 10
t = -1
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Answer: t = -1
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