2an^2-1
I think I calculated the product
I don't usually do calculus on Brainly and I'm pretty rusty but this looked interesting.
We have to turn K into the limits of integration on our integrals.
Clearly 0 is the lower limit for all three of x, y and z.
Now we have to incorporate
x+y+z ≤ 1
Let's do the outer integral over x. It can go the full range from 0 to 1 without violating the constraint. So the upper limit on the outer integral is 1.
Next integral is over y. y ≤ 1-x-z. We haven't worried about z yet; we have to conservatively consider it zero here for the full range of y. So the upper limit on the middle integration is 1-x, the maximum possible value of y given x.
Similarly the inner integral goes from z=0 to z=1-x-y
We've transformed our integral into the more tractable

For the inner integral we get to treat x like a constant.

Let's expand that as a polynomial in y for the next integration,

The middle integration is



Expanding, that's

so our outer integral is

That one's easy enough that we can skip some steps; we'll integrate and plug in x=1 at the same time for our answer (the x=0 part doesn't contribute).


That's a surprise. You might want to check it.
Answer: 0
Answer:
y = 12
Step-by-step explanation:
y = 8 is the equation of a horizontal line, parallel to the x- axis.
Thus a parallel line will also be horizontal.
The equation of a horizontal line is
y = c
where c is the y- coordinates of the points it passes through.
The line passes through (- 6, 12) with y- coordinate of 12, thus
y = 12 ← equation of parallel line
Answer:
$4.86
Step-by-step explanation:
2.97/11 =.27 .27 x 18= 4.86
Answer:
Short-Term investment: 5000$
Intermediate-Term investment: 65000$
Long-Term investment: 30000$
Step-by-step explanation:
To construct our first equation lets define sort-term bond investment as x, long-term investment as y.
So the equation is:

From the equation it is found that:

Instead of y, if we put 25000+x the equation will be as following:

From the equation it is found that:

Short-Term investment is 5000$

Long-Term investment is 30000$
Rest of the money is Intermediate-Term investment 65000$