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
Amount which is closest to the total balance of these two accounts at the end of the second year is $882.08
If a is the original area we can say that:
a+24=x^2+11x+24
a=x^2+11x now we have the original area which when factored gives you the dimension of the original flower bed
x(x+11)
So the dimensions were x by x+11
Answer: Choice A) 66 degrees
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Minor arc AB (marked in red in the attached diagram) is 45 degrees
Minor arc BE (marked in blue in the same diagram) is 87 degrees
Add the two arcs: 45+87 = 132
Then cut this value in half to get the inscribed angle ADE
132/2 = 66
We cut it in half due to the inscribed angle theorem
Notice how angle ADE cuts off arc ABE (which is composed of minor arc AB and and minor arc BE)