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:
$ 63
Step-by-step explanation:
All you have to do is see what point of the line falls right above 7, and then see what number corresponds to that point.
Hope it helped,
BioTeacher101
Answer:
The equation for the number lamps Aladdin have;
2x + 3 = 15
To solve for x;
2x = 15-3
x = 12/2 = 6
Aladdin have 6 lamps earlier.
Step-by-step explanation:
Let x be the number of lamps Aladdin have before;
When Aladdin buys three more lamps and adds to the double of the number of lamps he has, the total number of lamps goes up to 15.
2x + 3 = 15
To solve for x;
2x = 15-3
x = 12/2 = 6
Aladdin have 6 lamps earlier.
You aren't sharing much information (no directions??).
If your triangle is a right triangle AND 5x-1 and 4x+1 represent the lengths of the 2 shortest sides, then the Pyth. Theorem tells us that
(5x-1)^2 + (4x+1)^2 = (hypotenuse length)^2.
We know that this could not be an equilateral triangle, because 5x-1 differs from 4x+1.
This could be an isosceles triangle if the third side were either 5x-1 or 4x+1.
Please be more specific about what you're supposed to do here.