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
It most likely has a 0.3 chance
Answer:88
Step-by-step explanation:
You can simplify -8/-2 its 4 then take 4 to the 3rd power and you'll get 64 the take 3×-2 and you'll get -6 then multiply -6×4 and you'll get -24 then subtract 64 - (-24) which would end up being plus a positive and you'll get 88
Hello!
3/4 = 0.75 as a decimal
We know that Jen picks 0.75 of a gallon of strawberries in half an hour, and now we want to find out how many gallons she'll pick in 2 hours.
Half an hour = 0.5
2 ÷ 0.5 = 4 There are four half hours in 2 hours.
0.75 × 4 = 3
ANSWER:
Jen will have picked 3 gallons of strawberries in 2 hours.
Answer:
3+sqrt(13/2)
3-sqrt(13/2)
Step-by-step explanation:
2 (x-3) ^2 =13
Divide each side by 2
2/2 (x-3) ^2 =13/2
(x-3) ^2 =13/2
Take the square root of each side
sqrt((x-3) ^2) =±sqrt(13/2)
x-3 = ±sqrt(13/2)
Add 3 to each side
x-3+3 = 3±sqrt(13/2)
x = 3±sqrt(13/2)