Answer:
the ingegral I=π/4
Step-by-step explanation:
From the integral
I=∫0-1∫0-sqrt(1-y^2) (x^2 + y^2) dxdy
from polar coordinates
r²=x² + y²
then for r=1
√(1- y²) = x
for y=1 → x=0 , for y=0 → x=1
then the integration area is a hemisphere or radius r=1
therefore
I= ∫0-1∫0-sqrt(1-y^2) (x^2 + y^2) dxdy = (1/2)∫2π-0 ∫1-0 r² *r drdθ ( the additional r is due to the Jacobian of the transformation to polar coordinates , 1/2 because is an hemisphere so it would be the half of the value of the total sphere)
I= (1/2)∫2π-0 ∫1-0 r³drdθ = (1/2)∫2π-0 (1⁴/4 - 0⁴/4) dθ = (1/2)∫2π-0 (1/4)*dθ = (1/2)*(1/4)*2π = π/4
Answer:
f is the number that is being hidden
2x is the number u use w/ the alegebra term
Step-by-step explanation:
Answer:
36 numbers
Step-by-step explanation:
Number of digits in a number between 4000 and 5000 = 4
_ _ _ _
First digit of the number will be filled by 4.
So, the number of ways to fill the first digit = 1
4 _ _ _
If the given number is divisible by 5 then the last digit should be 5.
4 _ _ 5
So, the number of ways that the last digit should be 5 is = 1
Remaining 2 digits between 4 and 5 can be filled by any number given.
Therefore, number of ways that second place can be filled = 6
Similarly, number of ways that the third place of the number can be filled = 6
Now total number of ways = 1 × 6 × 6 × 1
= 36
Therefore, numbers between 4000 and 5000, divisible by 5 = 36
-15+11=-4 so Maggie has -4 in her account
