To approximate the volume with 8 boxes, we have to split up the interval of integration for each variable into 2 subintervals, [0, 1] and [1, 2]. Each box will have midpoint 
that is one of all the possible 3-tuples with coordinates either 1/2 or 3/2. That is, we're sampling 
at the 8 points,
(1/2, 1/2, 1/2)
(1/2, 1/2, 3/2)
(1/2, 3/2, 1/2)
(3/2, 1/2, 1/2)
(1/2, 3/2, 3/2)
(3/2, 1/2, 3/2)
(3/2, 3/2, 1/2)
(3/2, 3/2, 3/2)
which are captured by the sequence
with each of 
being either 1 or 2.
Then the integral of 
over 
is approximated by the Riemann sum,
(compare to the actual value of about 4.159)
Answer:
56
Step-by-step explanation:
Given that Lydia is painting flower vases.
Paint required for painting one flower case = 3/16 quart
total paint available with Lydia = 21/2 quart
We have to find the no of flower cases that can be painted.
This is a problem of direct variation since when no of flower cases increase paint required also increases.
3/16 quart for 1 flower case
Hence 21/2 quart for 21/2 divided by 3/16
= 21*16/(3*2) (by rule for fraction division)
= 7(8)
= 56
You start off with 4*(cos(x+(pi/3)))
Let's place the 4 aside for the time being:
Cos(u+j) = cos(u)*cos(j) - sin(u)*sin(j)
cos(x+(pi/3)) = cos(x)*cos(pi/3) - sin(x)*sin(pi/3)
cos(x+(pi/3)) = cos(x)/2 - (sqrt(3)/2)*sin(x)
Multiplying by the 4 we put aside:
4*cos(x+(pi/3)) = 2*cos(x) - 2*sqrt(3)*sin(x)
The correct answer is B
Answer:
Did you want me to simplify the expression???
Step-by-step explanation:
3f+5b+3d+8
