Answer:
Step-by-step explanation:
Let's re-write the equations in order to get the variables as separated in independent terms as possible \:
First equation:
Second equation:
Third equation:
Now let's subtract term by term the reduced equation 3 from the reduced equation 1 in order to eliminate the term that contains "y":
Combine this last expression term by term with the reduced equation 2, and solve for "x" :
Now we use this value for "x" back in equation 1 to solve for "y":
And finally we solve for the third unknown "z":
Answer:
C= 25.12 cm
Step-by-step explanation:
Answer:
the dimensions of the box that minimizes the cost are 5 in x 40 in x 40 in
Step-by-step explanation:
since the box has a volume V
V= x*y*z = b=8000 in³
since y=z (square face)
V= x*y² = b=8000 in³
and the cost function is
cost = cost of the square faces * area of square faces + cost of top and bottom * top and bottom areas + cost of the rectangular sides * area of the rectangular sides
C = a* 2*y² + a* 2*x*y + 15*a* 2*x*y = 2*a* y² + 32*a*x*y
to find the optimum we can use Lagrange multipliers , then we have 3 simultaneous equations:
x*y*z = b
Cx - λ*Vx = 0 → 32*a*y - λ*y² = 0 → y*( 32*a-λ*y) = 0 → y=32*a/λ
Cy - λ*Vy = 0 → (4*a*y + 32*a*x) - λ*2*x*y = 0
4*a*32/λ + 32*a*x - λ*2*x*32*a/λ = 0
128*a² /λ + 32*a*x - 64*a*x = 0
32*a*x = 128*a² /λ
x = 4*a/λ
x*y² = b
4*a/λ * (32*a/λ)² = b
(a/λ)³ *4096 = 8000 m³
(a/λ) = ∛ ( 8000 m³/4096 ) = 5/4 in
then
x = 4*a/λ = 4*5/4 in = 5 in
y=32*a/λ = 32*5/4 in = 40 in
then the box has dimensions 5 in x 40 in x 40 in
Answer:
The answer is 6720
Step-by-step explanation:
(210 x 2) x 2) x 2) x 2) x 2) = 6720
Step by step its:
210 x 2 = 420
420 x 2 = 840
840 x 2 = 1680
1680 x 2 = 3360
3360 x 2 = 6720
Answer: A. 1120 in³
Step-by-step explanation:
the formula for the volume of the pyramid: 
l (length)=16
w (width)=14
h (height)=15
