Answer:
x=21.
Step-by-step explanation:
First you distribute 3 to the parenthesis. You should get 3x-21=42 at this point. Then you add 21 to 42 to get 63. Here you should be at 3x=63. Divide 63 by 3 to get x=3
Answer:
B. -500
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
Paper he needs = total surface area
So to break it down into 2D shapes, that prism has 2 2D triangles, and 3 2D rectangles of different sizes.
The triangles are the same size, since you have 2, just multiply 2 by the formula for the area of a triangle: 1/2(base)(height) which is 2x1/2(5)(12) = 60
Next you'll need the area of all the rectangles: length x width. which would be (5 x 5) + (13 x 5) + (12 x 5) = 150
So the total amount of wrapping paper he'd need is 150mi^2
The ordered pair would be (-5,8)
