Answer:
Step-by-step explanation:
Lines l and m are the parallel lines and 't' is a transversal line,
Therefore, ∠1 ≅ ∠5 [Corresponding angle postulate]
∠5 ≅ ∠7 [Vertical angles theorem]
∠1 ≅ ∠7 [Transitive property]
Therefore, ∠1 ≅ ∠7 [Alternate exterior angles theorem]
Answer:
The bottom one to the right. It only reaches 1000 and no higher
Step-by-step explanation:
Answer:
it would be a 25% increase.
Step-by-step explanation:
15-12 / 12 * 100 =
3/12 * 100 = 25
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
area of rectangle = length x width
this is the formula to find it.
now , put the values of length and width,
=> area= 12 x 3 x 6 x 2
=> area = 432 feet^2
Hope this helps!
