Answer:
30
Step-by-step explanation:
TAN (R) = SR / ST
TAN (R) = 2/ 2sqr3
CONVERT OF TAN ^-1 (2 / 2sqr3) = 30
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 equivalent expressions are;
9x + 9
and
9(x + 1)
Step-by-step explanation:
Mathematically, we should understand that an equilateral triangle has all of its sides equal
So if one side is 3x+ 3, the other sides too measures same
Therefore, the length of the rope represents the perimeter of the triangle
This is obtainable by adding all the side lengths together
This will be;
3x + 3 + 3x + 3 + 3x + 3 = 9x + 9
This is also same as 9(x + 1)
Answer:
inequality
Step-by-step explanation:
Answer:
0.35
Step-by-step explanation:
this is the answer.........
