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 D.
Step-by-step explanation:
As was the case in your previous question, this problem involves setting two ratios equal to each other. We call such an equation a proportion.
16 miles = x miles
(1/2) inch 2 3/4 inches
x = (11/4) * 16 = (11/4) * 2 * 16 = 88 miles
(1/2)
Answer:
see explanation
Step-by-step explanation:
Since KL = KM then the triangle is isosceles and the 2 base angles are congruent, that is
∠KLM = ∠KML, thus
y - 9 = x + 4 (add 9 from both sides )
y = x + 13 → (1)
The sum of the 3 angles in the triangle = 180°, thus
x + 4 + y - 9 + x + y + 3 = 180
2x + 2y - 2 = 180 ( add 2 to both sides )
2x + 2y = 182 → (2)
Substitute y = x + 13 into (2)
2x + 2(x + 13) = 182 ← distribute and simplify left side
2x + 2x + 26 = 182
4x + 26 = 182 ( subtract 26 from both sides )
4x = 156 ( divide both sides by 4 )
x = 39
Substitute x = 39 into (1)
y = 39 + 13 = 52
Hence
∠K = x + y + 3 = 39 + 52 + 3 = 94°
Answer:
28/21
Step-by-step explanation:
You would do y1 - y2 for the numerator which gets you 28. Then you would do x1 - x2 for the denominator which gets you 21. The rate of change is also the slope.
Hope this helps!
