The answer is > ndjsjdjddh
Answer:
Step-by-step explanation:
Biquadratic Equation
It's a fourth-degree equation where the terms of degree 1 and 3 are missing. It can be solved for the variable squared as if it was a second-degree equation, and then take the square root of the results
Our equation is
If we call 
, our equation becomes a second-degree equation
Dividing by -3
Factoring
It leads to these solutions
Taking back the change of variable, we have for the first solution
Now for the second solution, we get imaginary (complex) values
Summarizing, the four solutions for x are
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
To reduce<span> a </span>fraction to lowest terms<span> (also called its simplest form), divide both the numerator and denominator by the GCD. For example, 2/3 is in </span>lowest<span> form, but 4/6 is not in </span>lowest<span> form (the GCD of 4 and 6 is 2) and 4/6 can be expressed as 2/3.
38/80= 19/40</span>
