The answer is abd with 170. you gotta set all those angles sum as 540 wich is the sum of the angles for a pentagon. if you do that and solve for x=28 plug 28 in for 6x+2 you end up with 170
Answer:
4.8 x 10⁷
Step-by-step explanation:
Refer to attachment.
<em>Hope</em><em> </em><em>it</em><em> </em><em>helps</em><em>.</em>
Answer:
The equation is y = -2/5x + 4
Step-by-step explanation:
First we have to find the slope of the line. In order to do so, solve the first equation for y.
2x + 5y = 20
5y = -2x + 20
y = -2/5x + 4
This gives us a slope of -2/5. Given that information, we now can plug the slope and point into point-slope form and get the final equation.
y - y1 = m(x - x1)
y - 6 = -2/5(x - -5)
y - 6 = -2/5(x + 5)
y - 6 = -2/5x - 2
y = -2/5x + 4
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