Answer:
The time taken for the flare to hit the ground is approximately 10.7 seconds.
Step-by-step explanation:
Given : Suppose a flare is shot from the top of a 120 foot building at a speed of 160 feet per second. The equation 
models the h height at t seconds of the flare.
To find : How long will it take for the flare to hit the ground?
Solution :
The equation models the h height at t seconds of the flare.
The flare to hit the ground when h=0.
Substitute in the equation,
Applying quadratic formula, 
Where, a=-16, b=160 and c=120
Reject the negative value.
Therefore, the time taken for the flare to hit the ground is approximately 10.7 seconds.
Answer:
1428 in³
Step-by-step explanation:
To find the volume of this figure, we will need to use two formulas. The volume of a Rectangular Prism (
) and volume of a triangular prism. 
If we look at the Rectangular Prism, we can find that l = 17, w = 8, and h = 5. Multiply these to find the volume:
17 × 8 × 5 = 680 in³.
Solving for the triangular prism gives us:
A = 1/2 (11 × 8 × 17)
A = 748.
Add these two volumes to find the volume of the composite figure:
748 + 680 = 1428 in³
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: I-
ok
Step-by-step explanation:
follow me on tktk
charlidamelio
Answer:
Angle UST= 180
Step-by-step explanation:
Im not so sure but angle U= 25 degrees+ angle S=95 degrees+ angle T=60 degrees. Dont rely on me too much I'm only a middle school kid that got put in a highschool course for some apparent reason.
