Answer: No
Step-by-step explanation: First, we need to understand that parallel lines are coplanar lines that do not intersect. On the other hand, perpendicular lines are lines that intersect at a right angle.
However, lines can't be both parallel and perpendicular because they either intersect each other at a right angle or never intersect.
So no, two lines can't be both parallel and perpendicular.
Answer:
6x^8y^5
Step-by-step explanation:
(3)(2)= 6
add the exponents for the variables
The answer is that there are more particles in 1 cubic cm. this is because within 1 cubic cm lead has 11.3g in compared to the 2.6 glass has. m/v= density. divide the masses over the volume and that will prove your answer.
Part A : 60miles would represent 4.8 inches
Part B : 1/4 inch would represent 3 and 1/8 miles
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
