Answer:
x + 3
Step-by-step explanation:
if x represents a number then 3 more than the number means addition of 3 to the number ( x )
so, required phrase is ;
=》x + 3
The mathematical term for a set<span> of </span>ordered pairs<span> is a </span>relation<span>. A </span>relation<span> is any </span>set <span>of </span>ordered pairs<span>. The </span>set of all<span> first </span>components<span> of the </span>ordered pairs<span> is called the domain of the </span>relation<span>, and the </span>set of all second components<span> is called the range of the </span>relation<span>.
I hope my answer helped you.</span>
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:
Step-by-step explanation:
we have
step 1
Exchange x for y and y for x
step 2
isolate the variable y
take the square root both sides
step 3
Let
----> equation of the inverse
Answer:
z=4/3
z=-1/3
Step-by-step explanation:
|6z-3|=5
1. 6z-3=5 6z=8 z=4/3
2. 6z-3=-5 6z=-2 z=-1/3
