Answer:
Step-by-step explanation:
Answer:
10.5
Step-by-step explanation:
You can use ratios to solve this problem.
The original dimensions of the photo is
5 in. by 7 in.
This can be written as:
5:7
And the next is 7.5:?
Then you can use ratios to solve this.
5:7=
7.5:?
5*1.5=7.5 so you can multiply the other side by the same thing. 7*1.5=10.5
The width is 10.5 inches.
0.98 . Z z. ...... z .. .
The answer you are looking for is x=-2.
Solution/Explanation:
Writing out the equation
3[-x+(2x+1)]=x-1
Simplifying inside of the brackets first
Combining like terms, since -x+2x=x
3(x+1)=x-1
*You can remove the parenthesis, if preferred.
Using the Distributive Property on the left side of the equation
3x+3=x-1
Now, subtracting the "x" variable from both sides
3x+3-x=x-x-1
"x-x" cancels out to 0.
3x+3-x=-1
Combining like terms and simplifying
3x-x+3=-1
2x+3=-1
Subtracting 3 from both sides of the equation
2x+3-3=-1-3
"3-3" cancels out to zero.
2x+0=-1-3
2x=-1-3
Simplifying the right side of the equation
2x=-4
Finally, dividing both sides by 2
2x/2=-4/2
Simplifying the final part of the problem
Since 2x/2=x and -4/2=-2
x=-2
So, therefore, the final answer is x=-2.
Hope that this has helped you. Good day to you.
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
