The function in variable w giving the cost C (in dollars) of constructing the box is C(w) = 30w² + 270/w. The result is obtained by using the formula of volume and area of the box.
<h3>How to determine the function?</h3>
We have a rectangular storage container without a lid.
- Volume, V = 10 m³
- Length, l = 2w
- Width, w = w
- Base costs $15/m²
- Sides costs $9/m²
The formula of volume of the box is
V = l × w × h
Where
- l = length
- w = width
- h = height
So, the height is
10 = 2w × w × h
10 = 2w² × h
h = 10/2w²
h = 5/w²
To find the total cost, calculate the area of base and sides of the box!
See the picture in the attachment!
The base area is
A₁ = 2w × w = 2w² m²
The sides area is
A₂ = 2(2wh + wh)
A₂ = 2(3wh)
A₂ = 6wh
A₂ = 6w(5/w²)
A₂ = 30/w m²
The total cost is
C = $15(2w²) + $9(30/w)
C = $30w² + $270/w
The function of the total cost is
C(w) = 30w² + 270/w
Hence, the function of constructing the box is C(w) = 30w² + 270/w.
Learn more about function of area here:
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It is A. We have a ratio of
900 workers : 3.2×10⁵
Dividing by 9×10² becomes
1 worker :
×10³
3.2/9 is just 0.36 rounded so it is
1 worker : 0.36×10³
or A
Answer:
Approximately 1.9 seconds (correct to nearest tenth)
Step-by-step explanation:
Looks like the function is d = -16t^2 + 55 ( you left out the t)
The answer is the value of t when d = 0 so we have the equation:-
0 = -16t^2 + 55
16t^2 = 55
t^2 = 55/16
t = sqrt (55/16)
= 1.85 seconds
Answer:
Second choice:
Fifth choice:
Step-by-step explanation:
Let's look at choice 1.
I'm going to subtract 1 on both sides for the first equation giving me 
. I will replace the 
in the second equation with this substitution from equation 1.
Expand using the distributive property and the identity 
:
So this not the desired result.
Let's look at choice 2.
Solve the first equation for by dividing both sides by 2:
.
Let's plug this into equation 2:
This is the desired result.
Choice 3:
Solve the first equation for by adding 3 on both sides:
.
Plug into second equation:
Expanding using the distributive property and the earlier identity mentioned to expand the binomial square:
Not the desired result.
Choice 4:
I'm going to solve the bottom equation for since I don't want to deal with square roots.
Add 3 on both sides:
Divide both sides by 2:
Plug into equation 1:
This is not the desired result because the 
variable will be squared now instead of the 
variable.
Choice 5:
Solve the first equation for by subtracting 1 on both sides:
.
Plug into equation 2:
Distribute and use the binomial square identity used earlier:
.
This is the desired result.
