Answer:
13.425¢ per pencil
Step-by-step explanation:
The per-pencil cost is the total cost divided by the number of pencils.
<h3>Application</h3>
The total cost is the cost for 200 pencils plus the cost for shipping:
total cost = $19.90 +6.95 = $26.85
The cost per pencil is ...
total cost / number of pencils = $26.85 / 200 = $0.13425 = 13.425¢
The average cost per pencil is 13.425 cents.
X = 9.5/19*30=15 i hope it helps
This is the answer y=-4x-4
Answer:
The value of double derivative at x=4.834 is negative, therefore the trough have a maximum volume at x=4.834 inches.
Step-by-step explanation:
The dimensions of given metal strip are
Length = 160 inch
Width = 20 inch
Let the side bend x inch from each sides to make a open box.
Dimensions of the box are
Length = 160-2x inch
Breadth = 20-2x inch
Height = x inch
The volume of a cuboid is
![V=length\times breadth \times height](https://tex.z-dn.net/?f=V%3Dlength%5Ctimes%20breadth%20%5Ctimes%20height)
Volume of box is
![V(x)=(160-2x)\times (20-2x)\times x](https://tex.z-dn.net/?f=V%28x%29%3D%28160-2x%29%5Ctimes%20%2820-2x%29%5Ctimes%20x)
![V(x)=(160-2x)(20-2x)x](https://tex.z-dn.net/?f=V%28x%29%3D%28160-2x%29%2820-2x%29x)
![V(x)=4 x^3 - 360 x^2 + 3200 x](https://tex.z-dn.net/?f=V%28x%29%3D4%20x%5E3%20-%20360%20x%5E2%20%2B%203200%20x)
Differentiate with respect to x.
![V'(x)=12x^2 - 720 x + 3200](https://tex.z-dn.net/?f=V%27%28x%29%3D12x%5E2%20-%20720%20x%20%2B%203200)
Equate V'(x)=0, to find the critical points.
![0=12x^2 - 720 x + 3200](https://tex.z-dn.net/?f=0%3D12x%5E2%20-%20720%20x%20%2B%203200)
Using quadratic formula,
![x=30\pm 10\sqrt{\frac{\left(19\right)}{3}}](https://tex.z-dn.net/?f=x%3D30%5Cpm%2010%5Csqrt%7B%5Cfrac%7B%5Cleft%2819%5Cright%29%7D%7B3%7D%7D)
The critical values are
![x_1=30+10\sqrt{\frac{\left(19\right)}{3}}\approx 55.166](https://tex.z-dn.net/?f=x_1%3D30%2B10%5Csqrt%7B%5Cfrac%7B%5Cleft%2819%5Cright%29%7D%7B3%7D%7D%5Capprox%2055.166)
![x_2=30-10\sqrt{\frac{\left(19\right)}{3}}\approx 4.834](https://tex.z-dn.net/?f=x_2%3D30-10%5Csqrt%7B%5Cfrac%7B%5Cleft%2819%5Cright%29%7D%7B3%7D%7D%5Capprox%204.834)
Differentiate V'(x) with respect to x.
![V'(x)=24x - 720](https://tex.z-dn.net/?f=V%27%28x%29%3D24x%20-%20720)
The value of double derivative at critical points are
![V'(55.166)=24(55.166) - 720=603.984](https://tex.z-dn.net/?f=V%27%2855.166%29%3D24%2855.166%29%20-%20720%3D603.984)
![V'(4.834)=24(4.834) - 720=-603.984](https://tex.z-dn.net/?f=V%27%284.834%29%3D24%284.834%29%20-%20720%3D-603.984)
Since the value of double derivative at x=4.834 is negative, therefore the trough have a maximum volume at x=4.834 inches.
B- x=-9
Y is the dependent variable because it relies on the x variable for the outcome.
Since x is 2 the whole equation is
-14+5 which equals -9