Answer:
1.15x + 0.35x = 22.50
Step-by-step explanation:
Let x = number of days
If:
- DVD incurs an overdue fine of $1.15 per day
- book occurs an overdue fine of $0.35 per day
- total fine = $22.50
1.15x + 0.35x = 22.50
Answer:
10
Step-by-step explanation:
1. The area of triangle is = (A*h)/2, where h is the height grounded on side A.
2. Given the height 5 and the side 4 we get S(area)=(5*4)/2=10.
The volume, surface area and the ratios of the SA to volume will be as follows:
Volume=πr²h
Area=2πr²+πdh
Ratio of SA to volume=Area/volume
π=3.14
Thus using the above formula:
1.
a]
Radius: 3 inches
Height: 2 inches
Volume=πr²h
volume=π×3²×2=56.52 in³
b]
Area=2πr²+πdh
2×π×3²+π×2×3×2
=56.55+37.68
=94.23 in²
c]
Ratio=area/volume
=94.23/56.52
=1.6672
1.
Radius: 2 inches
Height: 9 inches
a]
V=πr²h
V=3.14*2^2*9
V=113.04 in³
b]
Area=2πr²+πdh
=2*3.14*2^2+3.14*2*2*9
=25.12+113.04
=138.16 in²
c]
Ratio=area/volume
=138.16/113.04
=11/9
3.
Diameter=4 inches
Height= 9 inches
a]
V=πr²h
V=3.14×2²×9
V=113.04
b]
Area=2πr²+πdh
=2*3.14*2^2+3.14*4*9
=25.12+113.04
=138.16 in²
c]
Ratio=area/volume
=138.16/113.04
=11/9
4]
Diameter: 6 inches
Height: 4 inches
a]
Volume=πr²h
=3.14×3²×4
=113.04 in³
b]
Area=2πr²+πdh
=2×3.14×3²+3.14×6×4
=56.52+75.36
=131.88 in²
c] Ratio
131.88/113.04
=7/6
1. For the surface area to volume to be small it means that the area is smaller than the volume, for surface area to volume be larger it means that the surface area is larger than the volume. It is more economical for the surface area to volume to be small because it will mean that small amount of materials make cans with large volume. This means cost of production is cheaper.
2. To evaluate this process let's use one of the dimensions:
Radius: 3 inches
Height: 2 inches:
i. add radius and height:
3+2=5 inches
ii. Multiply radius and height:
3×2=6
iii. Dividing the result from step 1 by the result in step 2:
5/6
iv. Multiply the result from step 3 by 2:
5/6×6
=5
This result does not seem to add up to the result in our earlier ratio. Thus we conclude that Khianna was wrong. This method can't work with 3-D figures.
Use distributive property: a(b + c) = ab + ac
x(2x + 3) = (x)(2x) + (x)(3) = 2x² + 3x
Let x ft be the length of the base square and y ft be the height of the box.
The volume of the box is
Since the box has a volume of 15 cubic feet, then
You need to construct two squares from the metal that cost $3 per square foot.
The area of each square is 
and the total cost for these two squares is 
The area of each side face is 
Then the total cost for sides is 
Let S(x) be the function that represents total cost of the box, then
Find the derivative:
When 
then ![12x-\dfrac{600}{x^2}=0,\\ \\12x^3=600,\\ \\x^3=50,\\ \\x=\sqrt[3]{50}\ ft.](https://tex.z-dn.net/?f=12x-%5Cdfrac%7B600%7D%7Bx%5E2%7D%3D0%2C%5C%5C%20%5C%5C12x%5E3%3D600%2C%5C%5C%20%5C%5Cx%5E3%3D50%2C%5C%5C%20%5C%5Cx%3D%5Csqrt%5B3%5D%7B50%7D%5C%20ft.)
The dimensions of the box are:
length and width - ![\sqrt[3]{50}\ ft](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B50%7D%5C%20ft)
height - ![\dfrac{15}{\sqrt[3]{2500}}\ ft.](https://tex.z-dn.net/?f=%5Cdfrac%7B15%7D%7B%5Csqrt%5B3%5D%7B2500%7D%7D%5C%20ft.)
