Answer:
<u>The exponential model is: Cost after n years = 400 * (1 + 0.02)ⁿ</u>
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Cost of the TV set in 1999 = US$ 400
Annual increase rate = 2% = 0.02
2. Write an exponential model to represent this data.
Cost after n years = Cost in 1999 * (1 + r)ⁿ
where r = 0.02 and n = the number of years since 1999
Replacing with the real values for 2020, we have:
Cost after 21 years = 400 * (1 + 0.02)²¹
Cost after 21 years = 400 * 1.5157
Cost after 21 years = $ 606.28
The TV set costs $ 606.28 in 2020.
<u>The exponential model is: Cost after n years = 400 * (1 + 0.02)ⁿ</u>
If we slice this down the middle and fit it together like a puzzle we'll get a rectangle base 9.6/2 and height 4.8+9 so area (9.6/2)(4.8+9) = 66.24 square units.
Choice d
Answer:
The box should have base 16ft by 16ft and height 8ft Therefore,dimensions are 16 ft by 16 ft by 8 ft
Step-by-step explanation:
We were given the volume of the tank as, 2048 cubic feet.
Form minimum weight, the surface area must be minimum.
Let the height be h and the lengths be x
the volume will be: V=x²h then substitute the value of volume, we have
2048=hx²
hence
h=2048/x²
Since the amount of material used is directly proportional to the surface area, then the material needs to be minimized by minimizing the surface area.
The surface area of the box described is
A=x²+4xh
Then substitute h into the Area equation we have
A= x² + 4x(2048/x²)
A= x² + 8192/x
We want to minimize
A
dA/dx = -8192/x² + 2 x= 0 for max or min
when dA/dx=0
dA/dx= 2x-8192/x²=0
2x=8192/x²
Hence
2x³=8192
x³=4096
x=₃√(4096)
X=16ft
Then h=2048/x²
h=2048/16²
h=8ft
The box should have base 16ft by 16ft and height 8ft
Hence the dimensions are 16 ft by 16 ft by 8 ft
Answer:
36 = 2² * 3²
84 = 2² * 3 * 7
Explanation:
Pf of 36 = 2 * 2 * 3 * 3 which then becomes 2 (to the power of 2) times 3 (to the power of 2)
Pf of 84 = 2 * 2 * 3 * 7 which then becomes 2 (to the power of 2) * 3 * 7
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Answer:
4, 6, 8, 10, 30
Step-by-step explanation:
