If f(x) = -8x – 6 and g(x) = x+8, what is (fºg)(-7)? Enter the correct answer.
1 answer:
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Answer:
Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box has largest volume.
Step-by-step explanation:
Given that,
A box is being created out of a 15 inches by 10 inches sheet of metal.
The length of the one side of the squares which are cut out of the each corners of the metal sheet be x.
The length of the metal box be = (15-2x) inches.
The width of the metal box be =(10-2x) inches
The height of the metal box be =x inches
Then, the volume of the metal box= length×width×height
=(15-2x)(10-2x)x cubic inches
=(150x-50x²+4x³) cubic inches
∴ V= 4x³-50x²+15x
Differentiating with respect to x
V'=12x²-100x+15
Again differentiating with respect to x
V''=24x-100
For maximum or minimum value, V'=0
12x²-100x+15=0
Apply quadratic formula , here a=12, b= -100 and c=15
For x= 8.18, The value of (15-2x) and (10-2x) will negative.
∴x=0.1528 .
Now,
∴At x=0.1528 inch, the volume of the metal box will be maximum.
Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box has largest volume.
Answer:
Where T is the hight temperature and t is the day
Explanation:
The table shows that every day the<em> High temperature, T (degrees F) </em>increases 1 unit.
Then, this is a linear function with slope = 1ºF / day.
You can use the point-slope equation to determine the <em>function of the high temperature:</em>
- Point-slope equation:
- Choose any point from the table and m = 1. I will use the first point (1,95)
- m = 1
- x₁ = 1
- y₁ = 95
Substitute:
Make the variables y = T, and x = t: