The number of adults at an amusement park, measured in hundreds of people, is represented by the function a(w)=−0.4w^2+5w+9, whe
re w is the number of weeks since the amusement park opened for the season.
The number of children at the same amusement park, measured in hundreds of people, is represented by the function c(w)=−0.2w^2+9w+12, where w is the number of weeks since the amusement park opened for the season.
What function, f(w) , can be used to determine how many more children than adults are at the amusement park any week during the season?
The number of children at the same amusement park, measured in hundreds of people, is represented by the function c(w)=−0.2w^2+9w+12, where w is the number of weeks since the amusement park opened for the season.
What function, f(w) , can be used to determine how many more children than adults are at the amusement park any week during the season?
1 answer:
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Let's substitute the value of x as 8 in the given equation to find the value of y ~
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.