On a quiz, Tom received 2 points for each correct spelling word, and 4 points for each correct definition, Tom received 80 point
s for a total of 30 correct
responses. The equations and graph below can be used to determine the number of Tom's correct responses, where x represents the number of
correct spelling words and y represents the number of correct definitions.
Correct responses: 2 + y = 30
Total points: 2x + dy = 80
*Graph*
Tom got BLANK words correct and BLANK definitions correct
Words correct
A. 10
B. 20
C. 30
Definitions correct
A. 10
B. 20
C. 30
responses. The equations and graph below can be used to determine the number of Tom's correct responses, where x represents the number of
correct spelling words and y represents the number of correct definitions.
Correct responses: 2 + y = 30
Total points: 2x + dy = 80
*Graph*
Tom got BLANK words correct and BLANK definitions correct
Words correct
A. 10
B. 20
C. 30
Definitions correct
A. 10
B. 20
C. 30
1 answer:
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Answer:
1.81 inch by 8.38 inch by 6.38 inch
Smallest Value=1.81 inch
Largest Value=8.38 inch
Step-by-step explanation:
The cardboard is 12 in. long and 10 in. wide
Let the length of the square cut off=x
Length of the box=12-2x
Width of the box=10-2x
Height of the box=x
Volume of the box=lwh
V=x(12-2x)(10-2x)
The dimensions of the box that will yield maximum volume occurs at the point where the derivative of V=0.
Thus:
4(30-22x+3x²)=0
Since 4≠0
3x²-22x+30=0
Solving for x using a calculator gives:
x=1.81 or x=5.52
x cannot be 5.52 inch since the width is 10 inch and removing 2(5.52) from the width gives a negative result.
When x=1.81 inch
Length of the box=12-2x=12-2(1.81)=8.38inch
Width of the box=10-2x=10-2(1.81)=6.38 inch
Therefore, the dimensions at which the Volume is maximum are: 1.81 inch by 8.38 inch by 6.38 inch