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Galina-37 [17]
3 years ago
5

A rectangular piece of tin has an area of 1056 square inches. A square of 3 inches is cut from each corner, and an open box is m

ade by turning up the ends and sides. If the volume of the box is 2052 cubic inches, what were the original dimensions of the piece of tin. PLEASE SHOW WORK
Mathematics
1 answer:
kvv77 [185]3 years ago
8 0

Answer:

44 inches and 24 inches

Step-by-step explanation:

Let l,b denotes length and breadth of a rectangle.

lb=1056

A square of 3 inches is cut from each corner, and an open box is made by turning up the ends and sides.

New length =l-6 inches

New breadth =b-6 inches

Height of box =3 inches

Volume of box = length × breadth × height

(l-6)(b-6)3=2052

lb-6l-6b+36=684\\6(l+b)=408\\l+b=68\\b=68-l

Put b=68-l in lb=1056

l(68-l)=1056\\l^2-68l+1056=0\\l^2-44l-24l+1056=0\\l(l-44)-24(l-44)=0\\(l-24)(l-44)=0\\l=24,44

At l=24,b=\frac{1056}{24}=44 inches

At l=44,b=\frac{1056}{44}=24 inches

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Answer: the tuition in 2020 is $502300

Step-by-step explanation:

The annual tuition at a specific college was $20,500 in 2000, and $45,4120 in 2018. Let us assume that the rate of increase is linear. Therefore, the fees in increasing in an arithmetic progression.

The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + (n - 1)d

Where

a represents the first term of the sequence.

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From the information given,

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The fee in 2018 is the 19th term of the sequence. Therefore,

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Therefore,

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Therefore, an

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Therefore, at 2020,

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3 years ago
Round your answer to this problem to the nearest degree.
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