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Crazy boy [7]
3 years ago
12

An open box will be made from a rectangular piece of cardboard that is 8 in. by 10 in. The box will be cut on the dashed red lin

es, removing the corners, and then folded up on the dotted lines. What is the MAXIMUM possible volume for the box?
A) 1.5 in3
B) 5.8 in3
C) 52 in3
D) 64 in3
Mathematics
1 answer:
ANEK [815]3 years ago
4 0
The correct answer is this one: "<span>C) 52 in3."
</span>
Given the illustration, we can be able to know the dimensions of the formed box.

The dimensions are
Length: 10 - 2x
Width: 8 - 2x
Height: x

So the volume is
Volume = (10-2x) * (8-2x) * (x)
Let x = 2.5
Volume = (5) * (3) * (2.5) = 37.5
Let x = 2
Volume = (6) * (4) * (2) = 48
Let x = 1.5
Volume = (7) * (5) * (1.5) = 52.5
Let x = 1
<span>Volume = (8) * (6) * (1) = 48
</span>Let x = 0.5
<span>Volume = (9) * (7) * (.5) = 31.5
</span>
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3 years ago
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Answer:

1. \frac{\sqrt{13} }{3}

2. 3.2362

3. \frac{60}{11}

Step-by-step explanation:

1.

Cot is the trigonometric ratio defined by "adjacent" over "opposite". <em>So, adjacent = 2 and opposite = 3.</em>

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<em />

<em>First answer choice is right.</em>

<em />

2.

By definition, Csc \theta is the inverse of Sine \theta. <em>If given the value of sin theta, to find value of csc theta, we take the reciprocal of it. Hence:</em>

Csc\theta=\frac{1}{0.3090}\\=3.2362

Third answer choice is right.

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By definition tan and cot are inverse of each other. <em>So the value of tan is the reciprocal of the value of cot.</em> We can simply "flip" the value of tan theta to get the value of cot theta. Hence:

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Third answer is right.

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