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4 years ago

Which box will hold more? Explain.

Mathematics

1 answer:

alexandr402 [8]4 years ago

7 0

Answer:

Box X

Step-by-step explanation:

In order to find which box holds the most material, you have to find the volume of each box.

The formula for volume of a prism (or box) is [area of the base] * height. So, you can solve the problem as follows:

Step 1) Find the area of the base for box X (7 * 3). You can use any side as your base, as long as the opposite side of the shape is congruent (which in this case, it is)

Step 2) Multiply the area of your base (21) times the distance between the opposite congruent side (6). (21 * 6) = 126

Step 3) By repeating this process with box Y, you will find that the volume of box Y (10*11) = 110, which is less than the volume of box X.

Since the volume of box X is greater than that of box Y, box X can hold more material.

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Verify in the following whether g(x) is a factor of p(x)

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$\red{\large\underline{\sf{Solution-i}}}$

Given that,

$\rm \longmapsto\: p(x) = {x}^{4} - {x}^{3} - {x}^{2} - x - 2$

and

$\rm \longmapsto\:g(x) = x - 2$

We know,

Factor theorem states that if g(x) = x - a is a factor of polynomial f(x), then remainder f(a) = 0.

So, using Factor theorem, Consider

$\rm \longmapsto\:p(2)$

$\rm \: = \: {2}^{4} - {2}^{3} - {2}^{2} - 2 - 2$

$\rm \: = \: 16 - 8 - 4 - 4$

$\rm \: = \: 16 - (8 + 4 + 4)$

$\rm \: = \: 16 - 16$

$\rm \: = \: 0$

$\rm\implies \:p(2) \: = \: 0$

So, 

$\bf\implies \:g(x) \: is \: factor \: of \: p(x)$

$\red{\large\underline{\sf{Solution-ii}}}$

$\rm \longmapsto\: p(x) = 2{x}^{3} + {x}^{2} - 2x + 1$

and

$\rm :\longmapsto\: g(x) = x + 1$

Now, By using Factor Theorem, Consider

$\rm \longmapsto\:p( - 1)$

$\rm \: = \: 2 {( - 1)}^{3} + {( - 1)}^{2} - 2( - 1) + 1$

$\rm \: = \: - 2 + 1 + 2 + 1$

$\rm \: = \: 2$

$\rm\implies \:p( - 1) \: \ne \: 0$

So, 

$\bf\implies \:g(x) \: is \: not \: a\: factor \: of \: p(x)$

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