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ZanzabumX [31]
3 years ago
10

The volume of a triangular prism is 20 cubic mm. If the dimensions were doubled, what would the new

Mathematics
1 answer:
anygoal [31]3 years ago
7 0

Answer:

The new volume will be 160 mm^3

Step-by-step explanation:

The volume of a triangular prism can be calculated by multiplying the area of the triangular base by the height.

Let’s say we have the base with dimensions a and b, while the height can be h

The volume can be calculated as

V = 1/2 * a * b * h

Now , to answer this question, we shall be choosing arbitrary lengths for a, b and h. Whatever length we shall be choosing , we should make sure that they must be equal to 20 mm^3.

Let’s say we have a as 2mm , b as 4 mm and H as 5 mm

Plugging these into the equation, we surely have our volume as 20 mm^3

Now let’s double these dimensions. Our new dimensions become , 4mm by 8mm by 10mm

Plugging these new values into the equation, we have;

1/2 * 4 * 8 * 10 = 160 mm^3

Thus, our volume is expected to be increased by a factor of 8

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3 years ago
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(i) Write the expansion of (x + y)² and (x - y)². (ii) Find (x + y)² - (x - y)² (iii) Write 12 as the difference of two perfect
zaharov [31]

Answer:

1a (x + y)² = x² + 2xy + y²

1b. (x - y)² = x² - 2xy + y²

2. (x + y)² - (x - y)² = 4xy

3. 4² – 2² = 12

Step-by-step explanation:

1a. Expansion of (x + y)²

(x + y)² = (x + y)(x + y)

(x + y)² = x(x + y) + y(x + y)

(x + y)² = x² + xy + xy + y²

(x + y)² = x² + 2xy + y²

1b. Expansion of (x - y)²

(x - y)² = (x - y)(x - y)

(x - y)² = x(x - y) - y(x - y)

(x - y)² = x² - xy - xy + y²

(x - y)² = x² - 2xy + y²

2. Determination of (x + y)² - (x - y)²

This can be obtained as follow

(x + y)² = x² + 2xy + y²

(x - y)² = x² - 2xy + y²

(x + y)² - (x - y)² = x² + 2xy + y² - (x² - 2xy + y²)

= x² + 2xy + y² - x² + 2xy - y²

= x² - x² + 2xy + 2xy + y² - y²

= 2xy + 2xy

= 4xy

(x + y)² - (x - y)² = 4xy

3. Writing 12 as the difference of two perfect square.

To do this, we shall subtract 12 from a perfect square to obtain a number which has a perfect square root.

We'll begin by 4

4² – 12

16 – 12 = 4

Find the square root of 4

√4 = 2

4 has a square root of 2.

Thus,

4² – 12 = 4

4² – 12 = 2²

Rearrange

4² – 2² = 12

Therefore, 12 as a difference of two perfect square is 4² – 2²

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Whats the difference between coplanar and collinear
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In terms of points, a point that is coplanar is one that lies anywhere on the given plane while a point that is collinear is a point that lies anywhere on the given line.
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