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3 years ago

What is the length of the interior diagonal, d, rounded to the nearest hundredth cm

Mathematics

1 answer:

inn [45]3 years ago

4 0

Answer:

The length of the diagonal, d is approximately 24.49 cm

Step-by-step explanation:

The question asks to find the length of the interior diagonal of a rectangular prism, also known as a cuboid;

The parameters of the prism are;

The height of the prism = 10 cm

The width of the prism = 10 cm

The length of the prim = 20 cm

The length of the given diagonal of the cuboid is found by Pythagoras's theorem from the height, 'h', of the cuboid and the diagonal of the base of the cuboid

Let 'l' represent the diagonal of the base of the cuboid, we have, by Pythagoras's theorem;

l² = ((20 cm)² + (10 cm)²) = 500 cm²

The length of the diagonal, 'd', by Pythagoras's theorem is given as follows;

d = √(l² + (²10 cm))

By plugging in the known value for 'l² = 500 cm²', we get;

d = √(500 cm² + (²10 cm)) = √(600 cm²) = 10·√6 cm

The length of the diagonal, d = 10·√6 cm ≈ 24.49 cm (by rounding to the nearest hundredth cm)

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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3 years ago

If r and s are positive integers, is \small \frac{r}{s} an integer? (1) Every factor of s is also a factor of r. (2) Every prime

Yuri [45]

Answer:

If statement(1) holds true, it is correct that $\small \frac{r}{s}$ is an integer.

If statement(2) holds true, it is not necessarily correct that $\small \frac{r}{s}$ is an integer.

Step-by-step explanation:

Given two positive integers $r$ and $s$ .

To check whether $\small \frac{r}{s}$ is an integer:

Condition (1):

Every factor of $s$ is also a factor of $r$ .

$r \geq s$

Let us consider an example:

$s = 5^2 \cdot 2\\r = 5^3 \cdot 2^2$

$\dfrac{r}{s} = \dfrac{5^3\cdot2^2}{5^2\cdot2} = 10$

which is an integer.

Actually, in this situation $s$ is a factor of $r$ .

Condition 2:

Every prime factor of s is also a prime factor of r.

(But the powers of prime factors need not be equal as we are not given the conditions related to powers of prime factors.)

Let

$r = 2^2\cdot 5\\s =2^4\cdot 5$

$\dfrac{r}{s} = \dfrac{2^3\cdot5}{2^4\cdot5} = \dfrac{1}{2}$

which is not an integer.

So, the answer is:

If statement(1) holds true, it is correct that $\small \frac{r}{s}$ is an integer.

If statement(2) holds true, it is not necessarily correct that $\small \frac{r}{s}$ is an integer.

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3 years ago

What is the length of the interior diagonal, d, rounded to the nearest hundredth cm​

What is the length of the interior diagonal, d, rounded to the nearest hundredth cm