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2 years ago

Prove that if m, d, and k are integers and d > 0, then (m + dk) mod d = m mod d.

1 answer:

6 0

From the rules of modular arithmetic, (A+B)mod C= (A)modC +(B)modC

So, (m + dk) mod d = (m) mod d+<span> (dk) mod d

clearly </span>(dk) mod d = 0, as one of the things (dk) mod d represents, is the remainder of dk, when divided by d, which is clearly 0.

Thus

(m + dk) mod d = (m) mod d+ (dk) mod d= (m) mod d+ 0=(m) mod d

(m + dk) mod d =(m) mod d

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Use the definition of continuity and the properties of limit to show that the function f(x)=x sqrtx/ (x-6)^2 is continuous at x=

jasenka [17]

Answer:

The function $\\ f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}}$ is continuous at x = 36.

Step-by-step explanation:

We need to follow the following steps:

The function is:

$\\ f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}}$

The function is continuous at point x=36 if:

The function $\\ f(x)$ exists at x=36.
The limit on both sides of 36 exists.
The value of the function at x=36 is the same as the value of the limit of the function at x = 36.

Therefore:

The value of the function at x = 36 is:

$\\ f(36) = \frac{36*\sqrt{36}}{(36-6)^{2}}$

$\\ f(36) = \frac{36*6}{900} = \frac{6}{25}$

The limit of the $\\ f(x)$ is the same at both sides of x=36, that is, the evaluation of the limit for values coming below x = 36, or 33, 34, 35.5, 35.9, 35.99999 is the same that the limit for values coming above x = 36, or 38, 37, 36.5, 36.1, 36.01, 36.001, 36.0001, etc.

For this case:

$\\ lim_{x \to 36} f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}}$

$\\ \lim_{x \to 36} f(x) = \frac{6}{25}$

Since

$\\ f(36) = \frac{6}{25}$

And

$\\ \lim_{x \to 36} f(x) = \frac{6}{25}$

Then, the function $\\ f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}}$ is continuous at x = 36.

8 0

2 years ago

What was discovered because of the changing phases of the moon? Please Help!!! Will Give Lots Of Points!

elena-14-01-66 [18.8K]

Answer:

Firstly, the moon keeps changing its shape with 4 distinct moon phases that depend on the position of the moon and also on the position of the Earth. The moon orbits around the planet Earth, and the Earth orbits around the Sun.

Step-by-step explanation:

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2 years ago

Josh can walk 4 miles in 1 hour. How many miles can he walk in 3 hours

bulgar [2K]

Im pretty sure it’s 12 miles, hope this helped :)

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2 years ago

Read 2 more answers

The sum of a number times 7 and 30 is at most -24

NARA [144]

Answer:

x•7+30=-24

Step-by-step explanation:

This might be your answer, if not please comment and let me know what it really was! Thanks!

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2 years ago

How many ways can an 8-question True/False quiz be answered

tresset_1 [31]

Answer:

256

Step-by-step explanation:

two choices for each question so

2^8=256

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3 years ago