Find the x-intercept and y-intercept of the line. 3x-6y=12

Answer:

It can be written 60 different three digit numbers.

Step-by-step explanation:

For, calculate how many different three digit numbers can be written, we can use the rule of multiplication as:

    5              *         4         *             3                =      60

   1st digit         2nd digit          3rd digit

Taking into account that there is no repeating digits, we have 5 options for the first digits, this options are the number 5, 6, 7, 8 or 9. Then, we have 4 options for the second digit and then we have 3 options for the third digit.

So, there are 60 different three digit numbers that we can create with the set  5, 6, 7, 8, 9 without any repeating digits.

Step-by-step explanation:

To make the function f(x) = {sin(1/x), x ≠ 0; k, x = 0} continuous at x = 0, we need to find the value of k that ensures the limit of f(x) as x approaches 0 exists and is equal to k.

First, let's find the limit of sin(1/x) as x approaches 0:

lim(x -> 0) sin(1/x)

This limit does not exist because sin(1/x) oscillates wildly as x gets closer to 0. Therefore, in order for the function to be continuous at x = 0, we need to choose k such that it compensates for the oscillations of sin(1/x) as x approaches 0.

A suitable choice for k is 0 because the limit of sin(1/x) as x approaches 0 is undefined, and setting k = 0 ensures that f(x) becomes a continuous function at x = 0.

So, the correct choice is:

d. None (k = 0)

Final answer:

The value of k that would make the function f(x) = sin(1/x) when x ≠0 and f(x) = k when x=0 continuous at x=0 doesn't exist. This is because the limit of sin(1/x) as x approaches 0 is undefined, hence the function cannot be made continuous at x = 0 for any value of k.

Explanation:

To find the value of k that makes the function continuous at x=0, we can apply the definition of continuity, which states that a function, f(x), is continuous at a certain point, x0, if three conditions are met:

• the function is defined at x0
• the limit as x approaches x0 of f(x) exists
• the limit as x approaches x0 of f(x) is equal to f(x0)

In the case of the function f(x) = sin(1/x), the value for x = 0 is undefined, but we've been given that f(0) = k. To make the function continuous at x = 0, the value of k should ideally be equal to the limit of sin(1/x) as x approaches 0.

However, as x approaches 0, sin(1/x) oscillates between -1 and 1, making the limit non-existent. Because the limit does not exist, the function is not continuous at x=0 no matter the chosen value of k. Therefore, the correct answer is (d) None.

Learn more about Limits and Continuity here:

brainly.com/question/32625617

#SPJ11