Scott drinks 6 cups of water a day. How many fluid ounces of water does Scott drink? (2 points)

For what values of x is f(x) = |x + 1| differentiable? I'm struggling my butt off for this course

pav-90 [236]

By definition of absolute value, you have

$f(x) = |x+1| = \begin{cases}x+1&\text{if }x+1\ge0 \\ -(x+1)&\text{if }x+1$

or more simply,

$f(x) = \begin{cases}x+1&\text{if }x\ge-1\\-x-1&\text{if }x$

On their own, each piece is differentiable over their respective domains, except at the point where they split off.

For x > -1, we have

(x + 1)' = 1

while for x < -1,

(-x - 1)' = -1

More concisely,

$f'(x) = \begin{cases}1&\text{if }x>-1\\-1&\text{if }x$

Note the strict inequalities in the definition of f '(x).

In order for f(x) to be differentiable at x = -1, the derivative f '(x) must be continuous at x = -1. But this is not the case, because the limits from either side of x = -1 for the derivative do not match:

$\displaystyle \lim_{x\to-1^-}f'(x) = \lim_{x\to-1}(-1) = -1$

$\displaystyle \lim_{x\to-1^+}f'(x) = \lim_{x\to-1}1 = 1$

All this to say that f(x) is differentiable everywhere on its domain, except at the point x = -1.

4 0

3 years ago

These solids all have the same volume. Which has the least surface area?

ipn [44]

Answer: I’m not sure, but I think it is solid C.

Step-by-step explanation: Please, make sure you have some knowledge when you answer this question. My answer is an educated guess. I do not want to be responsible for your wrong answers.

4 0

3 years ago

I will give brainliest!!!!!!!!!!!!! please answer all the questions and no links! :)

Scilla [17]

Answer:

1. a

2. b (i think)

3. b

4. a

5. d

im not sure bout all this but h ope it helps you

3 0

3 years ago

This year the CDC reported that 30% of adults received their flu shot. Of those adults who received their flu shot,

Vlad [161]

Using conditional probability, it is found that there is a 0.1165 = 11.65% probability that a person with the flu is a person who received a flu shot.

Conditional Probability

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this problem:

Event A: Person has the flu.

Event B: Person got the flu shot.

The percentages associated with getting the flu are:

20% of 30%(got the shot).

65% of 70%(did not get the shot).

Hence:

$P(A) = 0.2(0.3) + 0.65(0.7) = 0.515$

The probability of both having the flu and getting the shot is:

$P(A \cap B) = 0.2(0.3) = 0.06$

Hence, the conditional probability is:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.06}{0.515} = 0.1165$

0.1165 = 11.65% probability that a person with the flu is a person who received a flu shot.

To learn more about conditional probability, you can take a look at brainly.com/question/14398287

7 0

2 years ago

What is the square root of: 36 81 121 and 49 Please answer like a six grader

harina [27]

The square root of 49 is the number, which multiplied by itself, is 49. In other words, the square of this number equals forty-nine. If you have been looking for square root of forty-nine, then you are right here, too. On this page you can also find what the parts of √49 are called, and in addition to the terminology of √49, we also have a calculator you don’t want to miss. Read on to learn everything about the sqrt 49.

this should help u answer it

6 0

3 years ago

Read 2 more answers