Differentiate. y=ln (17-x)

Answers

Answer 1

Answer: We have to use the chain rule's

$f(x)=ln(17-x)$

$f[g(x)]=ln[g(x)]$

therefore

$f(u)=ln(u)$

and

$u=g(x)=17-x$

them we have

$f'(x)=f'(u)*g'(x)$

$f'(u)=(1)/(u)$

$g'(x)=-1$

$f'(x)=f'(u)*g'(x)$

$f'(x)=(1)/(u)*(-1)$

$f'(x)=-(1)/(u)$

$\boxed{\boxed{\therefore~f'(x)=-(1)/(17-x)}}$

Answer 2

Answer: $y'=(17-x)'\cdot (1)/(ln(17-x)) =- (1)/(ln(17-x)) \n\n \ \ and\ \ \ D: \ 17-x > 0\ \ \ \Rightarrow\ \ \ x<17\ \ \ \Rightarrow\ \ \ D=(17;+\infty)$

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What 2 numbers add up to get 17 and multiply to get 42??

The area of a sector of a circle with a radius of 4 centimeters is 2.512 square centimeters. The estimated value of ╥ is 3.14. The measure of the angle defining the sector is

Answers

The equation for the area of a sector of a circle is expressed as the product of pi, square of the radius and the ratio of the angle of the sector and 360 degrees.

Area = πr^2 (α / 360°)

We obtain the angle by manipulating the equation.

α = (Area x 360°) / πr^2
α = (2.512 cm^2 x 360°) / (π x 4^2)
α =35.98°

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Answers

Answer:

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Find the indicated limit, if it exists. (2 points) limit of f of x as x approaches 5 where f of x equals 5 minus x when x is less than 5, 8 when x equals 5, and x plus 3 when x is greater than 5

Answers

It looks like we have

$f(x)=\begin{cases}5-x&\text{for }x<5\n8&\text{for }x=5\nx+3&\text{for }x>5\end{cases}$

and we want to find $\lim\limits_(x\to5)f(x)$ .

Since $x$ is approaching 5, we don't care about the value of $f(x)$ when $x=5$ .

We do care about how $f(x)$ behaves to either side of $x=5$ . If $x\to5$ from below, then $f(x)=5-x$ , so that

$\displaystyle\lim_(x\to5^-)f(x)=\lim_(x\to5)(5-x)=5-5=0$

On the other hand, if $x\to5$ from above, then $f(x)=x+3$ , so that

$\displaystyle\lim_(x\to5^+)f(x)=\lim_(x\to5)(x+3)=5+3=8$

The one-sided limits do not match, since 0 ≠ 8, so the limit does not exist.

15 sweets are shared equally between 5 boxes.a) How many sweets will there be in each box?
b) Ali takes all of the striped pink boxes. How many sweets does Ali get?

Answers

Step-by-step explanation:

a) 15 sweets / 5 boxes = 3 sweets per box

b) need more information

Find two consecutive whole numbers that sqrt40 lies between

Answers

Answer:

To find two consecutive whole numbers between which √40 lies, we can calculate the square roots of consecutive whole numbers until we find the desired range.

Let's start by calculating the square roots of consecutive whole numbers:

√1 ≈ 1.00

√2 ≈ 1.41

√3 ≈ 1.73

√4 = 2.00

√5 ≈ 2.24

√6 ≈ 2.45

√7 ≈ 2.65

√8 ≈ 2.83

√9 = 3.00

√10 ≈ 3.16

√11 ≈ 3.32

√12 ≈ 3.46

√13 ≈ 3.61

√14 ≈ 3.74

√15 ≈ 3.87

√16 = 4.00

...

Continuing this process, we find that √40 lies between 6 and 7 because:

√36 = 6.00

√37 ≈ 6.08

√38 ≈ 6.16

√39 ≈ 6.24

√40 ≈ 6.32

√41 ≈ 6.40

√42 ≈ 6.48

...

Therefore, the two consecutive whole numbers between which √40 lies are 6 and 7.

Step-by-step explanation:

What is the solution to the linear equation?

Answers

The answer is p=1

First you have to subtract 2/5 on both sides to get p=2/5x+3/5p.

Then subtract 3/5p on both sides to get 2/5p=2/5.

Then you divide by 2/5 on both sides to isolate p and you get 1 :)

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