All categories

3 years ago

If f(x)= 2a|3x – 9| – ax, where a is some constant not equal to zero, find f ′(3).

Mathematics

1 answer:

sineoko [7]3 years ago

8 0

Hmm, it actually doesn't exist because at x=3, that is where the absoluve value turns into 0. the graph has a point at x=3 and there is no slope of a pointy part of a function. I mean the slope is undinfed, it is DNE

You might be interested in

During the first hour of operation the farm stand owner sold 15% of the apples he had. On the second hour he sold 20% of the rem

liraira [26]

Answer:

3.825 kg apples.

Step-by-step explanation:

Let x kg be the amount of apples stand owner had initially.

We have been given that during the first hour of operation the farm stand owner sold 15% of the apples he had. Then the amount of sold apples will be:

$\text{The amount of sold apples during 1st hour}=\frac{15}{100}x=0.15x$

$\text{The amount of remaining apples after 1st hour}=x-0.15x$

$\text{The amount of remaining apples after 1st hour}=0.85x$

On the second hour he sold 20% of the remaining apples. So the amount of sold apples on the second hour will be 20% of 0.85x.

$\text{The amount of sold apples during 2nd hour}=0.85x*\frac{20}{100}$

$\text{The amount of sold apples during 2nd hour}=0.85x\times 0.20$

$\text{The amount of sold apples during 2nd hour}=0.17x$

During the second hour 25.5 kg of apples were sold, so we can set up an equation as:

$25.5=0.17x$

$\frac{25.5}{0.17}=\frac{0.17x}{0.17}$

$150=x$

So, stand owner had initially 150 kg of apples.

$\text{The amount of remaining apples after 2nd hour}=0.85x-0.17x$

$\text{The amount of remaining apples after 2nd hour}=0.68x$

On the third hour he sold 25% of the remaining apples. So the amount of sold apples on the 3rd hour will be 25% of 0.68x

$\text{The amount of sold apples during 3rd hour}=0.68x*\frac{25}{100}$

$\text{The amount of sold apples during 3rd hour}=0.68x*0.25$

$\text{The amount of sold apples during 3rd hour}=0.17x$

$\text{The amount of remaining apples after 3rd hour}=0.68x-0.17x$

$\text{The amount of remaining apples after 3rd hour}=0.51x$

As remaining apples were sold 5% more each following hour.

$\text{The amount of sold apples during 4th hour}=0.51x*\frac{5}{100}$

$\text{The amount of sold apples during 4th hour}=0.51x*0.05$

$\text{The amount of sold apples during 4th hour}=0.0255x$

Let us substitute x=150 into above equation we will get,

$\text{The amount of sold apples during 4th hour}=0.0255*150$

$\text{The amount of sold apples during 4th hour}=3.825$

Therefore, 3.825 kg of apples were sold during the 4th hour.

7 0

2 years ago

Josh pays $19.60 for a pack of 4 towels find the unit price in dollars per towel. If necessary, round your answer to the nearest

Elena-2011 [213]

Answer: $4.9 each towel

Step-by-step explanation:

You divide 19.6 by 4

5 0

3 years ago

Helpp me answer this i will give 15 points if u answer

Reil [10]

Answer:

G, the second option

Step-by-step explanation:

A triangle's degrees all adds up to 180.

45 + 60= 105 degrees

180-105= 75 degrees

<u>that in which makes </u><u>z=75 degrees.</u>

Since z is sharing a straight angle, which is 180 degrees

180-75= 105 degrees.

<u>Therefore, </u><u>w=105 degrees</u>

next time when you are asking a question, be sure to crop the screen shot because the screen contains some private information that may be used against you! :)

<u />

5 0

3 years ago

Identifying an Error

Burka [1]

The incorrect step is ln(x²) = ln(3x/0) because ln(x/y) = lnx - lny and the solutions are x = 0, 3

<h3>What is a logarithm? </h3>

It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.

$\rm a^b = c\\log_ac =b$

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

2ln(x) = In(3x) - [In(9) - 2ln(3)]

In(x²) = In(3x) - [In(9) - In(9)]

ln(x²) = ln(3x) - 0

ln(x²) = ln(3x/0) (incorrect step)

ln(x²) = ln(3x)

x² = 3x (correct step)

x² - 3x =0

x(x - 3) = 0

x = 0, 3

Thus, the incorrect step is ln(x²) = ln(3x/0) because ln(x/y) = lnx - lny and the solutions are x = 0, 3

Learn more about the Logarithm here:

brainly.com/question/163125

#SPJ1

3 0

1 year ago

I need helppppp........

grin007 [14]

Answer:

Step-by-step explanation:

To do this, you need to complete the square.

$y=-2x^2-8x-13 \\\\y=-2(x^2+4x)-13 \\\\y=-2(x^2+4x+4)+8-13 \\\\y=-2(x+2)^2-5$

Therefore, the correct answer is choice B. Hope this helps!

7 0

3 years ago