1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
storchak [24]
2 years ago
6

Does anyone understand how to solve this?

Mathematics
1 answer:
yanalaym [24]2 years ago
3 0

You solve it by filling in the function value and simplifying the result.

a.

\displaystyle \frac{f(x)-f(a)}{x-a}=\frac{\left(3x^{2}+x+3\right)-\left(3a^{2}+a+3\right)}{x-a}\\\\=\frac{3\left(x^{2}-a^{2}\right)+\left(x-a\right)}{x-a}\\\\=\frac{3(x+a)(x-a)+(x-a)}{x-a}=3(x+a)+1

b.

\displaystyle \frac{f(x+h)-f(x)}{h}=\frac{\left(3(x+h)^{2}+(x+h)+3\right)-\left(3x^{2}+x+3\right)}{h}\\\\=\frac{\left(3\left(x^{2}+2hx+h^{2}\right)+(x+h)+3\right)-\left(3x^{2}+x+3\right)}{h}\\\\=\frac{3\left(2hx+h^{2}\right)+h}{h}=6x+1+3h

You might be interested in
Initially a tank contains 10 liters of pure water. Brine of unknown (but constant) concentration of salt is flowing in at 1 lite
zhenek [66]

Answer:

Therefore the concentration of salt in the incoming brine is 1.73 g/L.

Step-by-step explanation:

Here the amount of incoming and outgoing of water are equal. Then the amount of water in the tank remain same = 10 liters.

Let the concentration of salt  be a gram/L

Let the amount salt in the tank at any time t be Q(t).

\frac{dQ}{dt} =\textrm {incoming rate - outgoing rate}

Incoming rate = (a g/L)×(1 L/min)

                       =a g/min

The concentration of salt in the tank at any time t is = \frac{Q(t)}{10}  g/L

Outgoing rate = (\frac{Q(t)}{10} g/L)(1 L/ min) \frac{Q(t)}{10} g/min

\frac{dQ}{dt} = a- \frac{Q(t)}{10}

\Rightarrow \frac{dQ}{10a-Q(t)} =\frac{1}{10} dt

Integrating both sides

\Rightarrow \int \frac{dQ}{10a-Q(t)} =\int\frac{1}{10} dt

\Rightarrow -log|10a-Q(t)|=\frac{1}{10} t +c        [ where c arbitrary constant]

Initial condition when t= 20 , Q(t)= 15 gram

\Rightarrow -log|10a-15|=\frac{1}{10}\times 20 +c

\Rightarrow -log|10a-15|-2=c

Therefore ,

-log|10a-Q(t)|=\frac{1}{10} t -log|10a-15|-2 .......(1)

In the starting time t=0 and Q(t)=0

Putting t=0 and Q(t)=0  in equation (1) we get

- log|10a|= -log|10a-15| -2

\Rightarrow- log|10a|+log|10a-15|= -2

\Rightarrow log|\frac{10a-15}{10a}|= -2

\Rightarrow |\frac{10a-15}{10a}|=e ^{-2}

\Rightarrow 1-\frac{15}{10a} =e^{-2}

\Rightarrow \frac{15}{10a} =1-e^{-2}

\Rightarrow \frac{3}{2a} =1-e^{-2}

\Rightarrow2a= \frac{3}{1-e^{-2}}

\Rightarrow a = 1.73

Therefore the concentration of salt in the incoming brine is 1.73 g/L

8 0
3 years ago
Find the product.<br> (3b + 6at)(b - at)
adoni [48]

Answer:

3bat + 3b² - 6a²t²

Step-by-step explanation:

First you have to expand it to get;

3b(b - at) + 6at(b - at)

Then you can now multiply.

3b² - 3bat + 6bat - 6at²

Group like terms

6bat - 3bat + 3b² -6at²

3bat + 3b² - 6a²t²

4 0
3 years ago
Read 2 more answers
Which of the following is a coefficient in the expression 822 + 6?
ioda

Answer:

There are no coefficients.

Step-by-step explanation:

6 0
2 years ago
One year on Venus is equivalent to 224.7 days on Earth. How many days on Earth, in decimal from, are equivalent to 9 ½ years on
Ivan

By using simple rule of three, a period of 9.5 years on Venus is equivalent to 2134.65 terrestrial days.

<h3>How many terrestrial days are equivalent time in Venus?</h3>

One year on Earth is equivalent to 365.3 days and one year on Venus is equivalent to 224.7 days, the equivalent terrestrial time of 9.5 years on Venus is found by simple rule of three:

x = 9.5 yr × (224.7 days / 1 yr)

x = 2134.65 days

A period of 9.5 years on Venus is equivalent to 2134.65 terrestrial days.

To learn more on simple rule of three: brainly.com/question/15209325

#SPJ1

6 0
1 year ago
2) Which choice best represents:<br> Divide 8 by N<br> A. 8-N<br> B. N -8
Nataly_w [17]

Answer: A

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • Question 4
    9·1 answer
  • I only need the Evens ;-;
    5·1 answer
  • What is the value of x
    12·2 answers
  • The surface area of a rectangular prism is 220 cm2. Two of the dimensions are 5 cm. Find the measure of the other dimension.
    6·1 answer
  • There are 4 people that have ipads and there are 3 people who have a kindle. if 500 more people own an ipad then a kindle, how m
    6·2 answers
  • (2,3), (4,-7) midpoint
    9·1 answer
  • Simplify the ratio 24:81
    10·1 answer
  • Estimate the product 0.62 x 104
    10·1 answer
  • Between 2000 and 2010, the percentage of fatal automobile accidents due to speeding decreased by 34% to 16%. What percentage of
    5·1 answer
  • Someone help me with this
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!