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
uysha [10]
3 years ago
14

Please show me how to do this.

Mathematics
1 answer:
Aloiza [94]3 years ago
7 0

Answer:

f(x) = \dfrac{1}{2}(x - \ln (x - 1) - 2)

Step-by-step explanation:

f'(x) = \dfrac{1}{2} - \dfrac{1}{2x - 2}

f(x) = \int (\dfrac{1}{2} - \dfrac{1}{2x - 2}) dx

f(x) = \int [\dfrac{1}{2} - \dfrac{1}{2(x - 2)}] dx

f(x) = \int \dfrac{1}{2}dx - \dfrac{1}{2} \int \dfrac{1}{x - 1} dx

f(x) = \dfrac{1}{2}x - \dfrac{1}{2} \ln (x - 1) + C

f(x) = \dfrac{x - \ln (x - 1)}{2} + C

f(2) = \dfrac{2 - \ln (2 - 1)}{2} + C = 0

f(2) = \dfrac{2 - \ln (1)}{2} + C = 0

f(2) = \dfrac{2}{2} + C = 0

f(2) = 1 + C = 0

C = -1

f(x) = \dfrac{x - \ln (x - 1)}{2} - 1

f(x) = \dfrac{1}{2}[x - \ln (x - 1) - 2]



You might be interested in
Consider functions f and g.
nikklg [1K]

Answer:

C. 1

Step-by-step explanation:

Looking to the Venn's diagram, we can realize that g(1) = 0

If g(1) = 0, you just need to put 0 in place of x in f(x), so we have:

f(0) = 3√0 + 1

f(0) = 3•0 + 1

f(0) = 1

7 0
2 years ago
Please help i don’t understand
choli [55]

Is that everything for the problem??

||-//

6 0
2 years ago
You have exatly 200 feet of fencing to enclose 2 adjacent square regions. assuming you use all the fencing provided what will th
bekas [8.4K]
Adjacent so that means 1 wall will be shared

each square has 4 sides,
but they share a side so 4+4-1=7 sides total

200 divided by 7 sides=200/7 ft per side

the area of a square is side^2
side=200/7
so area=(200/7)^2=40000/49
that's for 1 square
times 2
80000/49 square feet
about 1632.6530612244897959183673469388 square feet
rounded is 1633 square feet

7 0
3 years ago
Write in vertex form<br> f(x)=x^2+12x+34
svp [43]

Answer:

(-6, -2)

Step-by-step explanation:

f(x) =  {x}^{2}  + 12x + 34

= f(x) =  {1x}^{2}  + 12x + 34

= a = 1, b = 12

= x =  -  \frac{12}{2 \times 1}

= x =  -  \frac{12}{2}

= x = -6

= f(x) =  {x}^{2}  + 12x + 34.. =  - 6

= f( - 6) =  - 2

= (-6, -2)

8 0
2 years ago
Jared creates a number sequence that has a first term of 2 and a second of term of 5. Each term after the second is created by s
dexar [7]

The rule for the sequence is S(n) = 2S(n-1) - S(n-2)

Alternative form: S(n) = S(n-1) + 3

Step-by-step explanation:

In this problem, we know the first two terms of the sequence:

S(1) = 2

S(2) = 5

We are told that each term after the second is created by subtracting the term before the previous term from twice the previous term. In other words, if we call:

S(n) the current term

S(n-1) the previous term

S(n-2) the term before the previous term

This statement translates into the following sequence:

S(n) = 2S(n-1) - S(n-2)

Because we are subtracting the term before the previous term, S(n-2), from twice the previous term, 2S(n-1).

We can apply now the rule to find the first few terms of the sequence after S(1) and S(2):

S(3) = 2S(2) - S(1) = 2(5)-2=10-2 = 8

S(4) = 2S(3) - S(2) = 2(8)-5=16-5 = 11

S(5) = 2S(4) - S(3) = 2(11)-8=22-8 = 14

We notice also that each term of the sequence is just equal to the previous term plus 3, so the sequence can also be written as

S(n) = S(n-1) + 3

Learn more about sequences:

brainly.com/question/1522572

brainly.com/question/3280369

#LearnwithBrainly

4 0
3 years ago
Other questions:
  • I need help i don’t get it
    8·2 answers
  • (4) (5) Geometry help
    7·1 answer
  • What is the value of x? Enter your answer in the box.
    7·2 answers
  • Y=<br><img src="https://tex.z-dn.net/?f=y%20%3D%20%20%5Csqrt%7Bx%20-%207%20-%201%7D%20" id="TexFormula1" title="y = \sqrt{x - 7
    10·2 answers
  • Good answer fast Find the value of y
    12·1 answer
  • A 2.2 kg ball strikes a wall with a velocity of 7.4 m/s to the left. The ball bounces off with a velocity of 6.2 m/s to the righ
    5·1 answer
  • $12 for 6 bagels; $9 for 24 bagels.
    13·1 answer
  • Which is the ordered pair for the translated point D'?
    10·2 answers
  • Need help with this question.
    7·1 answer
  • Please help me i give brainliest
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!