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hjlf
3 years ago
14

Consider the curve y=ln(3x-1).let p be the point on the curve where x=2.

Mathematics
1 answer:
Eduardwww [97]3 years ago
4 0
A. Yes you are correct that the gradient at any point is 3/(3x-1). However at point P it would be 3/(3*2-1)=2/5
b. The gradient of the normal would therefore be -5/2
We can use the general formula of an equation to get y-ln(5)=-5/2 (x-2)
Now multiply both sides by 2 to get:
2y-2ln(5)=-5x+10
Now when it crosses the x axis we know that y=0 therefore:
5x=10+2ln(5)
Therefore:
x=2+2/5 ln(5) when y=0
You could find an estimate of this number to be 2.64 (3sf) but this might not be sufficient

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here is a list of numbers: 12, 13, 19, 16 ,32, 15, 13.a)work out the range of the numbers in the list.b)work out the mean of the
ratelena [41]

Answer: Mean: 17.14                                                                                           Range: 20.

Step-by-step explanation: 12+13+13+15+16+19+32                             25+13+15+16+19+32                                                                                             38+15+16+19+32                                                                                               53+16+19+32                                                                                                         69+19+32                                                                                                               88+32                                                                                                                     120/7                                                                                                                     17.14                                                                                                                                                    

32-12                                                                                                                       20

6 0
3 years ago
Help me out! plsss ​
a_sh-v [17]

Answer:

Step-by-step explanation:

ITS THE  THRID ONE!

5 0
3 years ago
Read 2 more answers
Does anyone know how to solve this? It’s really starting to stress me out.
bekas [8.4K]

Answer:

π − 12

Step-by-step explanation:

lim(x→2) (sin(πx) + 8 − x³) / (x − 2)

If we substitute x = u + 2:

lim(u→0) (sin(π(u + 2)) + 8 − (u + 2)³) / ((u + 2) − 2)

lim(u→0) (sin(πu + 2π) + 8 − (u + 2)³) / u

Distribute the cube:

lim(u→0) (sin(πu + 2π) + 8 − (u³ + 6u² + 12u + 8)) / u

lim(u→0) (sin(πu + 2π) + 8 − u³ − 6u² − 12u − 8) / u

lim(u→0) (sin(πu + 2π) − u³ − 6u² − 12u) / u

Using angle sum formula:

lim(u→0) (sin(πu) cos(2π) + sin(2π) cos(πu) − u³ − 6u² − 12u) / u

lim(u→0) (sin(πu) − u³ − 6u² − 12u) / u

Divide:

lim(u→0) [ (sin(πu) / u) − u² − 6u − 12 ]

lim(u→0) (sin(πu) / u) + lim(u→0) (-u² − 6u − 12)

lim(u→0) (sin(πu) / u) − 12

Multiply and divide by π.

lim(u→0) (π sin(πu) / (πu)) − 12

π lim(u→0) (sin(πu) / (πu)) − 12

Use special identity, lim(x→0) ((sin x) / x ) = 1.

π (1) − 12

π − 12

3 0
3 years ago
What is the slope and y-intercept of the graph? (write your answer in simplest form)
Basile [38]

Answer:

ok

Step-by-step explanation:

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8 0
2 years ago
The sum of three certain consecutive numbers is 240. Find the three numbers. [Hint: Let x stand for the smallest number. Since t
aleksley [76]
Write an equation based on the problem in the terms of x and solve the equation
first number + second number + third number = 240
x + x + 1 + x + 2 = 240
3x + 3 = 240
3x = 240 - 3
3x = 237
  x = 237/3
  x = 79
The smallest number, x, is equal to 79

Find the next two numbers
the second number = x + 1
the second number = 79 + 1
the second number = 80

the third number = x + 2
the third number = 79 + 2
the third number = 81

ANSWER: The three numbers are 79, 80, 81
7 0
3 years ago
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