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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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Please help out with some of these.
nikdorinn [45]

Answer:

1. 1/12

2. 1/8

3. 1/6

4. 1/6

5. 1/4

6. 1/8

7. 1/6

8. 1/8

9. 1/12

Step-by-step explanation:

6 0
3 years ago
the volume of a cube is increasing at a constant rate of 824 cubic centimeters per minute. At the instant when the volume of the
Maurinko [17]

Answer:

DA/dt  = 75.27 cm²

Step-by-step explanation:

Cube Volume    =   V(c)   =  683  cm³

DV(c) /dt    =  824 cm³

V(c,x) = x³    

Then

DV(c,x)/ dt   =  3x² Dx/dt

( DV(c,x)/ dt )/ 3x²  =  Dx/dt       (1)

Now  as  V(c,x) = x³    when    V(c,x)  =  683 cm³     x = ∛683

x  =  8.806     ( from excel)

And by subtitution of this value in equation (1)

Dx/dt   =  ( DV(c,x)/ dt )/ 3x²   ⇒  Dx/dt  =  824 / 3*x²

  Dx/dt   = 824 /3*77.55

Dx/dt   =  824/232,64

Dx/dt   = 3,542

Then we got  Dx/dt  where x is cube edge. The area of the face is x² then

the rate of change of the suface area is  

DA/dt  = ( Dx/dt )²*6         ( 6 faces of a cube)

DA/dt  = (3.542)²*6

DA/dt  = 75.27 cm²

6 0
2 years ago
Pleasee anyonnee help me assaaapppp
nekit [7.7K]
30, 34
You add 4 on
44
Because it starts at 10 and 10 cannot be divided by 4
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10x = 2x -8 what is this answer
julia-pushkina [17]

Answer:

x=-1

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
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erma4kov [3.2K]
Isolate the variable by dividing each side by factors that don't contain the variable.
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2 years ago
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