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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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The parallelogram shown below has an area of <br> 20 units squared. Find the missing base
valkas [14]

Answer: 5 units

Step-by-step explanation:

The area of a parallelogram is A=bh. SInce we know the area and the height, we can directly plug the values into this equation and solve for the base.

20=b(4)         [divide both sides by 4]

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5 0
3 years ago
Read 2 more answers
Solve question 10 using substitution or elimination. Show all work.
BlackZzzverrR [31]
Solid paper costs 1.75 each
Printed paper costs 2.50 each

Given:
Ben = $43.50 (12 rolls solid paper and 9 rolls of
printed paper)
Joel = $51.50 (8 rolls solid paper and 15 rolls of
printed paper)
Let x = solid paper
Let y= printed paper
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Find X:
8x + 15y = 51.50
8x = 51.50 - 15y
x= (51.50 - 15y)8

Substitute X:
12x + 9y = 43.50
12(51.50 - 15y)/8 + 9y = 43.50
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8 (618 - 180y)/8 + 8*9y = 43.50 * 8
618-180y + 72y =348
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Y= 2.50

x = (51.50 - 15y)/8
x = (51.50 - 15(2.5) /8
x= (51.50 - 37.50\8
X = 14/8

X = 1.75

To check: x = 1.75; y = 2.5
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12(1.75) + 9(2.5) = 43.50
21 + 22.50 = 43.50
43.50 = 43.50
8x + 15y = 51.50
8(1.75) + 15(2.5) = 51.50
14 + 37.50 = 51.50
51.50 = 51.50

Hope that helps! Have a good day :)
5 0
2 years ago
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