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malfutka [58]
3 years ago
12

The line on the graph passes through points A(1,3) and B(7,1). A) Calculate the gradient of line AB. B) Find the gradient of a l

ine perpendicular to AB. C) Find the equation of passing through the point (4,2) and perpendicular to AB.
Mathematics
1 answer:
garik1379 [7]3 years ago
3 0

Answer:

Step-by-step explanation

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What is the value of c such that the line y=2x+3 is tangent to the parabola y=cx^2
satela [25.4K]

The value of c such that the line y = 2\cdot x + 3 is tangent to the parabola y = c\cdot x^{2} is -\frac{1}{3}.

If y = 2\cdot x + 3 is a line <em>tangent</em> to the parabola y = c\cdot x^{2}, then we must observe the following condition, that is, the slope of the line is equal to the <em>first</em> derivative of the parabola:

2\cdot c \cdot x = 2 (1)

Then, we have the following system of equations:

y = 2\cdot x + 3 (1)

y = c\cdot x^{2} (2)

c\cdot x = 1 (3)

Whose solution is shown below:

By (3):

c =\frac{1}{x}

(3) in (2):

y = x (4)

(4) in (1):

y = -3

x = -3

c = -\frac{1}{3}

The value of c such that the line y = 2\cdot x + 3 is tangent to the parabola y = c\cdot x^{2} is -\frac{1}{3}.

We kindly invite to check this question on tangent lines: brainly.com/question/13424370

3 0
2 years ago
Determine how much money you will have after 20 years if you invest 20,000$ at 8%, compounded continuously?
Westkost [7]
20 000 * 0.08(8%)= 1600
1600 * 20(years) = 32 000

Therefore you would have $32 000 after 20 years
8 0
3 years ago
Read 2 more answers
The volume of 10,000drops of a liquid is 10 fluid ounces. what is the volume of 100 drops.
KIM [24]

We can write a proportion for this problem

10,000drops of a liquid is 10 fluid ounces

100 drops of a liquid is x fluid ounces

x=100*10/10000 =1/10 = 0.1 fluid ounces

8 0
3 years ago
A triangle has one angle that is 70 degrees and another that is 75 degrees. What is the third angle value in degrees?
mote1985 [20]

Answer:

35 degrees is the third angle's value.

5 0
2 years ago
5and 2/5 plus 2 and 3/5
HACTEHA [7]

Answer:

8

Step-by-step explanation:

Add the whole numbers:

5 + 2 = 7

Add the fractions:

2/5 + 3/5 = 5/5 = 1

Add these together:

7 + 1 = 8

Hope this helps!

4 0
2 years ago
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