What is the equation of the line that passes through the point (3, 4) and has a slope of - 2/3?
1 answer:
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Answer:
y = 13*( -x/9 + 1/5)
Step-by-step explanation:
Given:
- The curve has an equation as follows:
Find:
a. Verify that the given point (2,2) lies on the curve.
b. Determine an equation of the line tangent to the curve at the given point.
Solution:
- To verify whether the point lies on the given curve we will substitute the coordinates of the point into the equation as follows:
44 = 5*(2)^2 + 3*(2)(2) + 3*(2)^2
44 = 20 + 12 + 12
44 = 44 ......Hence proven.
- The equation of the line tangent to the curve is expressed as a linear function as follows:
y = m*x + C
Where, m is the gradient of the line.
C is the y-intercept.
m = Δy / Δx = dy/dx
- We will take the derivative of the given curve with respect to x as follows:
- Evaluate y' at the point (2,2) we get:
y' = - ( 10(2) + 3(2) ) / ( 3(2) + 6(2) )
y' = - ( 26 ) / (18)
y'= m = - 13/9
- To evaluate C, we will use the point (2,2) for linear expression above with m as follows:
y = -13*x/9 + C
2 =-13*(2)/9 + C
C = 13 / 5
- The equation of the tangent is as follows:
y = 13*( -x/9 + 1/5)
Answer: 75/7 or 10.71 (rounded)
Step-by-step explanation:
Mean = Average
To find the average you should add all the numbers together and then divide it by the amount of numbers.
In this question, the formula is
----------------------------------------------------------------------------------------
The list of the first 7 odd prime numbers:
3, 5, 7, 11, 13, 17, 19
Now, add them together
3+5+7+11+13+17+19=75
Divide the sum by 7
75÷7=75/7=10.71 (rounded)
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