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daser333 [38]
3 years ago
8

Find an equation of the tangent line to the curve at the given point. y=secx (pi/3,2)

Mathematics
1 answer:
hichkok12 [17]3 years ago
6 0
To get the equation of tangent, we need a point on it and its slope.

we already have (x1,y1) = (pi/3,2) on the tangent line.

To get the slope of tangent,
m = derivative of y at the given point.

y = sec x
y' = sec x tan x
at x = pi/3,
y' = sec pi/3 tan pi/3
y'= 2 \sqrt 3

so the slope of tangent is 2 \sqrt 3

equation will be
y -y1 = m (x-x1)
y - 2 = 2 \sqrt 3 (x- pi/3)

Thats your equation of tangent.
you can simplify if you want.


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What is y=2 plus 4?<br>​
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Answer:

We conclude that (4, 2) is NOT a solution to the system of equations.

Step-by-step explanation:

Given the system of equations

y = x - 2

y = 3x + 4

Important Tip:

  • In order to determine whether (4, 2) is a solution to the system of equations or not, we need to solve the system of equations.

Let us solve the system of equations using the elimination method.

\begin{bmatrix}y=x-2\\ y=3x+4\end{bmatrix}

Arrange equation variables for elimination

\begin{bmatrix}y-x=-2\\ y-3x=4\end{bmatrix}

Subtract the equations

y-3x=4

-

\underline{y-x=-2}

-2x=6

Now, solve -2x = 6 for x

-2x=6

Divide both sides by -2

\frac{-2x}{-2}=\frac{6}{-2}

Simplify

x=-3

For y - x = -2 plug in x = -3

y-\left(-3\right)=-2

y+3=-2

Subtract 3 from both sides

y+3-3=-2-3

Simplify

y=-5

The solution to the system of equations is:

(x, y) = (-3, -5)

Checking the graph

From the graph, it is also clear that (4, 2) is NOT a solution to the system of equations because (-3, -5) is the only solution as we have found earlier.

Therefore, we conclude that (4, 2) is NOT a solution to the system of equations.

8 0
3 years ago
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