I WILL MARK BRAINLIEST

Derivatives concept:

mr Goodwill [35]

9514 1404 393

Answer:

A. y = -2x +13

B. y = 8x -7

Step-by-step explanation:

A. We can read the y-intercept of the secant line from the graph. It is 13.

The slope can also be read from the graph, but we choose to use the slope formula:

m = (y2 -y1)/(x2 -x1)

m = (19 -9)/(-3 -2) = 10/-5 = -2

Then the slope-intercept formula for the line is ...

y = mx + b . . . . . . line of slope m and y-intercept b

y = -2x +13

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B. The vertex of the given parabola is (0, 1). We notice that when x=1 (1 unit right of the vertex), y = 3 (2 units up from the vertex). This tells us the vertical scale factor of the parabola is 2. That means the vertex form equation is ...

y = a(x -h)^2 +k . . . . . . . . vertex (h, k), scale factor 'a'

y = 2(x-0)^2 +1 . . . . . . . use known values for (h, k)

y = 2x^2 +1

The derivative of this is ...

y' = 4x

So, at x=2, the given point A, the slope of the tangent line is ...

m = y' = 4(2) = 8

We have a point and the slope, so we can write the point-slope form of the equation for the tangent line:

y -9 = 8(x -2)

Rearranging to slope-intercept form, this is ...

y = 8x -7

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Additional comment

You can also read the slope of the tangent line from the graph. The line also goes through the point (1, 1), so has a rise of 8 for a run of 1. The y-intercept can be found from ...

b = y -mx = 9 -8(2) = -7

This lets you write the equation of the tangent line directly from the graph.

That is, the parameters of both lines can be read from the graph, so there is very little "development" required.

8 0

3 years ago

YA

irakobra [83]

Answer:

a) P(0, 2), Q(4, 0)

b) Please find attached the plot of the points P and Q on a chart made with MS Excel

c) Please find the graph of the line that represent the function 4·x + 2·y = 8 for values of x from -2 to 3 made with the Insert Chart feature on MS Excel

Step-by-step explanation:

The given equation for the line is 4·x + 2·y = 8

a) The coordinates of P = P(0, _)

Therefore, the point 'P', which is the point where the variable y = 0, is the point the (straight line) graph intercepts the x-axis (the x-intercept)

When y = 0 from the given equation, we get;

4·x + 2·y = 8

At the point y = 0;

4·x + 2 × 0 = 8

x = 8/4 = 2

x = 2

∴ The coordinates of P = P(0, _) = P(0, 2)

Similarly, when x = 0, we get;

4·x + 2·y = 8

At the point x = 0;

4 × 0 + 2·y = 8

y = 8/2 = 4

y = 4

∴ The coordinates of Q = Q(_, 0) = Q(4, 0)

b) Rewriting the given equation in terms of 'y' gives;

y = (8 - 4·x)/2 = 4 - 2·x

y = 4 - 2·x

With the help of MS Excel, the points P and Q are plotted in the attached graph

c) The line of the graph of the function 4·x + 2·y = 8 for values of x from -2 to 3 can be added by Changing the Chart Type to 'Scatter with Smooth Lines and Markers' within MS Excel as presented in the included graph of the line.

3 0

3 years ago

SECTION 1 OF 1 1234567891011121314 Consider the following three statements: As children grow older, their weight increases. As c

MA_775_DIABLO [31]

Correlation, not causation because weight has nothing to do with your vocabulary you could be super thin and be a genius or be super thin and be an idiot or the other way around with fat people

7 0

4 years ago

How do u do those two questions

lions [1.4K]

God loves you and will guide you to the anwser will external interference

3 0

3 years ago

Right triangles to find the exact length of: T 30° 14 in a) TI = in 60° R

ira [324]

<h3>Answer:</h3>

a) TI = 7√3 in

b) IR = 7 in