18.) What is the equation of the line L that passes through the point (?2, 4) an

Question

18.) What is the equation of the line L that passes through the point (?2, 4) and is perpendicular to the line with the equation x+ 2y = 8.

Select one:

a. y = 2x ? 8

b. y = x?/?2 + 8

c. y = 2x + 8

d. y = ?x?/?2 + 3

19.)

Sketch the parabola of equation
y = ?x?2 + 4x ? 8, and indicate its vertex.

Select one:

20.)

The position of a car at time t is given by the function p(t) = t2 + 2t ? 4. What is the velocity at t = 2? Assume t ? 0.

Select one:

a. 3

b. ?6

c. 6

d. ?3

21.)

Consider the function y = x2 ? x + 7. What is the equation of the tangent line at x = 2?

Select one:

a. y = 3(x + 2)– 9

b. y = 3(x + 2)+ 9

c. y = 3(x ? 2)– 9

d. y = 3(x ? 2)+ 9

22.)

Find the slope of a line tangent to f(x) = x3 at the point (x, f(x)).

Select one:

a. 0

b. 3x2 + 3x

c. 3x2

d. ?x3

23.)

If y changes from y = 1 to y = 2 along the curve xy = 1, which of the following is equal to ? (x ? y)?

Select one:

a. 1/2

b. ?3/2

c. 1

d. 0

Explanation / Answer

18. Given that the line L passes through the point (-2 , 4)

and perpandicular to the line with the equation x+2y = 8

So , the slope of the given line (m1) = (-a/b) =(-1/2)

Both line are perpendicular so slope (m1 * m2) = -1

Hence, slope of required line (m2) = -(1/m1)

So, m2 = -(1/(-1/2))

M2 = 2 and passing point (-2 , 4)

So, equation of required line is

(y-y1) = m (x- x1)

( y- 4) = 2 (x - (-2))

(y - 4) = 2x +4

y = 2x + 8 This is the equation of required line

Hence option C is correct

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