What is the equation of a line that is perpendicular to this line and goes through the given point?
y = 3x + 2 (3,-4)

x + 3y + 9 = 0

Step-by-step explanation:

y=3x + 2

Coefficient of x = 3

Gradient (m) of line y= 3x + 2 is 3

Since the line passing through point

(3,-4) is perpendicular to line y=3x + 2

hence gradient (m) of the line is -1/3;

And hence it equation is given as;

y - y1 = m(x - x1)

y - (-4) = -1/3(x - 3)

multiplying through by 3;

3 × y + 3 × 4 = 3 × -1/3(x - 3)

3y + 12 = -1(x - 3)

3y + 12 = -x + 3

x + 3y + 12 - 3 = 0

x + 3y + 9 = 0

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

1^3 + 2^3 + 3^3 +4^3 = (1+2+3+4)^2

step-by-step explanation:

i am only able to answer the first part. i am not sure about the second part. sorry