Find a formula for a line that is perpendicular to the line

Find a formula for a line that is perpendicular to the line 5x + 3y = 2 and passes through the point 3, 2.4 Let g(t) = 3 - 2t2. i. The average rate of change between (-1, g(-1)) and (4, g(4)) is ii. What does the quantity (g(4) - g(-1))/5 represent geometrically? iii. Evaluate g(t) = 1/t + 2 a. (G(t + h) - g(t))/h

Solution

1) given line 5x+3y =2

=>y=-(5_/3)x +(2_/3)

slope of given line=-(5_/3)

slope of perpendicular line will be negative reciprocal of slope of given line

slope of perpendicular line=(3_/5)

now equation of perpendicular line is

y-2.4=(3_/5)(x-3)

=>5(y-2.4)=3(x-3)

=>5y -12=3x-9

=>-3x+5y=3

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2)

g(t)=3-2t²

i)

average rate of change =(g(4)-g(-1))_/(4-(-1))

average rate of change =((3-2*4²)-(3-2*(-1)²))_/5

average rate of change =-30_/5

average rate of change =-6

ii)

(g(4)-g(-1))_/5 represent the slope of line joining (-1,g(-1)),(4,g(4))

iii)

g(t)=1/t+2

a.

[G(t+h) -g(t)]_/h

=[G(t+h) -(1/t+2)]_/h