List all thenumber that must be excluded from the domain of

List all thenumber that must be excluded from the domain of the given function f(x)= 3x+1/2x^2-7x-4 Write the quadratic equation standard from having the given solution set. {-3/5,- 1/2} 5.solve for the indicated varible. 1/R=1/R_1 + 1/R_2; for R_1

Solution

2. Let the walking speed = x mph

The running speed is 6 mph more than walking speed.

So running speed = (x+6) mph

The time taken to walk 1 mile = 1/x hrs

The time taken to run 5 miles = 5/(x+6) hrs

Yesterday Batman took 45 minutes to run 5 miles and walk 1 mile

The time in hours = 45/60 = 3/4

So 1/x + 5/(x+6) = 3/4

((x+6) + 5x) / x(x+6) = 3/4

(6x+6)/(x^2 + 6x) = 3/4

4(6x+6) = 3(x^2+6x)

24x + 24 = 3x^2 + 18x

3x^2 - 6x - 24 = 0

x^2 - 2x - 8 = 0

Factorising

x^2 - 4x + 2x -8 = 0

x(x - 4) + 2(x-4)

(x+2)(x-4) = 0

x= -2 or x= 4

Since speed can not be negative x = 4

Walking speed is 4 mph

Running speed = 4 + 6 = 10mph

3 f(x) = (3x^2+1) / (2x^2-7x-4)

Factorising denominator as shown

2x^2 + x - 8x -4

x(2x+1) - 4(2x+1)

(x-4)(2x+1)

If the denominator is equal to zero for the function will not be valid

(x-4)(2x+1) = 0

x = 4 or x = -1/2

The numbers to be excluded from the domain of the function ar x = 4 and x = -1/2

The domain is {x: x nor eaual to 4 and x not equal to -1/2)

4. The Quadratic equation for solution set {-3/5, -1/2} is

(x+3/5)(x+1/2) = 0

x^2 + (1/2)x + (3/5)x + 3/10 = 0

x^2 + x/2 + 3x/5 + 3/10 = 0

x^2 + (5x+6x)/10 + 3/10

x^2 = 11x/10 + 3/10 = 0

Multiplying both sides with 10 the equation is

10x^2 + 11x+ 3 = 0

5)

1/R = 1/R₁ + 1/R₂

1/ R₁ = 1/R - 1/R₂

1/R1 = (R₂ – R)/R*R₂

R₁ = R*R₂ / (R₂ – R)