Written Assignment Unit 2 PDF

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Written Assignment Unit 2: Graphs, Linear & Quadratic Equations. MATH 1201, College Algebra

Written Assignment Unit 2: Graphs, Linear & Quadratic Equations. MATH 1201, College Algebra

1. Determine whether the lines given by the equations below are parallel, perpendicular, or neither. Also, find a rigorous algebraic solution for each problem.

a.

b.

c.

Answers : a. screenshot of the first example {3y+4x=12, -6y-8x=1}: from the graph, the two equations are parallel and never meets at a point.

{3y+4x=12, -6y-8x=1}

To find a rigorous algebraic solution I will have to organize the equations: I will multiply the first equation by -2 {-6y-8x=-24, -6y-8x=1} from multiplying the first equation by -2 we can see that the slopes are the same and the y-intercepts are different, from this we can say these two equations are parallel. b. screenshot of the first example {3y+x=12, -y=8x+1}: from the graph, the two equations are not parallel but they intersect at a point but they are also not perpendicular because Their intersection form is not 90-degree angle.

To find a rigorous algebraic solution I will have to organize the equations: {3y+x=12, -y=8x+1} the slope of the first line is -1/3 and the slope of the second line is−8, that means they are not equal and one is not the opposite of the other line.

c. screenshot of the first example {4x-7y=10, 7x+4y=1}: from the graph, the two equations are perpendicular because their intersection forms a right angle or 90-degree angle in the point that meets in.

To find a rigorous algebraic solution I will have to organize the equations: {4x-7y=10, 7x+4y=1} from the equations, we know that the slopes are 4/7 and -7/4 so that means 4/7*-7/4 = -1 which means that the two lines are perpendicular to each other. --------------------------------------------------------------------------------------2. A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by . 1-What is the height of the building? What is the maximum height reached by the ball? How long does it take to reach maximum height? Also, find a rigorous algebraic solution for the problem. Answers: h(t) =-4.9t2+24t+8

1- we could find the height of the building by just saying that time equal to zero t=0. h(t)=4.9*0+24*0+8 so from this, we can say that the height of the building is 8 meters.

2- The ball reaches the maximum height at the horizontal coordinate in seconds so we can find this by using the following formula: x=-b/2a = -24/2(-4.9)= -24/-9.8=2.45 seconds.

3- to find the maximum height reached by the ball I will use this formula : h(-b/2a)= -4.9*(2.45) +24*2.45+8= -4.9*6+58.80+8= 37.40 meters. 2

3. A farmer finds that if she plants 75 trees per acre, each tree will yield 20 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 3 bushels. How many trees should she plant per acre to maximize her harvest? Also, find a rigorous algebraic solution for the problem. Answers: First, we need to put x for trees and y for blushes (75, 20). y-20=-3(x-75) y-20=-3x+225 y=-3x+225+20 y=-3x+245 the number of bushels To find how many trees per acre(T), she needs to maximize her harvest. We multiply x and y. T=x*y

# y=-3x+245

T=x(-3x+245) T= -3x +245x 2

T= -b/2a

# a=-3 and b= 245

T=-245/2*-3 = -245/-6 = 40.83

The farmer have to plant at lest 41 trees to be able to maximize her harvest....