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    Equations of Lines, Slopes, Intercepts and Word Problems (15 Problems in Total)

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    1. Find a linear function perpendicular to the function y= -5x + 12 at the point (2,5) in standard form, point slope form, and slope-intercept form.
    The orginal line is y = -5x + 12 (slope is -5), so the perpindicular line will be y = 1/5x + ?
    5 = (1/5)2 + ?.
    4 3/5 = ?
    y = 1/5x +4 3/5

    2. A ball is thrown up into the air.Measurements are taken and a function is found to model the height of the ball versus the time the ball is in the air. The function derived from the data, H(t) = -4.92 + 40.5t + 25.3, is the model for the height of the ball, H(t) in meters, at time t (in seconds)
    a) Calculate H(1.672) and interpret the meaning of this result?
    b) Find the domain & range of the function H(t)

    h=0 h(t)=function notation
    Acceleration near earth = 9.7 m/s
    h =-4.9t2+40.5t+25.3

    y-max = 20
    (t)x -10 10
    Plug in what t is
    At t=1, h=-4.9(1)2 = 40.5(1)+25.3 =60.9 m x-min=-1 x-max = 5
    At t=2, h=-4.9(2)2 = 40.5(2)=25.3 = 86.7m -10
    y (h)

    Avg. Slope= h = change in height (m) 60.9 - (86.7) = -25.8 m/s =25.8m/s
    t change in time (s) 1-2
    Represents the average speed traveled between pt. 1& pt. 2
    Avg. slope = avg. rate of chg. (speed) from t=1sec to t=2 sec which is 13.2 m/s downwards

    3.A business has a product that is sold in many local outlets. This product sells for $39.95 each. The weekly fixed cost of the business is $2675/week and each additional unit sold costs the company $17.85 to produce and sell.
    a. How much revenue is generated on the sale of 349 units? What is the cost of selling units?
    b. Create models for the revenue and the cost of sales for the sales of this product.
    c. Remembering that profit is revenue minus cost of sales, create a profit model from the revenue and the cost of sales models.
    d. Find the number of units you need to sell to "breakeven".
    e. What is the inverse of the profit function? Use this function to determine the number of units needed to be sold so that the profit is $13,000.
    I am sure there is a simple way to figure this all out but for some reason I can't figure it out!
    a)Revenue is 349 units x $39.95 each = $13,942.55
    Cost of sales is (349 units x $17.85 each) + $2675 fixed costs = $8,904.65
    Profit is $13,942.55 revenue - $8,904.65 cost of sales = $5,037.90
    or do I take 39.95(1)+ 348(17.85)=$6251.75 would I minus the 2675 here =3576.75 then would I divide the 349 by the final revenue? = $10.25ea
    b) I'm not sure of the technical way to write a "model" but it must have to do with... (# of units sold x price each) - (cost of unit to produce + fixed costs) = profit
    c) No clue
    d) I believe it's around 121 units to breakeven. Basically I just calculated the costs for 121 units [(121 x $17.85) + $2,675] and then the revenue for 121 units [121 x $39.95] until the two numbers are the same such that revenue - costs = zero. I think it's about121
    4) The height of a football (as a function of the horizontal distance traveled) is given by the function h(x) = 0.75x - 0.0192x2, where all measurements are in meters. Rewrite the function in vertes form and use the information to determine the initial horizontal and vertical position of the football.
    I honestly do not know how to start this??

    5)Find a linear equation (in slope-intercept, point-slope and standard forms) for the line through the points (2,4) and (-1,5)
    Another one!!!
    I know the formulas: a) y= mx+b (slope-intercept form)
    b) y - y1 = m(x-x1) (point-slope form)
    c) ax =by =c (standard form)

    a) 4=m(-1)+b I need more info don't I?
    b)m = 5 - 4
    -1 - 2 = -1/3
    y = -1/3x + b
    4 = (-1/3)2 + b
    4 2/3 = b
    y = -1/3x + 4 2/3.
    b) What are a & b?

    6) Find the inverse of the following functions:
    a) f(x) = -5x + 7
    b) g(t) = 3t+6

    a) f-1(y) =-7y + 5 =x Not to sure about this?
    b) g-1(t) = 1/3 (t+6)3 I think this is it's inverse?

    7) Find the following functions f(x) = -6x+5 and g(x) = 3x2 - 10 simplify results
    a) (fg)(x) =(-6x+5)(3x2-10) = (-6x + -50)3x2
    b) (g+f)(x) = 3x2-10+ -6x+5=-5+6x+3x2
    c) 3?g(x-4) = 3(3x2-10)-4 = 3x2-30-4 = 3x2-26

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    Solution Preview

    Please see the attached file for the complete solution.
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    1. We have a function , its slope is . Then the perpendicular function has the slope . It passes the point .
    The point-slope form is:
    The slope-intercept form is:
    The standard form is
    2. The height is .
    a. . This result means that the ball is still going upward and thus the height of the ball is increasing.
    b. The domain of the function is . ...

    Solution Summary

    Problems involving equations of lines and word problems are solved. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.