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math

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a) What is the area of the tri-angle determined by the lines y= − 1/ 2x + 5,y =6x and they-axis?

(b) If b > 0 and m < 0, then the line y = mx +b cuts off a triangle from the first quadrant. Express the area of that tri-angle in terms ofm andb.

(c) The lines y = mx +5, y = x and the y-axis form a triangle in the first quadrant. Suppose this triangle has an area of 10 square units. Findm.

  • math - ,

    a)
    Find where the two slanting lines intersect:
    -x/2 + 5 = 6x
    x = 10/13
    That's the height of a triangle with base on the y-axis, length 5.
    Area = 5 * 10/13 = 50/13

    b)
    the height = b
    the width is where y=0: x = -b/m
    Area = b * -b/m = -b^2/m

    c)
    where do they intersect?
    mx+5 = x
    x = 5/(1-m)
    That's the height of the triangle with base on the y-axis, length 5
    Area = 5/(1-m) * 5 = 25/(1-m)

    25/(1-m) = 10
    25 = 10m - 10
    m = 35/10 = 3.5

  • math - ,

    a) -x/2 +5 = 6x
    x=10/13
    A= 1/2 (b)(h)
    A= 1/2 (10/13)(5)= 25/13

    b) height=b
    width= x =-b/m
    A= 1/2 (-b/m)(b)= -b^2/2m

    c) x=5/(1-m)
    10=1/2 (5) (5/(1-m))
    m= -1/4

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