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Math Help - geometry and indices/log problem

  1. #1
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    geometry and indices/log problem

    1.
    A parallelogram PQRS with area ( 1+2\sqrt{7}) units^2 has length PQ ( 3+\sqrt{7}) units. Given that the distance between the two parallel sides, SR and PQ is ( a+b\sqrt{c}) units where a, b and c are integers. Find, without using a calculator, the values of a, b and c.

    2.
    Given that y=18+ax^b , y=56 when x=4 and y=20 when x=2.5, find the value of a and b.
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by wintersoltice View Post
    1.
    A parallelogram PQRS with area ( 1+2\sqrt{7}) units^2 has length PQ ( 3+\sqrt{7}) units. Given that the distance between the two parallel sides, SR and PQ is ( a+b\sqrt{c}) units where a, b and c are integers. Find, without using a calculator, the values of a, b and c.

    2.
    Given that y=18+ax^b , y=56 when x=4 and y=20 when x=2.5, find the value of a and b.
    1.
    A_{\mbox{parallelogram}} = Bh

    where B= 3+\sqrt{7}, h=a+b\sqrt{c} and A = 1+2\sqrt{7}

    2. just solve the system:

    56 = 18 + a(4)^b
    20 = 18 + a(2.5)^b
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