Question 144211
1.)If the length of the diagonal of a rectangle is 50 inches and the area is 1200 in^2,what are the dimensions?
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Using Pythag formula a^2 + b^2 = c^2
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Let x = the width (a) of the rectangle
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then because the area is 1200, we can say
{{{1200/x}}} = b; the length
and
50 = c; the diagonal of the rectangle
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x^2 +(1200/x)^2 = 50^2
:
x^2 + (1440000/x^2) = 2500
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Multiply equation by x^2 to eliminate the denominator, results:
x^4 + 1440000 = 2500x^2
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Arrange as quadratic:
x^4 - 2500x^2 + 140000 = 0
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Factor this to:
(x^2 - 900) (x^2 - 1600) = 0
Two solutions:
x^2 = 900
x = {{{sqrt(900)}}}
x = 30
and
x^2 = 1600
x = sqrt(1600)
x = 40 
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Dimensions: 40" by 30"
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2.) one secretary can do a particular typing jib in 6 hrs and another secretary ca do the same job in 4hrs.How long will it take if the job is done by two secretaries working together?
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Let t = time required working together
Let the completed job = 1
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{{{t/4}}} + {{{t/6}}} = 1
Multiply equation by 12:
3t + 2t = 12
t = {{{12/5}}}
t = 2.4 hrs working together
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3.)The sum of the reciprocals of two consecutive even integers is 9/40.What is the integers?
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x, (x+2) are the two even integers:
{{{1/x}}} + {{{1/((x+2))}}} = {{{9/40}}}
Multiply equation by 40x(x+2) to eliminate the denominators, results:
40(x+2) + 40x = 9x(x+2)
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40x + 80 + 40x = 9x^2 + 18x
:
80x + 80 = 9x^2 + 18x
Arrange as a quadratic equation:
9x^2 + 18x - 80x - 80 = 0 
:
9x^2 - 62x - 80 = 0
Factor this to:
(9x+10)(x-8) = 0
one integer solution
x = 8
Check
1/8 + 1/10 = 9/40
5/40 + 4/40 = 9/40
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4) If a rectangular polygon of ten sides is inscribed (means a figure is a another figure) in a circle of radius r units, then if s units is the length of a side
(r/s)=(s)/(r-s)
solve this formula for s in terms of r.
{{{r/s}}} = {{{s/((r-s))}}}
Cross multiply:
s^2 = r(r-s)
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s^2 = r^2 - rs
;
s^2 + rs = r^2
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s^2 + rs - r^2 = 0; treat it like a quadratic equation, and use the quadratic formula: a=1; b=r; c=-r^2
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{{{s = (-r +- sqrt( r^2-4*1*(-r^2) ))/(2*1) }}}
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{{{s = (-r +- sqrt( r^2 + 4r^2 ))/2 }}}
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{{{s = (-r + sqrt(5r^2 ))/2 }}}; probably only the positive is wanted here
or
{{{s = (-r + r*sqrt(5))/2 }}}
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5) A firm can sell at a price of $100 per unit all of a particular commodity it produces.If x units are produced each day,the number of dollars in the total cost of each days production is x^2+20x+700.How many units should be produced each day so that the firm is guaranteed a profit?
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Revenue (R) = 100x
Profit = Revenue - cost
To guarantee a profit: cost < revenue
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x^2 + 20x + 700 < 100x
x^2 + 20x - 100x + 700 < 0
x^2 - 80x + 700 < 0
Factor this to:
(x-10)(x-70) = 0
x < 70 units 
and
x > 10 units to ensure a profit
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It's getting late for me, will you need the last problem? it will be tomorrow. C
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6) A company that builds and sells desks can sell at a price of $400 per desk all the desk it produces if x desks are built and sold each week,then the numbers of dollars on the total cost of the weeks production is 2x^2+80x+3000.How many desk should built each week in order that the manufacturer is guaranteed a profit?
0 solutions