Question 144211: 1.)If the length of the diagonal of a rectangle is 50 inches and the area is 1200 in^2,what are tge dimensions?
2.) one secretary can do aparticular typing jib in 6hrs 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?
3.)The some of the receprocals of two consecutive even integers is 9/40.What is the integers?
4) If a rectangular polygon of ten sides is inscribed (means a figure is a another figure) in a circle of raduis 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.
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 ia x^2+20x+700.How many units should be produced each day so that the firm is guaranteed a profit?
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?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 1.)If the length of the diagonal of a rectangle is 50 inches and the area is 1200 in^2,what are the dimensions?
:
Using Pythag formula a^2 + b^2 = c^2
:
Let x = the width (a) of the rectangle
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then because the area is 1200, we can say
 = b; the length
and
50 = c; the diagonal of the rectangle
:
x^2 +(1200/x)^2 = 50^2
:
x^2 + (1440000/x^2) = 2500
:
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 = 
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
:
 +  = 1
Multiply equation by 12:
3t + 2t = 12
t = 
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:
 +  = 
Multiply equation by 40x(x+2) to eliminate the denominators, results:
40(x+2) + 40x = 9x(x+2)
:
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.
 = 
Cross multiply:
s^2 = r(r-s)
:
s^2 = r^2 - rs
;
s^2 + rs = r^2
:
s^2 + rs - r^2 = 0; treat it like a quadratic equation, and use the quadratic formula: a=1; b=r; c=-r^2
:
:
:
 ; probably only the positive is wanted here
or
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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?
:
Revenue (R) = 100x
Profit = Revenue - cost
To guarantee a profit: cost < revenue
:
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
:
:
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?
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