Word problem help

A

alyren

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Sep 9, 2010
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59
1)A rectangle that is x feet wide is inscribed in a circle of radius 29 feet. express the area of the rectangle as a function of x.


2) Given the function f(x)=x^2+6/x+5, find the x-intercept algebraically, if any, of the graph of f.
after i solve for x i got +- sqrt of -6, because x-int cant be negative # under sqrt, was wondering if i do it right.
 
\(\displaystyle 2) \ Given: \ f(x) \ = \ x^2+\frac{6}{x}+5, \ find \ x-intercept.\)

\(\displaystyle Now, \ when \ the \ function \ intercepts \ the \ x-axis, \ its \ y \ value \ is \ zero.\)

\(\displaystyle Ergo, \ 0 \ = \ x^2+\frac{6}{x} \ +5, \ \implies \ x^3+5x+6 \ = \ 0, \ x \ \ne \ 0.\)

\(\displaystyle Therefore \ x^3+5x+6 \ = \ (x+1)(x^2-x+6) \ = \ 0, \ x \ = \ -1, \ QED.\)

\(\displaystyle See \ graph, \ note \ x \ = \ 0 \ is \ a \ vertical \ asymptote.\)

[attachment=0:2145pnxr]ddd.jpg[/attachment:2145pnxr]
 
the first there is no diagram provide. im sorry on the second 1wasn't post clearly, the equation is F(x)=(x^2+6)/(x+5)
 
alyren said:
the first there is no diagram provide. im sorry on the second 1wasn't post clearly, the equation is F(x)=(x^2+6)/(x+5)
Click to expand...
First: I meant YOU draw a diagram to help YOU solve the problem:
you will see that the rectangle's diagonal = diameter = 29*2 = 58

Second: since we have (x^2+6)/(x+5), when set to 0, then x^2 + 6 = 0, and x<>-5
 
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