Calculus Path
Statistics Path
MTH095
Intermediate Algebra
Pre-PreCalculus, part 2
vs.
MTH098
Quantitative Literacy 2
Math for "Real" Life
Which class is right for you?
Is calculus in your future or NOT?
Rational Equations
Solve for `x` in `3/(x+2)-4/(x-5)=2/(x^2-3x-10)`
Factor all denominators:
`3/(x+2)-4/(x-5)=2/((x+2)(x-5))`
Find the lowest common denominator:
`LCD=(x+2)(x-5)`
Multiply all terms in the equation by the LCD:
`(x+2)(x-5)*3/(x+2)-(x+2)(x-5)*4/(x-5)` `=(x+2)(x-5)*2/((x+2)(x-5))`
Divide out the common factors:
`cancel((x+2))(x-5)*3/cancel(x+2)-(x+2)cancel((x-5))*4/cancel(x-5)`
`=cancel((x+2)(x-5))*2/cancel((x+2)(x-5))`
The equation simplifies to:
`3(x-5)-4(x+2)=2`
Simplify:
`3x-15-4x-8=2`
`x=-25`
CHECK:
`3/((-25)+2)-4/((-25)-5)=-3/23+2/15=(-45+46)/(23*15)``=1/345`
`2/((-25)^2-3(-25)-10)=2/(625+75-10)=1/690=1/345`
It checks!!!
Balancing Blood Alcohol
Problem Situation: Calculating Blood Alcohol Content
`BAC = -0.015*"hours"+(2.84*"drinks")/("Weight"*"gender")`
| Hours | Blood Alcohol Content |
|---|---|
| 0 | 0.116 |
| 1 | 0.101 |
| 2 | 0.086 |
| 3 | 0.071 |
| 4 | 0.056 |
| 5 | 0.041 |
Radical Equations
Solve for `x` in `sqrt(10-x^2)-x=2`
Isolate the radical:
`sqrt(10-x^2)=x+2`
Square both sides:
`(sqrt(10-x^2))^2=(x+2^2)`
Clean up:
`10-x^2=(x+2)(x+2)`
`10-x^2=x^2+4x+4`
Collect all terms on one side:
`0=2x^2+4x-6`
Pray you can factor, or use Quadratic Formula:
`0=2(x^2+2x-3)`
`0=2(x+3)(x-1)`
So, `x=-3` or `x=1`
CHECK:
`sqrt(10-(-3)^2)-(-3)=sqrt(1)+3=4`, but NOT `2`
`x=-3` does not check!?!
`sqrt(10-(1)^2)-(1)=sqrt(9)-1=3-1=2`, This Checks!!!
So, only `x=1` is a solution
Compunding Interest Makes Cents
Problem Situation: The Value of a CD
Suppose you invest $1,000 principal in a two-year CD, advertised with an annual percentage rate (APR) of 2.4%, where compounding occurs monthly.
`I=P*r*t`
Disclaimer:
You should check with your advisor before taking a math class leading to calculus. Algebra classes are known to cause stress, anger, depression, and occasionally rashes, as well as lead to calculus. Please consult a physician if negative symptoms persist.