College Algebra 3.6 Polynomial and Rational Inequalities 3.7 Variation.
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Transcript of College Algebra 3.6 Polynomial and Rational Inequalities 3.7 Variation.
College Algebra
3.6 Polynomial and Rational Inequalities
3.7 Variation
3.6 Polynomial InequalitiesObj: solve polynomial and rational inequalities with the critical
value method
• Critical Value Method– Zeros (solutions) of polynomials are called the
critical points.
– Critical Points of a polynomial divide positive values from negative values.
Example
Solve x2 – 2x – 15 < 0
• Factor and solve for x. These are the critical points.• Choose a value in each interval.
Let x = • Plug each value into the factored form ( + or - ).• Compare relations.• Write solution in interval notation.
Rational Inequalities
Steps:1. Set = to 0 and simplify.2. Find the zeros of the numerator and denominator to
find the critical points.3. Test the intervals.4. Compare the relations.5. Write the solution.
Example
Solve 35
95
x
x
3.7 VariationObj: to set up and solve problems using variation
• Direct Variation
• Inverse Variation
• Joint Variation
• Combined Variation
Direct Variation
Varies directly or is directly proportional toMeaning as one unit increases, the other
increases or as one decreases, the other decreases also
y = kx k is the constant of
proportionality
Examples:
ExampleThe distance d that a ball rolls down an inclined
plane is directly proportional to the square of time t. If the ball rolls 5 feet in 1 second, how far will it roll in 4 seconds?
Set up the equation using initial info.
Solve for k.
Set up new equation with k value and new info.Solve.
Inverse VariationVaries inversely or is inversely proportional toMeaning as one unit increases, the other
decreases and vice versa.
y =
Examples:
x
k
ExampleThe speed v of a gear varies inversely as the
number of teeth t. If a gear that has 48 teeth makes 20 revolutions per minute, how many revolutions per minute will a gear that has 30 teeth make?
Joint Variationmore than one variable
z = kxy
The cost of a concrete patio varies jointly as the area of the patio and the depth of the patio. It costs $500 for a patio with an area of 80 square feet and a depth of 4 inches. Find the cost of a patio with an area of 144 square feet and a depth of 6 inches.
Combined Variationmore than one type of variation
The volume of a given mass of a gas varies directly as the temperature T and inversely as the pressure P. If the volume of the gas is 220 cm3 when T = 40˚C and P = 20 kg/cm2, what is the volume when T = 35˚C and P = 10 kg/cm2?
Assignment
• 3.6 page 420 1 – 13 eoo, 29 – 45 eoo
• 3.7 page 430 1 – 29 eoo