Section 3.5 Geometric and Scientific Applications

Transcription

1 Section. Geometric and Scientific Applications 6 Section. Geometric and Scientific Applications.. I Prt I I Note: 8 monts. years Te interest is $49.9. I Prt r 4 r r r Te interest rate is 6%.. 7. A b 6 b b 6 b b 4 b Te lengt of te base is 4 inces. V lw Te dept of te pool is. meters. 9. Verbal Model: Total interest Interest from investment A Interest from investment B Labels: Total interest $00 Principal for investment A P dollars Annual interest rate for investment A 0.07 Time in investment A year Interest from investment A 0.07 dollars Principal for investment B 6000 dollar Annual interest rate for investment B 0.09 Time in investment B year Interest from investment B P dollars P P P P P 40 P P and 6000 P 4000 P P s So, $000 was invested at 7% and $4000 was invested at 9%. 04 Cengage Learning. All Rigts Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in wole or in part.

2 64 Capter Linear Equations and Problem Solving. Verbal Model: Amount of alcool in Amount of alcool in Amount of alcool in 9% alcool solution 00% alcool solution final alcool solution Labels: 9% solution: Percent alcool 0.9 decimal form Amount of alcool solution 00 milliliters 00% solution: Percent alcool 00 decimal form Amount of alcool solution x milliliters 40% solution: Percent alcool 0.40 decimal form Amount of alcool solution 00 x milliliters x x 9 x x 0.6x x 0.6 x You sould add milliliters of pure alcool to te 9% solution.. Verbal Model: Work done Portion done by you Portion done by friend Labels: Bot persons: work done job, time t ours Your work: rate job per our, time t ours Friend s work: rate job per our, time t ours t t t 6 6t t t 6 6 t It would take 6 ours (or our, minutes) to mow te lawn. 04 Cengage Learning. All Rigts Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in wole or in part.

3 Section. Geometric and Scientific Applications 6. Verbal Model: Work Portion done Portion done done by first worker by second worker Labels: Bot persons: work done task, time t minutes First worker: rate tasks per our, time t minutes m Second worker: rate tasks per our, time t 9m minutes m 9m t m 9m 9 t 9m 9m 0 t 9m 9m 9m0 t 0 0 9m 9 m t 0 t t Working togeter, te two people can complete te task in 9 0 m minutes. 7. Verbal Model: Volume Rate Time Labels: Volume 000 milliliters Rate r Time 8 ours 000 r r 8 8 r milliliters per our Te solution flows troug te tube at te rate of milliliters per our. 9. Verbal Model: Cost of carnations Number of dozens Cost of roses Number of dozens Total cost per dozen of carnations per dozen of roses of flowers Labels: Cost of carnations per dozen dollars per dozen Number of dozens of carnations x dozens Cost of dozens of roses 8 dollars per dozen Number of dozens of roses x dollars Total cost of flowers 84 dollars x x 8 84 x 6x 84 48x 84 x 8 and x 6 So, 8 dozen carnations and 6 dozen roses were ordered. 04 Cengage Learning. All Rigts Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in wole or in part.

4 66 Capter Linear Equations and Problem Solving. Te formula for te volume of a circular cylinder is V r.. Perimeter is measured in linear units, suc as inces, yards, and meters. Area is measured in square units, suc as square feet, square centimeters, and square miles. Volume is measured in cubic units, suc as cubic inces, cubic feet, and cubic meters.. Verbal Model: Distance Rate Time Labels: Distance d meters Time minutes d 4 Rate 4 meters per minute d 48 Te distance is 48 meters. 7. Verbal Model: Distance Rate Time 9. Labels: Distance 0 miles Time t ours Te time is 4. ours. A b A b A b A b b b A b Rate 0 miles per our 0 0t 0 t 0 4. t. Verbal Model: Amount of alcool Amount of alcool Amount of alcool in Solution in Solution in final solution Labels: Solution : Percent alcool 0.0; amount gallons Solution : Percent alcool 0.0; amount x gallons Final solution: Percent alcool 0.; amount x gallons x 0. x. 0.0x 6. 0.x. 0.0x 0.x 6. 0.x 0.x. 0.0x x x.7 0.0x x 7 and x 00 Tere are 7 gallons of Solution and 00 gallons of te final solution. 04 Cengage Learning. All Rigts Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in wole or in part.

5 Section. Geometric and Scientific Applications 67. Verbal Model: Amount of alcool Amount of alcool Amount of alcool in Solution in Solution in final solution Labels: Solution : Percent alcool 0.; amount quarts Solution : Percent alcool 0.4; amount x quarts Final solution: Percent alcool 0.0; amount x quarts x 0.0 x x.0 0.0x x 0.0x.0 0.0x 0.0x x x x x x and x 0 Tere are quarts of Solution and 0 quarts of te final solution.. Common formula: I Prt Labels: I P r $8.98 $00 annual interest rate t year I r r r r Prt Te annual interest rate is approximately 8.6%. 7. Verbal Model: Perimeter Side a Side b Side c Labels: Perimeter 8 meters Side a x meters Side b x meters Side c 4x 7 meters 8 x x 4x 7 8 6x x x 90 6x 6 6 x and 4x Te lengts of te tree sides of te triangle are meters, meters and meters. 9. Verbal Model: Faster car s Slower car s Distance distance distance between cars Labels: Faster car s rate Slower car s rate 4 Time 4 miles per our miles per our our Distance between cars x miles 4 44 x x 8 x Te cars will be 8 miles apart. 04 Cengage Learning. All Rigts Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in wole or in part.

6 68 Capter Linear Equations and Problem Solving 4. Verbal Model: Distance driven Distance driven Total at iger speed at lower speed distance Labels: Higer rate miles per our Lower rate 48 miles per our Time at iger rate x ours Time at lower rate 4. x ours Total distance miles x x x 04 48x 7x 04 7x x 4. x 4.. Te mp speed was maintained for ours and te 48 mp speed was maintained for. ours (or our and minutes). 4. To do tis calculation mentally, you could divide 80 miles by to obtain 90 miles, te distance you traveled in ours. Ten divide by again to obtain 4 miles, te distance you traveled in our. Your average speed is 4 miles per our. Distance 80 Rate 4 miles per our Time 4 4. Solving for : A x y A x y A x y A x y x y x y A x y You would use tis result to find te eigt of a trapezoid. Solving for x: Solving for y: A x y A x y A x y A x y A x y A x y A x y A x y A A x y x y A A y x y y x x y x A A y x x y You would use tis result to find te base x of a trapezoid. You would use tis result to find te base y of a trapezoid. 04 Cengage Learning. All Rigts Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in wole or in part.

7 Section.6 Linear Inequalities Yes, if te radius of a circle is doubled, te circumference is doubled. c r r 4r r c No, if te radius is doubled, te area is not doubled; te area is multiplied by 4. A r r 4r 4r 4A 49. (a) Natural numbers: 7, (b) Integers: 7,,. (c) Rational numbers:.8,, 7,.7,, (d) Irrational numbers: None 0 y Cross-multiply 6 4y 6 4y y y Section.6 Linear Inequalities.. 9 x x 9 Cross-multiply x 8 x 8 x x Cross-multiply 6 0x 6 0x x x. x is greater tan or equal to x is less tan or equal to 0.. y is less tan x x y 7. z is greater tan or equal to and less tan or equal to y is greater tan and less tan or equal to z y. (a) x (b) x (c) x (d) x is a solution. is not a solution. is a solution. is not a solution. 04 Cengage Learning. All Rigts Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in wole or in part.