ASSIGNMENT 10DYLAN ZWICK’S MATH 1010 CLASS6.6 Solving Rational EquationsDetermine whether each value of x is a solution of the equation.6.6.1:x3−x5=43(a) x = 0 (b) x = −2 (c) x =18(d) x = 10Solve the equation.6.6.5:x6− 1 =236.6.7:14=z + 186.6.11:z + 23= 4 −z126.6.12:2y − 96= 3y −3412 DYLAN ZWICK’S MATH 1010 CLASS6.6.14:4x − 27−514= 2x6.6.15:t2= 12 −3t226.6.18:z − 49−3z + 118=326.6.20:u − 26+2u + 515= 36.6.22:2x − 710−3x + 15=6 − x5ASSIGNMENT 10 36.6.23:925 − y= −146.6.25: 5 −12a=536.6.28:53=67x+2x6.6.30:78−16t − 2=346.6.32:10x + 4=154(x + 1)4 DYLAN ZWICK’S MATH 1010 CLASS6.6.35:3x + 2−15=15x6.6.39:t4=4t6.6.45:4x(x − 1)+3x=4x − 16.6.47:2x5=x2− 5x5x6.6.49:y + 1y + 10=y − 2y + 4ASSIGNMENT 10 56.6.50:x − 3x + 1=x − 6x + 56.6.55:42x + 3+175x − 3= 36.6.57:2x − 10−3x − 2=6x2− 12x + 206.6.61:xx − 2+3xx − 4= −2(x − 6)x2− 6x + 86 DYLAN ZWICK’S MATH 1010 CLASS6.6.65:x3=1 +4x1 +2x6.6.83 Painting: A painter can paint a fence in 4 hours, whilehis partner can paint the fence in 6 hours. How long would ittake to paint the fence if b oth worked together?6.7 Applications and VariationsWrite a model for the statement.6.7.1: l varies directly as V .6.7.2: C varies directly as r.6.7.3: V directly proportional to t6.7.4: A is directly proportional to w.6.7.5: u is directly proportional to the square of v.6.7.6: s varies directly as the cube of t.ASSIGNMENT 10 76.7.7: p varies inversely as d.6.7.8: S varies inversely as the square of v.6.7.10: P is inversely proportional to the square root of 1 + r6.7.13 Boyle’s Law : If the temperature of a gas is not allowedto change, its absolute pressure P is inversely proportional toits volumeV .6.7.14 Newton’s Law of Universal Gravitation: The grav-itational attraction F between two particles of masses m1andm2is directly proportional to the product of the masses andinversely proportional to the square of the distance r betweenthe particles.Write a verbal sentence using variation terminology to describe theformula.6.7.18 Volume of a Sphere: V =43πr3Find the constant of proportionality and write an equation that relatesthe variables.6.7.21: s varies directly as t, and s = 20 when t = 4.6.7.25: n varies inversely as m, and n = 32 when m = 1.58 DYLAN ZWICK’S MATH 1010 CLASS6.7.32: z is directly proportional to x and inversely proportionalto the square root of y, and z = 720 when x = 48 and y = 81.6.7.43: Average Speeds You and a friend jog for the same amountof time. You jog 10 miles and your friend jogs 12 miles. Yourfriends’s average speed is 1.5 miles per hour faster than yours.What are the average speeds of you and your friend?6.7.47: Working Rate It takes a lawn care company 60 minutesto complete a job using only a riding mower, or 45 minutesusing the riding mower and a push mower. How long does thejob take using only the push mower.6.7.52: Learning Curve A psychologist observes that the numberof lines N of a poem that a four-year-old child can memorizedepends on the number x of short sessions spent on the task,according to the mode N =20xx + 1.(a) What is the domain of the function?(b) Use a graphing calculator to graph the function.ASSIGNMENT 10 9(c) Use the graph to determine the number of sessions neededfor a child to memorize 15 lines of poem.(d) Verity the result of part(c) algebraically.6.7.69: Revenue The weekly demand for a company’s frozen piz-zas varies directly as the amount spent on advertising and in-versely as the price per pizza. At $5 per pizza, when $500 isspent each week on ads, the demand is 2000 pizzas. If advertis-ing is increased to $600, what price will yield a demand of 2000pizzas? Is this increase worthwhile in terms of revenue?7.1 Radicals and Rational ExponentsFind the root if it exists.7.1.1:√647.1.2: −√1007.1.4:√−257.1.5:3√−277.1.7:√−17.1.8: −√−1State whether the number is a perfect square, a perfect cube,or nei-ther.10 DYLAN ZWICK’S MATH 1010 CLASS7.1.9: 49 7.1.13: 96 7.1.14: 225Find all of the square roots of the perfect square.7.1.15: 25 7.1.16: 121Evaluate the radical expression without using a calculator. If notpossible, state the reason.7.1.39:√827.1.42:p(−12)27.1.62: (3√−6)3Evaluate without using a calculator.7.1.75: −361/27.1.78: 81−3/47.1.86: (82)3/2Rewrite the expression using rational exponents.7.1.91: x3√x67.1.95:√x√x37.1.99:3√x2·3√x77.1.105: z2py5z4Simplify the expression.7.1.107: 31/4· 33/47.1.125:(x + y)3/44√x +