Sequences & Series Questions and Answers
Algebra
Sequences & SeriesFill in the blank A value of the variable that makes the equation a true statement is called a n A value of the variable that makes the equation a true statement is called a n of the equation of the equ solution expression
Algebra
Sequences & SeriesUse the finite difference formulae from page 126 of the notes print version to find approximate values of the derivatives f in the following table Use the centred difference approximation wherever possible Enter your answers to two decimal place accuracy tj fj f Number 0 1 0 3 0 22 Number 0 6 0 11 Number 0 9 0 09 Number
Algebra
Sequences & Series5 Si cot 2 a y cos B B entonces halla el valor exacto de sen a 12 O 33 65 O 33 63 35 65 33 45
Algebra
Sequences & Series27 Express the following using exponents 4x y O 2x y O 2x y 3 O 2 x y 2 x y
Algebra
Sequences & SeriesAfter his lunch G del tells you that he ate either apples or bananas also that if he had corn then he had a decaf coffee also that he didn t drink either decaf coffee or espresso Define propositions A through E for relevant parts of G del s statements For example define A to be G del ate apples and so on Write each of the statements G del made about his lunch in terms of the propositions A through E Note that since G del is a logician he uses the word or to mean a logical OR rather than the or used by everyday mortals It is not widely known but G del lied about everything every statement he said was false Determine what G del had for lunch Justify your answer
Algebra
Sequences & SeriesWhat will it cost to carpet a rectangular floor measuring 24 feet by 18 feet if the carpet costs 21 92 per square yard It will cost www
Algebra
Sequences & SeriesF 24 Use the following similar triangles AABC ADEP If AC 10 when DF 19 and AB 13 what is DE Solve mathematically Round your answer to the nearest tenth B E
Algebra
Sequences & Series16 How much water should be added to 105 oz of 60 acid solution to dilute it to a 40 acid solution O 52 5 oz O45 65 oz O 5 25 oz O impossible to do 17 Given two circles X and Y with radii 1 in and 12 in respectively the ratio of the areas is Write your answer as a fraction
Algebra
Sequences & Series27 If there are 11 girls in a class of 16 what is the ratio of girls to boys in the class O Of O O 28 The perimeters of two similar figures are 42 in and 48 in What is the ratio of lengths of corresponding sides State your answer as a fraction x
Algebra
Sequences & SeriesMultiply the monomials 3x y 4xy4 5x y 3 3x y 4xy4 5x y Simplify your answer
Algebra
Sequences & SeriesEvaluate the algebraic expression for the given value x 4x 2 for x 7 When x 7 x 4x 2
Algebra
Sequences & Seriesd u dt2 u sin t a linear b third order c second order d nonlinear e first order Of fourth order
Algebra
Sequences & SeriesSuppose U x x 3x x E IR and W x x 3x x E IR a Prove or disprove that U and W are subspaces of IR3 b Describe U W using symbols c Describe U W without symbols
Algebra
Sequences & Seriesto a poster that is 3 ft by 1 ft 5 How many milliliters of pure acid should be added to 25 ml of 50 acid to make 80 acid solution Round your answer to the nearest hundredth if necessary x ml 6 17 9 of 43 is O 769 7 O 7 697 O 76 97 O2 402
Algebra
Sequences & SeriesExplain how to solve the following 5 8 10 x 100 X Choose the correct answer below OA Apply the cross products principle then isolate x on one side of the equation X OB Subtract from both sides 8 Oc Multiply each side by the reciprocal of the other side OD Divide the numerators by their respective denominators
Algebra
Sequences & Series10 HW Write the English phrase as an algebraic expression Let x represent the number Twelve more than a number The phrase written as a algebraic expression is
Algebra
Sequences & SeriesPerform the indicated operation 35 36x 72x 6x 5 35 36x 72x 6x 5 x 7 x 7 the
Algebra
Sequences & SeriesPerform the indicated operation 5xy2 3x y 3x y 8xy 5xy 3x y 3x y 8xy Simplify your answ
Algebra
Sequences & SeriesPerform the indicated operation 6ab b a b 7ab a Cab 1 2 2 b 7b Simplify your answe
Algebra
Sequences & SeriesA cyclist is riding a bicycle whose wheels have a radius of 12 inches Suppose the wheels turn at a rate of 230 revolutions per minute a Find the angular speed of the wheels in radians per minute b Find the speed of the cyclist in miles per hour Use the fact that I mi 5280 ft Do not round any intermediate computations and round your answer to the nearest whole number a Angular speed radians per minute b Speed of the cyclist miles per hour X
Algebra
Sequences & SeriesUse the law of exponents to simplify Write the answer with positive exponents All variables are nonzero 7x y 3 2 C 7x y 3 2 Simplify your answer Type exponential notation with positive exponents Use integers or fractions for any numbers in
Algebra
Sequences & SeriesUse the negative exponent rules to simplify 1 1 3 11 4 Simplify your answer
Algebra
Sequences & Seriesse the negative exponent rule to simplify Write the answer with only positive exponents All variables are nonzero
Algebra
Sequences & Seriesimplify the following expression All variables are nonzero 2wz 7w 2wz 2 2 2 2 7w II 2
Algebra
Sequences & SeriesSimplify Step by Step Solution Step 1 Rearrange factors Part 1 of 4 Write the answer with only positive integer exponents All variable O Points 0 of 1 4 D D
Algebra
Sequences & SeriesSimplify each expression so that all exponents are positive All variables are nonzer a y 9 b y 9 c y 9
Algebra
Sequences & SeriesComplete the sentence If a is a nonzero real number and n is a positive integer then a If a is a nonzero real number and n is a positive integer then a 1 C
Algebra
Sequences & SeriesWhich of the following scenarios have a reasonable solution Read each one carefully and select all that apply Scenario A student takes out two loans totaling 5000 at 4 and 6 annual interest The total interest after 1 year is 254 Find the amount of each loan Solution The loan at 4 interest is 2300 and the loan at 6 is 2700 Scenario An athlete ran for part of an hour at 6 miles per hour and for the rest of the hour at 8 miles per hour The total distance traveled is 7 miles How long did the athlete run at each speed Solution The athlete ran for half an hour at 6 miles per hour and one and a half hours at 8 miles per hour Scenario The perimeter of a rectangle is 40 feet The rectangle s length is 3 times as long as it s width Find the dimensions of the rectangle Solution The width of the rectangle is 5 feet The length of the rectangle is 15 feet Scenario If 2 bags of popcorn and 3 soft drinks cost 7 and 3 bags of popcorn and 2 soft drinks cost 8 find the price of a bag of popcorn and the price of a soft drink Solution A bag of popcorn costs 3 and a soft drink costs 2
Algebra
Sequences & SeriesMarty is 3 years younger than 6 times his friend Warren s age The sum of their ages is greater than 11 What is the youngest age Warren can be Enter your answer as a whole number in the box years
Algebra
Sequences & SeriesPlot the inequality on the number line a 1 ora 8 Choose the proper tools with the correct endpoints then click and drag the endpoints to the correct location Notice the trash can is available if an error is made 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10
Algebra
Sequences & SeriesWhat is the interval notation for the compound inequality I 3 or 1 7 O 3 7 O 0 3 or 7 O 0 3 or 7 O 3 7
Algebra
Sequences & Serieshe slope and a point on a line are given Use this information to locate three additional points on Slope 3 point 2 4 etermine three points on the line with slope 3 and passing through 2 4 OA 1 1 3 7 4 10 O B 1 1 7 3 10 4 OC 5 5 3 1 2 4 O D 5 5 1 3 4 2
Algebra
Sequences & SeriesCalculate the change of enthalpy for the reaction CH4 g NH3 g HCN g 3H2 g from the following reactions Reaction 1 N g 3H2 g 2NH3 g Change in enthalpy 91 8 kJ mol Reaction 2 C s graphite 2H2 g CH4 g Change in enthalply 74 9 kJ mol Reaction 3 H g 2C s graphite N g 2HCN g Change in enthalpy 270 3 kJ mol To earn FULL POINTS you need to include ALL YOUR WORK used to complete the calculation the correct calculated value AND the correct units
Algebra
Sequences & Series14 15 16 17 18 19 20 21 Temperature C 22 Warm Up The dot plot shows a town s daily low temperature in degrees Celsius for 24 days Briefly describe the data distribution and relate the measure of center to the shape of the dot plot shown
Algebra
Sequences & SeriesUse the Quotient Rule to simplify All variables are nonzero 4z7w5 2z4w 4z7w5 2 4 3 11
Algebra
Sequences & SeriesFind the product 4x 4x 4 4x 6 Type an expression using x as the variable Simplify your a
Algebra
Sequences & SeriesExample Grace is making a model of a building that is shaped like a parallelogram The dimensions of the parallelogram in her model are shown What is the area of the parallelogram in Grace s model The segment labeled 4 in is perpendicular to the side labeled 18 in So the base of the parallelogram is 18 in and the height is 4 in You can use the formula for the area of a parallelogram A b h A 18 4 72 10 7 in The area of the parallelogram in Grace s model is 72 in 4 in 18 in Look at the parallelogram in the Example Describe a way to decompose the octangle
Algebra
Sequences & SeriesUse the graph of f x to find the x intercepts of the graph and the zeros of the function The x intercepts are Type ordered pairs Use a comma to separate answers 10 8 8 Ay 20 16 12 B R