Sequences & Series Questions and Answers

Find the exact values of sin If tan x sin COS tan N8N8N 8 5 12 7 cos 2 COS and x is in quadrant 2 and tan without solving for x Assume 0 x 2

Considering only the values of a and for which Select the correct answer below cot acot 1 tan a tan B cot cot a O1 tan atan Ocota cot sin a sin asin is defined sin a sin asin B

Given f x 9x and g x 2x 1 find the following expressions a fog 4 b gof 2 b gof 2 c fof 1 c fof 1 d gog 0 a fog 4 b gof 2 c f of 1 d gog 0 Simplify your answer Simplify your answer Simplify your answer Simplify your answer THE S

Consider the functions f x 3x 3 and g x 1 3 x 3 a Find f g x b Find g f x c Determine whether the functions f and g are inverses of each other a What is f g x f g x Simplify your answer Give any values of x that need to be excluded from f g x Select the correct choice below and fill in any answ boxes within your choice O A x Use a comma to separate answers as needed OB No values should be excluded from the domain

5 3 5 is a point on the graph of f x Under the transformation y f x 2 4 the point 3 5 will be translated to what point

3 Describe any changes from the parent graph a y 2 x 1 3 b f x x 5 c y x 2 1

How much money should Lisa invest today in a fund that earns interest at 3 06 compounded quarterly if he wants to receive 5 500 at the end of every 6 months for the next 3 years

a Check all the following numbers that are properly expressed in scientific notal 4 x 10 1 1 23 x 106 29 10 3 0 44 x 1014 1 x 104 0 035 x 1011 X

Approximating a Centroid In Exercises 27 30 use a graphing utility to graph the region bounded by the graphs of the equations Use the integration capabilities of the graphing utility to approximate the centroid of the region 27 y 10x 125 x y 0

point Match the following guess solutions y for the method of undetermined coefficients with the second order nonhomogeneous linear equations below A Yp x Ax Bx C B yp x Ae C yp x A cos 2x B sin 2x D Yp x A B cos 2x Cr D sin 2x E yp x Are and F yp x e A cos 2x B sin 2x d y dr 4y x 2 20 d y 6 8y p2r dy dx dr y 4y 20y 3 sin 2x y 2y15y e cos 2x

A professor is interested in the average length of books in her library She has divided her books into a few different categories 235 books on mathematics 290 books on sports and 166 books on interior design Rather than examining all the books she plans to use a stratified sample of 50 books How many sportsbooks should she choose Enter a whole number Provide your answer below

a through j 21 1 0 15 11 3 9 3 7 0 2 1 5 5 2 0 4 2 1 1 3 3 6 0 y f x 15X Q G

given f x In x 2 it to answer parts a through f below The range of f is 0 00 Type your answer in interval notation Determine the vertical asymptote of f Select the correct choice below and if necessary fill in the answer be complete your choice A The vertical asymptote of f is x 2 Simplify your answer OB There is no vertical asymptote d Find f the inverse of f f x Simplify your answer

Determine the amplitude frequency and period of the function in the graph below and find the equation of the function 2 2 3

If 10 7 what does 10 x equal 10 x Tyne a reduced fraction

ind the maximum value of f x1 x2 x3 3x 5x 4x3 subject to the following constraints Write the exact answer Do not round If the function has no maximum value write None Answer 2x 3x 2x3 5 5x 2x 2x3 5 Tables Keypad Keyboard Shortcuts

5 Shown below is a box on which a moment is applied The box has to be completely constrained using links that have pin joints Show detailed process as to how this can be done

3 If you are given a sequence of th powers ank is there a way to figure out the value of the coefficient a

7 Suppose that the terminal side of angle a les in Quadrant I and the terminal side of angle lies in Quadrant IV If sin 25 sin a b GULD sin a 8 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression and cos 29 find the exact value of

3 The surface area S in square meters of a hot air balloon is given by S r 4 where r is the radius of the balloon in meters If the radius r is increasing with time t in seconds according to the formula r t t t 0 find the surface area S of the balloon as a function of the time t 4 S t Type an expression using t as the variable Type an exact answer using as needed Use integers or fractions for any numbers in the expression Simplify your answer

1 For f x 9x and g x x find fog x and gof x Then determine whether fog x gof x What is fog x fog x

Suppose that 3x 2y t and x t cos 8 Find 8 and dy X

Use the unit circle to find the value of the trigonometric functions Sketch a circle indicating the angle for each part a tan 5 6 b sin 16 6 c cot 7 6 d sec 3

SHOW ALL WORK CAREFULLY IN YOUR BLUE BOOK NO CALCULATORS ALLOWED 1 21 pts Evaluate a tan cos b cos sin3 4 2 15 pts Simplify the following cosx tanx c cot cos 4 x COSX

Part 5 Lab Scenario Question 35 3 points STATION 1 At this station there are three test tubes to examine Test tube A contains a piece of magnesium Test tube B contains aqueous silver nitrate Test tube C has the product of the reaction when the contents of both tubes A and B are mixed together 1 What type of reaction was this and how do you know 1 mark 2 Write the chemical equation but do not balance 1 mark 3 What is the chemical formula for magnesium nitrate 1 mark Daragraph B T 11 A A

Assume that I is a linear transformation Find the standard matrix of 1 T R R first rotates points through radians and then reflects points through the horizontal x axis A

Rewrite the rational expression 5 x 8 with the LCD

1 3 5 7 25 24 22 6 4 2 A 300 1330 B 324 3 332 325

1 Find the mass and center of mass of the lamina that occupie the triangular region D with vertices 8 0 2 1 0 3 and has the density function p x y 8 z y

Find the z number associated with a 95 level of confidence Round your answer to two decimal places

Tire Right Front 75 Left Front Area traced Estimate of Area of on paper in tread Contact eft Rear 78 Right Rear 76 75 45 45 46 45 A1 A2 A3 A4 Pressure lb in 35 32 36 36 Force lb F F2 F3 F4

1 Approximately 0 02 of a 100 mg dose of the drug miglitol GLYSET has been shown to appear in human breast milk Calculate the quantity of drug detected in milligrams following a single dose Round to 3 significant figures Answer 2 Last month a patient paid 20 00 copay for his monthly supply of metoprolol a blood pressure medication This month it looks like the insurance company has raised the copay to 23 00 Express the increase of copay as a percentage Round to a whole number Answer 3 A tablet contains 50 mg drug and 150 mg excipients Calculate the percent of drug in this tablet by weight Round to whole number Answer

4 In a clinical study of divalproex sodium DEPAKOTE in patients prone to migraine headaches nausea occurred in 62 of 202 patients express the subjects reporting nausea in percent and decimal fraction Round both answers to three significant figures Answer 5 In a clinical study of niacin as a lipid altering agent 60 of the 90 patients in the study

Consider the following system of constraints associated with a linear programming problem 2x 3y 12 4x y 8 x 0 y 0 Maximize z 5x 3y

Decide whether the statement is possible or impossible cot 0 3 6 is the statement possible or impossible OA The statement is possible because the range of cot 0 is 0 00 OB The statement is possible because the range of cot 0 is 0 00 OC The statement is impossible because the range of cot 0 is 1 1 OD The statement is impossible because the range of cot 0 is 0

88 a An employee invests 500 per month in an ordinary annuity If the interest rate is 5 find the value of the annuity after 18 yr b If the employee invests 1000 per month in the annuity instead of 500 at 5 interest find the value of the annuity after 18 yr Compare the result to part a e If the employee invests 500 per month in the annuity at 5 interest find the value of the annuity after 36 yr Compare the result to part a

nstruct a polynomial function with the following properties fifth degree 4 is a zero of multiplicity 2 I is the only other zero leading coefficient is 3 nswer f x Keybc

47 32 Y 7 sin 3 31 x 50 25 ave been plotted on the same axes below 21 EN orrect to 10 significant figures Enter your answer in the box below 32 x and y 47 50 10 e 3 2 qu 1 ind an approximation to the smallest positive solution to 47 32 9 sin 2 x 10 e 50 25 47 50 X X 2

and the following limits x2023 1 a lim x 1 x2000 x ex 1 b lim x 0 tan 2x c lim x ln x int

Rewrite as sums or differences of logarithms log c x y z log x y z

Use the transformation u 4x 3y v x 3y to evaluate the given integral for the 4 1 region R bounded by the lines y 3x 3 y and 3x y 3x 1 SS 4x 1 15xy 9y dx dy R SS 4x R 15xy 9y dx dy DE x 4 x 4 y

12 3 Find the exact value of sin a B if sin a and sin and x and B are 13 5 between 0 and 2 sin B Type an integer or a simplified fraction

u 4 3 v 8 15 a u v b ul c v d d u v Need Help Submit Answer Read It 14 Points DETAILS LARLINALG8 5 2 019 Find u v u v and d u v for the given inner product defined on R u 4 0 v 3 2 u v 301v1 42V2 a u v b u

al po pa F 747 pribil A leading brand of toothpaste is available in four sizes 6 4 ounces 3 59 4 2 ounces for 2 79 4 0 ounces for 2 29 and a travel size of 0 85 ounces for 0 89 Based on unit price what size is the best buy 5 points

r x Use synthetic division to rewrite the following fraction in the form g x where d x is the denominator of the original fraction g x is the quotient and r x is the d x remainder Answer 3x 9ix 6x 1 i x 2i Keypad

Apply Descartes Rule of Signs Determine the number of possible positive and negative real zeros for the given function 16 1 1 x 1 0 x 1 x 1 2 t x 10 2 2 7 Each part may have more than one possibility Use commas to separate multiple responses Part 1 of 2 Number of possible positive real zeros Part 2 of 2 0 0 X S

Suppose that you decide to buy a car for 27 635 including taxes and license fees You saved 5000 for a down payment and PA CAT can get a three year car loan at 7 78 Use PMT loan GOLD to find the monthly payment and the total interest for the

2 6 points Sketch the graph and use it to solve the polynomial inequality below Give the solution set in interval notation x 3 x 4 x 5 0

6 points Give the polynomial function f x with the graph below 22 1 0 9 2 BLOD 3 0 o do 2 Answer f x

8 points Find a polynomial function f x of degree 3 with real coefficients that satisfies the given conditions Okay to leave the answer in factor form Zeros of 1 1 and 0 f 2 3