Vector Calculus Questions and Answers

tetan A sofa regularly sells for 430 The sale price is 382 70 Find the percent decrease of the sale price from the regular price

Suppose that you earned a bachelor s degree and now you re teaching high school The school district offers teachers the opportunity to take a year off to earn a master s degree To achieve this goal you deposit 2000 at the end of each year in an annuity that pays 7 compounded annually a b How much will you have saved at the end of five years Find the interest Click the icon to view some finance formulas a After 5 years you will have approximately Do not round until the final answer Then round to the nearest dollar as needed

Multiply or divide the following rational expressions as indicated and simplify your answer x 7x 12 x 4 27 x 3x 18 x 4

Question 5 of Add or subtract the following rational expressions as indicated and simplify your answer y 3 35 Answer y 2 y 3 2 y2 2y 31

Submit Answer 12 5 25 Points DETAILS PREVIOUS ANSWERS SCALCET8 3 8 017 PRACTICE MY NOTES When a cold drink is taken from a refrigerator its temperature is 5 C After 25 minutes in a 20 C room its temperature has increased to 10 C Round your answers to two decimal places a What is the temperature of the drink after 40 minutes 12 15 X

Find the derivative of log x O In 7 O 30 7x 30 1 x In 7

Suppose you are given a formula for a function f a How do you determine where f is increasing or decreasing b How do you determine where the graph of f is concave upward or concave downward c How do you locate inflection points

Find the time of flight range and maximum height of the following two dimensional trajectory assuming no forces other than gravity The initial position is 0 0 and the initial velocity is vo uo vo ov 40 70 m s The object is in the air for Type an integer or decimal seconds rounded to two decimal places as needed The range of the object is meters Type an integer or decimal rounded to two decimal places as needed The object reaches a maximum height of meters Type an integer or decimal rounded to two decimal places as needed SITE

Given the points A 2 0 B 7 13 C 1 6 D 4 5 E 2 2 and F 3 2 4 2 find the position vector equal to the following vector a AB C ET d cb b AC 2 ABD Type exact answers using radicals as needed b AC Type exact answers using radicals as needed C EF Type exact answers using radicals as needed d co Type exact answers using radicals as needed

Calculate the work done in the following situation A constant force F 3 5 1 in newtons moves an object from 0 0 0 to 2 4 8 Distance is measured in meters Simplif

Find two vectors parallel to v with three times the magnitude of v v 9 3 Select the correct two vectors below DA 9 3 3 10 3 10 B 9 3 C 9 3 10 3 3 10 3 10 D 27 9 E 9 27 F 27 9

X Given that f x 3x 4 and g x x 1 find 2f x g 2

Solve the quadratic by completing the square Show work WILL be required on the exam x 12x 32 0 Solution 1 Solution 2

The quantity in pounds of a gourmet ground coffee that is sold by a coffee company at a price of p dollars per pound is Q f p a What is the meaning of the derivative f 7 O The rate of change of the quantity of coffee sold with respect to the price per pound when the price is 7 per pound The rate of change of the price per pound with respect to the quantity of coffee sold when the price is 7 per pound O The price of the coffee as a function of the supply O The rate of change of the price per pound with respect to the quantity of coffee sold O The supply of coffee needed to be sold to charge 7 per pound b What are the units of f 7 O pounds dollar Odollars pound Odollars pound pound O pounds dollars pound Odollars pounds

f x In x 3 b Graph f Choose the correct graph A 10 G B 7 C c From the graph determine the range and any asymptotes of f The range of f is 0 00 Type your answer in interval notation OA The vertical asymptote of f is x Simplify your answer OB There is no vertical asymptote 10 Q Determine the vertical asymptote of f if it exists Select the correct choice and if necessary complete your choice

For f x a fog 6 X 5 and g x b gof 5x b gof x X 1 5 1 x Simplify your answer Use integers or fractions for any numbers in the expression find the following composite functions and state the domain of each c fof d gog The domain of fog is 0 U 0 1 U 1 00 Type your answer in interval notation Use integers or fractions for any numbers in the expressio your answer c fo f x 5X 25 6 Simplify your answer Use integers or fractions for any numbers in the expression The domain of g of is 5 U 5 00 Type your answer in interval notation Use integers or fractions for any numbers in the expressic your answer 6 x 5 31 5x Simplify your answer Use integers or fractions for any numbers in the expression The domain off of is Type your answer in interval otation Use integers or fractions for any numbers in the expressic your answer

If the tangent line to y f z at 7 5 passes through the point 0 4 find f 7 and f 7 f 7 f 7 Question Help Message incto

K f x In x 3 a Find the domain of f The domain of f is 3 00 Type your answer in interval notation to answer parts a through f b Graph f Choose the correct graph OA 110 Q Q M OB 40 Q Q L C c From the graph determine the range and any asymptotes of f The range of f is Type your answer in interval notation 40 10

d Use a graphing utility to find the line of best fit y 2 0357 x 1 3214 Type integers or decimals rounded to four decimal places as needed e What is the correlation coefficient r Type an integer or decimal rounded to three decimal places as needed

3x x 7 2 0 12 OA B Use the formula x b b 4ac 2a with a What is the solution set b and c 2 Rewrite the equation so the constant term is on the right side and the coefficient of x is equal to 1 Add Then take the square root and isolate x 1 to both sides and factor the left side as a perfect spare 36 2 Write the equation in the form x p by moving the constant term and x term to the right side of the equation and then dividing both sides by solve for x D Set the equation equal to 0 and factor the nonzero side of the equation Set each factor equal to 0 and solve The solution set is Simplify your answer Type an exact answer using radicals as needed Use a comma to separate answers as needed Take the sp

X y 20 2 3 3 5 X 4 6 20 5 9 A 6 11 a 7 13 y ZA 1 Type an equation Type your answer in slope intercept form Use integers or fractions for any numbers in the equation c Graph the line found in part b on the scatter plot Choose the correct graph below O A rough f 8 15 OB Ay 20 20 d Use a graphing utility to find the line of best fit y 0x 0 Type integers or decimals rounded to four decimal places as needed C 20 04 0 X 20 OD 20 Ay 0 20 COU

K For f x a fog 6 X 5 5 and and g x find the following composite functions and state the domain of each b gof c fof d gog a fog x 6x 5 1 x Simplify your answer Use integers or fractions for any numbers in the expression The domain off og is Type your answer in interval notation Use integers or fractions for any numbers in the expression Si your answer

9x 1 a Find its inverse function f and check your answer b Find the domain and 1 a f x X 9x 8 Simplify your answer b The domain of f is Type your answer in interval notation Use integers or fractions for any numbers

Use transformations to graph the function f x 2 2 Determine its domain range and horizontal asymptote D Horizontal compression or stretch E Horizontal shift F Vertical compression or stretch Use the graphing tool to graph the function What is the domain of f x 2 The domain of f x is 0 00 Type your answer in interval notation What is the range of f x 2 2 The range of f x is 0 00 Type your answer in interval notation What is the horizontal asymptote of the given function F The horizontal asymptote is the line Type an equation E 10 B 6

K Consider the functions f x 9x 1 and g x x 1 a Find f g x b Find g f x c Determine whether the functions f and g are inverses of each other AI Use a comma to separate answers as needed B No values should be excluded from the domain b What is g f x g f x x Simplify your answer Give any values of x that need to be excluded from g f x Select the correct choice and if box within your choice OA x Use a comma to separate answers as needed B No values should be excluded from the domain c Are the functions f and g inverses of each other Choose the correct answer O Yes O No

transformations to graph the function f x 2x 2 rmine its domain range and horizontal asymptote ch transformations must be applied to obtain the graph x 2x 22 Select all that apply A Vertical shift B Reflection about the x axis C Reflection about the y axis D Horizontal compression or stretch E Horizontal shift F Vertical compression or stretch se the graphing tool to graph the function What is the domain of f x 2x 2 The domain of f x is Type your answer in interval notation 10 B 6 4 2 10 Ay 8 6 4 2 2 6 8 40 INT L

13 4 i Let f x sin x 3 3x with xe 1 1 Given 0 1 find a 8 0 such that for all x y 1 1 if x y d then f x f y 0 1 E ii Consider x dx where f is as in part i The partition Pn cuts 1 1 into n equal pieces For what n we have U f P L f Pn 0 01 lot t

21 Find the center and radius for the circle a x 2 y 3 16 b x y 3 25

1 Describe how the graphs of the following functions relate to the graph of y f x b y f x 7 c y f x 4 4 a y f x 9 Xxx s d y 6 f x e y 3 f x 5 f y 2 f x 3 10

Ben and Evan start from Listowel and drive along perpendicular roads Ben drives at a speed of 45 km h and Evan travels at a speed of 40 km h ok it was icy If Evan begins one hour before Ben at what rate are their cars separating three hours after Evan leaves olesworth Bowling E B Palmerston Norgan theatre

X 6 x 2 7 OA 1 5 OB 5 1 OC 6 2 OD 2 6 zero product property

termine if the graph is symmetric with respect to the axis y axis or origin 27 Q OA Origin OB X axis OC Y axis OD No symmetry

h x 1 2 x 8 OA f x g x x 8 OB f x x g x x 8 OC f x g x x 8 OD 1 x g x x 100

rm the indicated operation Write the result in standare 3 2i 6 61 A 30 6i OB 12 6i 18 OC 30 6i OD 6 30i

Question 12 Use the distributive law to find the product 26 1 6 1

Solve the inequality analytically writing the solution set in interval n 10 4x 72 5x 8 OA 4 OB 9 00 OC 0 9 OD 4 00

Find the slope intercept form of the line satisfying the given conditi X 4 20 2 y 27 17 7 3 13 O A y 5x 7 OB y 10x 13 OC y 10x 13 P Y 5x 7

8x The function f x is one to one 9x 1 a Find its inverse function f1 and check your answer b Find the domain and the range of f and f a f x Simplify your answer

tion list estion 5 estion 6 uestion 7 uestion 8 Question 9 Question 10 K e11x 18 The solution set is Type an integer or a simplified fraction Use a comma to separate an

K Find the domain of the function g x In x 2 The domain of g is Type your answer in interval notat

K ange of Base Formula and a calculator to evaluate the logarithm log 742 log 42 Do not round until the final answer Then round to three decimal places as ne

K 1 Use transformations of the graph of either f x g x O A 3 x 3 Choose the correct graph below Q Q or h x OB 1 to sketch a graph of y g x by hand Show all asymptotes Write g x in terms of either f x or h x O C O D B

Find the period y cot x Graph the function

Find the period y tan x Graph the function AS AW A

For the data given below answer parts a through f 5 6 9 11 13 X y Ay 20 O 2 3 a Draw a scatter plot Choose the correct graph below O A 3 5 4 6 20 2 B 7 8 15 20 Q G OC 20 O D 20

Find the amplitude period and horizontal shift of the function y 8 sin 8 sin 3 x amplitude period horizontal shift Graph one complete period y TAJA 5 3 Z 3 O Nood Heln 2 84 9 y 8 6 Which y 8 6 y 6 2 3 I

plituc and period of the function and sketch its graph y 4 sin 2x amplitude period Sketch the graph of the function y y MA AN O 2 Need Help Read It Watch Master II 2 X y 3x 2 X

Use a graphing utility to graph the function and the damping factor of the function in the same viewing window f x 5x sin x X Analyze the graph of the function using the method in Example 6 Enter your answers as a comma separated list Use n to represent an arbitrary integer if necessar y te touches y e sin x at y ex sin x has x intercepts at 2 X X

Use a graphing utility to graph the function include two full periods Graph the corresponding reciprocal function in the same viewing window y csc 4x KIN 1 Need Help ULUI U Read It 2 2 1 KIN KIN X IN Tat 4 2 y 2

Find the equations of the tangent and normal lines to the parabola with vertex at 0 3 and focus at 0 0 where x 1 Graph the curve and lines Paragraph V B I UA 00 GO v I X