Vector Calculus Questions and Answers

Describe the relationship between the graphs of f and g Consider amplitude period and shifts 4 y 3 2 3 2x J 8 0 g 1 1 k X 2 3 B O The graph of g is a horizontal shift 3 units to the right of the graph of f O The graph of g is a reflection of f in the x axis O The amplitude of g is twice that of the amplitude of f O The graph of g is a vertical shift 3 units upward from the graph of f The period of a is 3 times that of f

Approximate the area under the curve graphed below from x approximation with 4 subdivisions 3 to x 7 using a Left En You will need to approximate the function values using the graph 5 4 3 2 1 1 2 3 A 4 5 6 7 Poot 8

A rectangular soccer field has dimensions 70 yards by 110 yards as shown in the figure A sprinkler placed at point P rotates 15 and sprays across the entire field as shown in the figure What percent of the soccer field is watered by thi one sprinkler Round to the nearest hundredth P 95 yd 15 110 yards 70 yards

2 The figure shows ABRO B 18 9 R 13 a Find the semi perimeter of ABRO b Find the area of ABRO Round to the nearest tenth

A Solve for the missing angle to 400 50 5 degrees 12 7 degrees 36 9 degrees 72 2 degrees 300

Solve for x 23 63 50 7 50 1 60 7 X

4 Oil is leaking from a pipeline on the surface of a lake and forms an oil slick whose volume increases at a constant rate of 2000 cubic centimeters per minute The oil slick takes the form of a right circular cylinder with both its radius and height changing with time Note the volume V of a right circular cylinder with radius r and height his given by V r h b A recovery device arrives on the scene and begins removing oil The rate at which oil is removed is R t 400 t cubic centimeters per minute where t is the time in minutes since the device began working Oil continues to leak at the rate of 2000 cubic centimeters per minute Find the time when the oil slick reaches its volume Just

cos 135 12 cos 2

15 sin 60 16

4 Find m N Round to the nearest tenth N 8 12 11 S

6 In AWAG mZA 64 WA 16 and GA 9 Solve the triangle by finding all the missing measures of the sides and angles Round to the nearest tenth

Write name date and period Show all sketches and work 1 Determine if APQR is an acute obtuse or right triangle Give a reason for your answer P 10 32 6 44 R Q 8 14

Vectors u 2 cos 30 i sin30 j v 6 cos 225 i sin225 j and w 8 cos 120 i sin120 j are given Use exact values when evaluating sine and cosine Part A Convert the vectors to component form and find 7 u v Show every step of your work 4 points Part B Convert the vectors to component form and use the dot product to determine if u and w are parallel orthogonal or neither Justify your answer 6 points

A horse owner has 50 lbs of hay that is 6 protein by weight He adds x lbs of oats that is 12 protein by weig The function y 0 06 50 0 12x 50 x models the percent of protein y in the final mixture of feed What is the y intercept of the function that models the percent of protein in the final mixture The y intercept is choose your answer choose your answer 50 50 0 06

Use the angle conversion capabilities of a graphing utility to convert the angle measure to D M S form 113 5

7 Kofi Haris and Sharon are in a disagreement about how to solve for QU shown in the figure Kofi suggests setting up the proportion cos 27 and solving for QU 18 QU Haris suggests using the Law of Sines but Sharon says there is not enough information to do so since no angle and its opposite side are given Who is correct Explain your reasoning 111 S 27 U 18

Kara wants to solve for m N using the Law of Sines What one additional measurement does Kara need in order t do this Explain H 65 11 M

3 y 2sec 3x 1 Per Asymptote

Find all solutions to each equation in radians 17 2 3 2tan 0 Solve each equation for 0 0 2 19 2cos 1 cos 1 0 21 sin 0 2sin 0 0

23 3x 2 9 3 7 4x 2 22 St a Period b Equation of all asymptotes c Possible equation for this graph acul d If the graph is defined as f x find where f x 1 over the interval 0 x 2

A guy wire is a cable used to restrain objects from moving They are used to support towers or poles A guy wire is attached to a cell tower The 50 foot long guy wire is attached to a tower such that the angle formed by the ground and the wire measures 35 The guy wire is replaced by a guy wire 120 feet long The point at which the new guy wire attaches to the tower is the same as it was with the original wire What is the approximate measure of the angle formed by this new guy wire and the ground

Solve the following Write all irrational and complex answers in simplest form 1 9d2 8 41 2 2y 12 14y 3 2 14v 97 0 4 5r2 2r 1 0

log 8 x

13 log 4 2x log 4 3 3

4 6t 1 36

se the change of base formula to evaluate the following expression log n

Solve the system of equations graphed on the coordinate axes below Answer Amprint of 2 y V WA SX

8 Consider the Pythagorean identity sin 0 cos 0 1 a Divide both sides of the equation by sin and simplify What do you notice b Divide both sides of the equation by cos and simplify What do you notice

A health magazine reported that 27 of adult males smoke cigarettes To test this claim they select 40 adult males at random and record if they smoke cigarettes They calculate a 95 confidence interval for the proportion of adult males who smoke and find it is 22 to 28 Interpret the confidence interval O We are 95 confident that the interval from 0 22 to 0 28 captures the true proportion of adult males who smoke O If the magazine took many random samples of 40 adult males then 95 of the constructed confidence intervals would capture the true proportion of adult males who smoke The interval from 0 22 to 0 28 captures 95 of the adult males who smoke

Find the missing side lengths Leave your answers as radicals in simplest 1 2 3 5 3 3 30 60 12 18 E n 60 4 6 30 45 4 3 X 3 2 30 2 3

74 A 2 6 Su 57 B uu Ac which lau Which law

Write and simplify a polynomial with 4 31 and 0 multiplicity 2 as roots Write yo

America s dependency on foreign oil has always been a hot political topic with the amount of imported oil fluctuating over the years due to political climate public awareness the economy and other factors The amount of crude oil imported can be approximated by the function given where x represents the year since 1980 and A x represents the number of barrels imported in billions Give your answer to the nearest hundredth If the hundredths place is a zero please include it A x is listed below 0 044x 2 0 369x 1 5 0 x 8 8 x What was the minimum number of barrels imported between 1980 and 1988 0 072x 2 1 496x 1 5

Are these functions inverses A 177 No 7 I need more information

7 Evaluate sin 8 Hint Draw a right triangle arccos

8 In order for y sin to be a function the domain of y sina is restricted to a Explain why the domain was restricted to this interval b Identify two other intervals that could have been chosen as the domain

S00 V tve 7 b 4

3 y cot A B D 0 3 1 27 2x 3x 4 2x 3x 4x 2x Period 3r Period Period 3x Period 3x

Instructions Use the image to help answer the questions about the trig values of the given angle in the Unit Circle unit circle trig EIN 3r 01 3 2 112 e 0 The given angle theta is shown with a terminal ray at point P which has 19 0 5 points tan 0 1 2 3 3 3 Clear my selection

If the vector v O a A 4 O b A 1 O c None Od A 1 O e A 5 is an eigenvector of the matrix A then the eigenvalue A that corresponds to vis

If A a O b 1 to then adj A 1 1 20 2 1 O e O c None O d 0 1 1 07 22 2 2 0 L 2 2

4 Find an equation of the line through the first quadrant that cuts off the least area from the first quadrant

10 Use the unit circle to explain why the graph of y tan is increasing for 0 0 2

Solve each triangle Round your answers to the nearest tenth 7 m B 27 a 28 ft b 18 ft 8 m C 54 b 24 km c 23 km

the number of possible triangles that can be formed using the given measurements 1 mA 110 c 19 cm a 32 cm 2 mA 131 a 25 yd c 8 yd 3 m B 100 a 33 km h 29 km 1 4 m B 61 a 35 mi b 32 mi

4 3 2 1 y 3 2 2 3 2 What is the slope of the line

4 Find an equation of the line through the first quadrant that cuts off the least area from the first quadrant

11 Let f be a function defined and continuous on the closed interval a b Iff has a relative maximum at c and a c b which of the following must be true I f c must exist II If f c exists then f c 0 III If c exists then c 0 A II and III only C III only B I and III only D II only SE

2 Graph y sin 2x TT V TT 2 1 5 1 0 5 0 0 5 TT 2 TT 3TT 2 2TT

5 Consider the graph of y f x where f x 2 5 cos x a Identify the midline of the graph of f b Identify the period of f c Identify the range of f d Identify the amplitude of f