Vector Calculus Questions and Answers

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20 Find the solution set of 0 x 2 in the interval cos x 3 sin x 1 A 2 B 7 2 C 0 D 0 2

10 Express sit sin 3x as a function of twice the given angle A cos 6x 2 B cos 2x C cos 3x D sin 6x

Question 6 of 7 A computer interface for a digital studio piano has five position These switches must be set properly for the in a In how many different ways can this group of switch

Plot the complex number 1 2i 5 4 3 2 1 3 24 7 2 3 4 5 Clear All Draw Dot 1 2 3 4 15

Ope fy each of the following and wr 13 6i 4 9i V EN

Next question 5 Without using a calculator compute the sine and cosine of by using the reference angle 3 What is the reference angle sin COS 5 T 3 In what quadrant is this angle 4 5 Get a similar question You can retry this question below 3 2 2 T I COIF 3 X radians answer 1 2 3 or 4

3 A bag has 6 red marbles 2 blue marbles and 5 green marbles Without looking two marbles are drawn out of the bag What is the probability of selecting 2 green marbles 2 13

Use a graphing calculator to graph y 5 0 same viewing window

The drawing shows a coin resting on the bottom of a beaker filled with an unknown liquid A ray of light from the coin travels to the surface of the liquid and is refracted as it enters into the air A person sees the ray as it skims just above the surface of the liquid How fast is the light traveling in the liquid Number Mi Units 6 00 cm 5 00 cm Coin

The angle between 0 and 27 in radians that is coterminal with the angle 14 5 in radians is

Stephanie was injured in a car accident and was rushed to the emergency room She received stitches for a facial wound and treatment for a broken finger Under Stephanie s PPO plan emergency room care at a network hospital is 70 percent covered after the member has met a 300 annual deductible Assume that Stephanie went to a hospital within her PPO network Her total emergency room bill was 840 This is Stephanie s first medical expense of the year a What amount did Stephanie have to pay Do not round intermediate calculations Amount to be paid b What amount did the PPO cover Do not round intermediate calculations Amount of coverage SA

2 This bar graph represents a comparison of school Using information from this graph please answer the following questions 600 500 400 300 200 100 0 Hillview Relative School Populations Central a How many students attend Central b What s the mean population of the 4 schools JDR c How many more students attend Grand than attend Hillview d What is the midrange of this data 5 marks Grand e Circle the correct answer The mode of this data is 200 True School VE False

f x y at the point x y a Find the gradient of f u such that and 2 1 b Find the unit vector U1 2x Duf 2 1 is at its maximum value and then find that maximum value c Find the two unit vectors U2 3y such that Duf 2 1 0

Write the given vector in terms of i and j 6 4 U 6i 4j X

Persamaan garis singgung melalui titik P 2 4 pada lingkaran x 2 2 y 1 2 25 adalah a 4x 3y 20 b 4x 3y 20 c 2x 3y 20 d 2x 3y 20 e 3x 4y 20

1070 98ft how much police tape is needed to tape off the entire area

Exercise 10 0 7 A level What goes wrong with saying R X Set X R if X is infinite For example show that the set of signals S Set Z R is not at least not obviously free If you want to read more check out this Math StackExchange conversation the following linear

0 e a ans Please show all your work NO WORK NO CREDIT Write the equation in logarithmic form

Write the partial fraction dec X x 4 x 5

Use the property to estimate the best possible bounds of the integral iint Q 5 e 3 left x 2 y 2 right 2 d A Q is the quarter circle with center the origin and radius 1 2 in the first quadrant Round your answers to four decimal places iint Q 5 e 3 left x 2 y 2 right 2 d A

Consider the function f x y z exyz 1 the point P 0 3 3 and the unit vector u a Compute the gradient of f and evaluate it at P b Find the unit vector in the direction of maximum increase of f at P c Find the rate of change of the function in the direction of maximum increase at P d Find the directional derivative at P in the direction of the given vector a What is the gradient at the point P 0 3 3 Type exact answers in terms of e 9 11 11

Find the max min outputs for f x y x 2y on the interior of the circle x 2 y 2 4 with 1 y 1

4 Evaluate the surface integral ff F r n dA if F 0 2 1 and S is given by the S equation 3x 2y z 6 x 0 y 0 z 0 Identify and plot the surface

A mass attached to a vertical spring has position function given by s t 2 sin 4t where t is measured in seconds and s in inches Round each of your answers below to the nearest hundredth Find the velocity at time t 1 2 39 Find the acceleration at time t 1 9 51 Xinches per second inches per second squared

Consider the function the following rational function 10 8 8 6 4 o 2 42 4 6 8 6 1 The equation of the horizontal asymptote for this function is 2 The equation of the vertical asymptote for this function is

Express this alternating sum S as a simple fraction S 1 3 12 7 1 9 H 65

Find any values of the variable that mak 8x x 2 49

7 4 points Let w and A 5 3 1 01 5 2 12 10 8 6 3 3 2 1 0 a Is w in the column space of A Show why or why not b Is w in the null space of A Show why or why not

15 6pts State the 3 variations of the double angle identity for cosine a Cos 2x b Cos 2x c Cos 2x 16 15 pts 3 each a Find the exact value sin 18 cos 27 cos 18 sin 27 b Find the exact value sin c Find the exact value cos d Find the exact value tan 1 A 1 e State the Pythagorean identity tan 0 1

2 Plot the point with the given polar coordinates Upload a picture of your graph a 3 41 3 b 1 2 5

Determine if the series converges or diverges k a Converges b Diverges

Find the sum of the series a c INT alin b d otto 335 ES

Question 25 A fireplace arch is constructed in the shape of a semi ellipse The opening has a height of 2 feet at its center and a width of 5 feet along its base Find the height of the fireplace 18 inches from its center 1 85

milling company wants to mix alfalfa which contain 20 protein and wheat mids which contain 15 protein to make cattle eed a If you make a mixture of 10 pounds of alfalfa and 60 pounds of wheat mids how many pounds of protein are in the mixture Hint In the 10 pounds of alfalfa there are 10 x 0 2 2 pounds of protein lbs b Write a formula that gives the amount of protein in a mixture of a pounds of alfalfa and w pounds of wheat mids p a w c Suppose the milling company wants to make 1000 pounds of cattle feed that contains 17 protein How many pounds of alfalfa and how many pounds of wheat mids must be used alfalfa lbs wheat mids lbs

Add the given vectors by components U 0 327 8 171 1 V 0 647 8 313 1 W 0 132 0w 104 2 The resultant magnitude is 0 306 Round to three decimal places as needed Round all intermediate values to five decimal places as needed GOLD The resultant direction is Type your answer in degrees Use angle measures greater than or equal to 0 and less than 360 Round to the nearest integer as needed Do not include the degre

51 54 Evaluating an Expression Involving Trigonometric Functions Evaluate each expression under the given conditions 51 cos 20 sin 0 3 0 in Quadrant III

37 42 Using a Half Angle Formula Find sin X 1 2 2 37 sin x 3 0 x 90 tan from the given information NIX 2 COS X 12 and

21 24 Cofunction Identities Prove the cofunction identity using the Addition and Subtraction Formulas Igun 21 tan TT 2 u cot u bi 22 cot TT 2 tan u

51 54 Expressions Involving Inverse Trigonometric Func tions Find the exact value of the expression 51 sin cos tan 1 52 cos sin cot 3 2

25 46 Proving Identities Prove the identity 25 sin x TT 2 COS X

Sketch the graph of f x y 4x y 4 State the domain and range of the function 0 0 4 0 4 0 1 0 0 OA x y x2 OB xy OC x y xs OD x y xs 1 0 0 y 0 4 0 0 0 4 4 0 0 Find the domain of the function Select the correct choice below and if necessary fill in the answer box es to complete your choice 0 1 0 Simplify your answer Simplify your answer Use a comma to separate answers as needed and x2 Simplify your answers Simplify your answer

Which of the following surface graphs represents f x y 4x y 4 OA OB 0 0 4 y 0 4 0 1 0 0 1 0 0 y 0 4 0 0 0 4 O C XA 0 0 4 4 0 0 y 0 1 0

Graph the point on a polar grid Select one Oa b OC 5x 6 0

ools net mod quiz attempt php attempt 2937073 cmid 408580 Question 2 Clear my choice Rectangular coordinates of point P are 3 3 Use an aln

Question 3 Not yet answered Marked out of 1 00 Oh 18 4 3 2 Use a graphing calculator to match t graph mentally before using a calcul r 4 cos 20 All graphs 6 6 by 6 6 Xscl

26 Find a vector function that represents the curve of intersection of the two surfaces Three Points 2 x y x y 25 16 25 16 1

Given f x 4x 25x 8x 84 answer the following Part 0 2 Part 1 of 2 Factor f x given that 2 is a zero

the number of apples and y is y 3x 52 x y lid Tay use

Obtain the solution in the form of the Fourier sine series and use Parseval s equality for the Fourier sine series to show that E t E t for every 0 t t where E t int 0 pi u x t 2 dx