Vector Calculus Questions and Answers

Graph the function defined by the equation f x whether the vertex is a maximum or minimum y

59 A 3 2 1 D by 1 2 3 4 5 The graph above shows the function f x The graph below shows g x 6 5 4 3 2 1 1 2 3 3 4 5 g x is a transformation of f x where g x Af Bx where 3

Find parametric equations for the line segment joining the first point to the second point 6 5 2 and 8 6 1 The parametric equations are x y z for

4 Plot the given points determine whether A 2 1 B 5 2

Use a graphing utility to find th X y 3 10 4 12 4 13

Select the standard form for each conic section equation below 12 x 4x 4y 20 0 75 A y 4 x 2 4 D B C E y 4 4 x 2 C y 4 x 2

Let f x sinx Determine the x value s where the function has a maximum or minimum value on 0 2 To enter type Pi with a capital P The fields below accept a list of numbers or formulas separated by semicolons e g 2 4 6 or x 1 x 1 The order of the lists do not matter On 0 27 the maximum value s of the function occur s at what x value s X On 0 2 the minimum value s of the function occur s at what x value s

The serum cholesterol levels in mg 2 of 17 individuals are dL 240 222 211 247 215 257 206 249 201 254 189 244 242 232 237 259 198 Send data to calculator Send data to Excel a The 25th percentile Find 25th and 70th percentiles for these cholesterol levels If necessary consult a list of formulas mg dL b The 70th percentile mg dr

a Sketch all together in one 3D plot the cylinders x 2 y 2 25 and y 2 z 2 20 and indicate the curve C that is the intersection of these two cylinders b Find a vector equation parameterizing the part of the curve C that is in the positive octant recall that the positive octant is the region defined by x 0 y 0 z 20 c Find a vector equation for the tangent line to the curve of the intersection of the cylinders x 2 y 2 25 and y 2 z 2 20 at the point 3 4 2

G Corporation produces just about everything but is currently interested in the lifetimes of its batteries To investigate its ew line of Ultra batteries BIG randomly selects 1000 Ultra batteries and finds that they have a mean lifetime of 844 hour ith a standard deviation of 84 hours Suppose that this mean and standard deviation apply to the population of all Ultra atteries Complete the following statements about the distribution of lifetimes of all Ultra batteries a According to Chebyshev s theorem at least Choose one lifetimes lie between 592 hours and 1096 hours b According to Chebyshev s theorem at least Choose one lifetimes lie between 676 hours and 1012 hours of the of the

the Trapezoidal Rule the Midpoint Rule and Simpson s Rule to approximate the given integral with the specified value of n Round your answers to six decimal plac 6 cos 5x X dx n 8 a the Trapezoidal Rule b the Midpoint Rule c Simpson s Rule

Evaluate the function f x 5x 2x for the given values of x a 3 b 2 c 1 d 0 e 1 Part 1 of 5 a f 3 60 Part 2 of 5 b f 2 30 Part 3 of 5 X X

suppose f x is given and you are asked to find the followings Explain in words what action do you take for each question a find f 2 b find f h 1

1 126 10 8 6 4 2 4 24 123 4 285 10442 21 2 21 5 375 to 8642 2 2 41 590 18

Based on these questions can you easily find another pair of orthogonal unit vectors using the given vectors I and J Drag n Drop here or Browse

Let a 1 4 1 7 7 4 a 23 and b 6 For what value s of h is b in the plane spanned by a and a2 h The value s of h is are 3 Use a comma to separate answers as needed

Consider the parallelepiped slanted box determined by the position vectors u v and w see figure Show that the volume of the parallelepiped is lu vxw ww u cos 0 VXW 11 W First determine the formula for the volume of a prism Choose the correct answer below OA The volume of a prism equals x multiplied by the area of its base B multiplied by its height h that is V xBh OB The volume of a prism equals the area of its base B multiplied by the square of its height h that is V Bh OC The volume of a prism equals the area of its base B multiplied by its height h that is V Bh OD The volume of a prism equals the area of its base B squared multiplied by the square of its heighth that

Find a vector orthogonal to 0 1 2 and 3 2 0 Choose the correct answer below OA 4 6 3 OB 4 6 3 OC 4 6 3 OD 4 6 3

Find the area of the triangle T with sides u 3 3 3 v 24 0 24 and u v The area of a triangle is half the area of the corresponding parallelogram The area is Type an exact answer using radicals as needed

Find the area of the following triangle T The vertices of T are A 0 0 0 B 3 0 1 and C 2 2 0 The area of triangle T is Simplify your answer Type an exact answer using radicals as needed

Three point masses m 1 m with masses of 8 and m3 9 are located respectively at points P 2 3 P 9 1 and P3 9 8 The center of mass for this system is located at x y

Find the cross product uxv in the figure 1 UXV Di Oj Ok Simplify your answers Type exact answers using radicals ac pooded u 3 0 0 X ZA v 0 y

Please complete the following questions a b C d e What is 75 of 640 What is 200 of 300 What is 0 75 of 2 400 What is 51 of 10 000 What is 100 of 1

Write the answer to each of the following questions in the space provided a b C d e What percent is 4 out of 10 What percent of 180 is 72 30 is what percent of 200 2 is what percent of 5 12 is what percent of 20

2 Find the roots of the equation z 27i 0 in the form a bi

In a certain animal species the probability that a healthy adult female will have no offspring in a given year is 0 29 while the probabilities of 1 2 3 or 4 offspring are respectively 0 24 0 18 0 16 and 0 13 Find the expected number of offspring E X Round to two decimal places as needed CITE

ALCULATOR 3 Find the value of 1 i 6 giving your answer in the form a bi

8 Find all values for x in the interval 0 x 360 for which 2cos 2 x 3sin 2 x 14cosx Give your answers to one decimal place

Simplify Write the answer as a single term w c 7 d 5

5 4 3 2 1 5 4 3 2 1 f 2 2 3 4 10 1 2 3 4 51 Use the graph of f x above to estimate the value of f 2 to one decimal place

Find the angles between the following pairs of vectors a 4 2 1 and 2 0 1 b x y 3 and y x 0 c 5i 6jk and 2i k d 1 1 and 0 4 In each of the first three examples above find a vector perpendicular to the plane produced by the pairs of vectors What is the area of the parallelogram produced her the main of ugotong oh nan

1 Fill in the missing statements for the following two column proof Given C is the midpoint of AD Prove x 2 Statements 1 C is the midpoint of AD 2 AC CD 3 AC CD 4 9x 5x 8 5 6 x 2 Statements 1 C is the midpoint of AD Reasons A 1 a 9x 1 a 2 b 3 4 c 5 d Subtraction property of 6 e Reasons C segments have equal Definition of mic Transitive prope

Price of Good X dollar S D s Di Quantity of Good X In the diagram above which of the following would most likely change equilibrium from point A to point D OA n decrease in the price of good X A n increase in population A n increase in the price of an input A n decrease in the price of a complementary good A n decrease in the price of a substitute good

0 1 pt 399 Find a complex number z where 4 1i z is a real number Details 0 0 i Then find the product of your number z and 4 li 2 z 4 1i i Question Help Video

Exis Where does the surface intersect the axis of Symmetry a 8 Pts 5x 2y 3z 20 Primary surface Type ellipiscid sub Type P one sheet Axis of Symmetry axis 66 Where does the surface intersect the axis of Symmetry 2

2 5 6 6 16 Points total Answer the following questions for these quadratic surfaces a 8 Pts 3x 2y 7z 12 Axis of Symmetry axis a 8 Pts 5x 2y 3z 20 Primary surface Type ellipsoid Axis of Symmetry axis Primary surface Type Where does the surface intersect the axis of Symmetry parableid Sub Sub Type 2 elliptic Sub Type Pane sheet Where does the surface intersect the axis of Symmetry

Fill in the blank The parts that are added or subtracted in a The parts that are added or subtracted in

A 6 foot tall student walks at a rate of 4 feet per second away from a light that is 15 feet above the ground see figure 16 12 8 4 8 12 16 20 a When the student is 10 feet from the base of the light at what rate in ft sec is the tip of their shadow moving ft sec b When the student is 10 feet from the base of the light at what rate in ft sec is the length of their shadow changing ft sec

Solve the formula for P c 4b 2a for c

r the domain using interval notation 2

of the following is a geometric sequence with ao O 3 12 48 192 O 3 7 11 15 O 4 7 10 13 O 4 12 36 108 4 and r 3

rmine the price per kayak when Wildernes per kayak TANFIN9 1 4 028 manded each month of Russo Espresso Ma arket 750 espresso makers when the unit

Simplify the trigonometric expression 2 cot x 1 csc x 2 CSC 2 cot x csc x 1

3 a Find the area of the triangle having vertices 1 2 3 2 1 1 1 2 3 b What is the equation of the plane that contains this triangle c The symmetric equation of the line containing 1 2 3 2 1 1 d The parametric equation of the line containing 1 2 3 1 2 3 and e The vector equation of the line containing 1 2 3 2 1 1

and S Use the formulas F 15 degrees Cels

tions K If the sales tax s 0 07d Dete

K Solve the equation 4 x 1 3 4 x 5

K Assume that the following statements are tr A If Trisha is drinking coffee then it is B If it is breakfast time then Julio is dr C If it is dinnertime then Anna is drink D If it is lunchtime then Sarah is drink E Trisha is drinking coffee Using only the information given above de Explain your reasoning

Find the arc length of the graph of y 1 x a 8 5621 0 0721 b d 32 8287 10 5832 1 y 5

Consider the system of equation and 2x 3y 2 8 2 4y 2z 1 5x 2y 15 2x 3y z 8 The second system is obtained from the first by adding twice the first equation to the second equation and then swapping the two equations What is true about the solutions of the two systems A solution to the second system can be obtained from a solution to the first system by multiplying each value by 2 O The two systems have exactly the same solutions O The solutions of the two systems have no relation