Vectors Questions and Answers

A bouncy ball will bounce 80 of the height it falls If a bouncy ball is dropped from 20 feet the first bounce will be 16 feet high The second bounce will be 12 8 feet high Question What will be the height of the third bounce What is the height in feet of the 3rd bounce of the supe ball Skip Question Scratch Paper Optional To Use Functions 7 4 1 Previous Question 0 8 5 2 AC 9 6 3 11 x

A farmer wants to make a rectangular field with a total area of 4000 square meters It is surrounded by a fence It is divided into 3 equal areas by fences as shown fence x fence 30 fence fence fence fence Express the total length L of all the fence required in terms of the length x of one of the fences which divide the field L x

Tom wants to plant grass in his backyard His backyard is in the shape of a rectangle Its length is 27 feet and its width is 26 feet Suppose each pack of seed covers 13 square feet How many packs of seed will he need to cover the backyard packs

the IB SL formula booklet Round to 3 s f if not otherwise specified 21 A garden includes a small lawn The lawn is enclosed by an arc AB of a circle with centre O and radius 6 m such that AOB 135 The straight border of the lawn is defined by chord AB The lawn is shown as the shaded region in the following diagram diagram not to scale 135 ing cal B a A footpath is to be laid around the curved side of the lawn Find the length of the

1 point What is a radian a radius that is 3 14 inches long an angle measure with an arc length equal to one diameter length an arc length that is the length of one diameter an angle measure with an arc length equal to one radius length Previous

16 If AB 12 and AC 5x 4 find x MWO SE alle atmoe niwe www P

16 If AB 12 and AC 5x 4 find x MMO Trades armloq gniwollst B

How different are the minor offense laws today from the laws discussed in the video and what effect do these laws have on employment income generation and wealth accumulation In what ways might we criminalize unemployment status or poverty today

Find a vector parametrization of the line through P 1 1 1 in the direction v 6 3 4 r t t i 9 it j

Let ro co yo zo be a fixed point r x y z be a variable point and v a b c be a vector If r ro tv is a vector equation for the line through ro xo Yo zo in the direction of v a b c then we can conclude that Select all that apply 0 x x at y yo bt z 20 ct are parametric equations for the line If r x y z is on the line then the displacement vector r ro x xo y yo z zo is parallel a b c to the vector v The equation v rro 0 that is a x xo b y yo c z zo 0 is an equation for the plane containing the line x xo y Yo a b z 20 C are symmetric equations for the line

Find a vector that is parallel to the yz plane and perpendicular to the vector 3 4 4 12 11

4 10 points Consider the line of intersection of the two planes 2x x2 4x3 5 and 3x3 2 and the line 2 1 0 s 1 2 3 Find the normal equation of the plane containin these two lines

The front view of the top of a house is in the shape of a triangle whose height is 10 inches less than the length of its base and its area is 75 in2 If b represents the length of the base which of the following equations can be used to find the value of b O b b 10 75 Ob b 10 150 Ob b 10 4 75 h h 10 Base Height 75 2

rested in predicting the temperature in Fahrenheit of the striped ground cricket from their chirps per second We take a simple random sample of 15 striped ground crickets Below are the R outputs for a linear regression model Coefficients Estimate Std Error t value Pr ltl Intercept 25 2323 10 0601 2 508 0 026183 chirps 0 6012 5 475 0 000107 Signif codes Multiple R squared 0 6975 01 O 0 0 001 0 01 0 000107 0 001085 Now suppose we want to test if chirps per second are a significant predictor of temperature in Fahrenheit of the striped ground cricket What is the p value in this scenario 0 05 0 1 1

Find the orthogonal projection of u projw 98359 4422 5309 ER 4422 889 1474 12 7 18 onto the subspace W spanned by HA CH S

K O Points 0 of 1 Use the value of the linear correlation coefficient to calculate the coefficient of determination What does this tell you about the explained variation of the data about the regression line About the unexplained variation r 0 747 Calculate the coefficient of determination Part 1 of 3 Round to three decimal places as needed

Consider selecting two elements a and b from the set A a b c d e List all possible subsets of A using both elements Remember to use roster notation ie a b c d e List all possible arrangements of these two elements Enter your answers as a comma separated list Enclose each arrangement in parentheses

9 If the exact volume of a right circular cylinder is 200 cm and its altitude measures 8 cm what is the measure of the radius of the circular base 10 Suppose that the volume of an aluminum can is to be 97 in

1 point Recall that similarity of matrices is an equivalence relation that is the relation is reflexive symmetric and transitive 14 8 18 10 Verify that A A T AT T P S We know that A and B Q R 3 1 1 We also know that B and C 3 2 0 29 are similar since A P BP where Verify that BA by finding an S such that B S AS 2 1 is similar to itself by finding a T such that 6 8 2 2 Verify that A C by finding an R such that A R CR are similar since B Q CQ where

Question 6 Points 3 Find the equation of a line perpendicular to 8x 2y 4 and passes through the point 4 3 O y 4 x 16 Oy 4x 8 O y 4 x 2 O y 4 X 4 R

Question 10 What is the shape of the polygon obtained when the square circle asterisk and heart are joined 94 8 74 6 5 4 3 2 1 Y Points 3 2 O Triangle 3 O Quadrilateral 4 5 6 7 8 9

Initial Point 8 3 Answer Terminal Point 6 1

In order to buy a vacation home Neal and Lilly took out a 10 year mortgage for 150 000 at an annual interest rate of 8 After 7 years they refinanced the unpaid balance of 58 123 at an annual rate of 5 Use the table to find the monthly payments on the original loan the monthly payments on the new loan and the total amount saved on interest by refinancing Click the icon to view a table of monthly payments on a 1 000 loan The monthly payments on the original loan are Type an integer or a decimal

11 If sin a 6 TT 11 2 11 2 following expressions Be sure to simplify radicals and rationalize the denominator a cos a a 0 and cos 1 0 B find the exact value of each of the b sin 3 c Enter the numerator and denominator separately in the boxes below If the denominator is 1 enter the number 1 Do not leave either box blank The sign in the denominator should be positive Answer sin a B

If 0 x 2 find all values of x that satisfy the equation Select the correct answer below O x 3 x 3 and S X 3 and 4 tan x 1 sec x 2

1 0 1 2 3 4 5 1 2 V 3 4 4 3 L D 5

9 Name the following relationship between theses circles B O Disjoint circles O Tangent circles

If an equation is true it doesn t matter which side of the equal sign informa writte 4 Give B Symmetric Property Reflexive Property Transitive Property Additive Property rty

In Exercises 7 to 12 use the angles provided to perform the constructions 1 4 A B Exercises 7 12 7 Construct an angle that is congruent to acute ZA 8 Construct an angle that is congruent to obtuse ZB 9 Construct an angle that has one half the measure of ZA 10 Construct an angle that has a measure equal to m B MZA

9 Find the equation of the circle whose center is 2 1 and radius 5 units O x 2 y 1 25 O 2 y 1 25 O x 2 y 1 25 O x 2 y 1 25

Rewrite the vector components using the unit vector form 7 13 3 U 13 3

Given the polar equation r 1 5sing Select one O a x 24y 30y 9 0 O b x 26y2 15y 9 0 Oc 24y x 15y 9 0 d None of these which is the rectangular equation

If a 5 4 and ka 30 24 then k 9 8 7 6 5

Given the vector 6 12 6 12 1 with a directional angle of

Given a vector begins at 3 and ends at 2 1 then the components of the vector are 4

i 8j 4w 6i 3j 3w I i 7 6 5 4 3 W

What values are required for A and B so that 3pi 4 is a solution to the following question Asin x Bcos 2x 1 A R

Glven Two Points Write the equation of the line with the two given points 5 1 3 and 3 5 6 1 4 and 6 1

Given the triangle below find tan 0 Enter the answer as a fraction Provide your answer below 3 4 5 0

4 Given Prove O 1 2 3 4 A B C m AOB m 1 m BOC m 1 OB bisects LAOC Statements 1 PROOF Reasons 1 Given 2 Substitution 3 Angles with equal measures are congruent 4 If a ray divides an angle into two congruent angle then the ray bisects the angle

If we write the following complex number in standard form then b Your answers here have to be simplified so that the 2 131 2 13i a bi

Suppose that AB AC AD AE and AF are coplanar F A B D E

Reduce the spanning set to a basis for R S 2 2 1 3 2 1 2 3 0 0 2 1

Suppose is the function defined by f x Ax where a The domain of fis R4 A 6 4 3 B 0 2 1 1 C 4 0 1 1 D 0 0 1 0 E 9 0 3 F 18 4 6 6 3 9 0 1 1 2 1 3 For instance enter R 5 for R5 b The codomain off is R3 For instance enter R 5 for Rs c Select all of the vectors that are in the kernel of f You should be able to justify your answers there may be more than one correct answer 3 A 0 A 4 0 1 1 B 0 2 1 1 C 0 0 1 0 D 9 0 3 E 184 63 d Select all of the vectors that are in the image of f You should be able to justify your answers there may be more than one correct answer

List the angles in order from least to greatest measure 9 E 10 11 X 9 cm D 15 cm 12 cm 3 0 m G 1 1m H 2 0 m 28 ft 19 ft 21 ft

6 CE 8 6 20 2 6 8 N Sequence 1 Figure 1 Is first reflected over the line y and then translated 8 units up and 2 units right to create figure 2 co Which two sequences of transformations could be used to prove figure 1 and figure 2 are congruent Sequence 3 Figure 1 is first reflected across the x axis X Sequence 2 Figure 1 is first translated down 10 units and then rotated 180 clockwise about the origin to create figure 2 Sequence 4 Figure 1 is first rotato 009

A 8 12 8 Determine the following cardinalities n A n C 19 n An C n AUB 21 n AUBUC n An BnC Help 7 7 Video B

Find a matrix P such that PTAP orthogonally diagonalizes A Verify that PTAP gives the proper diagonal form Enter each matrix in the form row 1 row 2 where each row is a comma separated list A P PT AP 0 10 10 10 5 0 10 0 5 2 1 1 1 3 2 2 1 0 0 0 0 15 0 0 0 15 X

A 1 2 3 4 6 12 B 2 4 6 8 10 12 C 1 3 5 7 9 11 U 1 2 3 4 5 6 7 8 9 10 11 12 What is An C A 1 3 B 2 4 6 8 10 12 C 1 2 3 4 5 6 7 9 11 12

Find the sum of each series 3 6 12 24 768 For the toolbar press ALT F10 PC or ALT FN F10 Mac