Coordinate system Questions and Answers

For a 2D problem given any combination of forces the direction of ALL moments created by those forces will ALWAYS be in what direction Explain why F d Mo O Sense of rotation Moment axis Mo O Sense of rotation

nas abo 15 drops One drop of

State two other ways to name Zx T y X U

e table below gives the shape and color of toy blocks in a certain set ese are the only toy blocks in the set Shape Star Square Circle Triangle Clover Color Purple Green Red Blue Red conditional statement is given below Give the converse contrapositive and inverse of the statement Also use the table abc ecide if each statement is true or false Assume that any toy block mentioned comes from the set Given statement If a toy block is a triangle then the toy block is blue Converse Contrapositive Inverse If Choose one then Choose one If Choose one then Choose one If Choose one then Choose one O True True True True False False False False X

The midpoint of ST is M 3 0 One endpoint is S 6 5 Find the coordinates of the other endpoint T T M 3 0

7 Jaime randomly surveyed some students at his school to see what they thought of a possible increase to the length of the school day The results of his survey are shown in the table below Lengthening School Day Survey In Favor Grade 9 10 11 12 12 15 8 5 Opposed 6 3 12 16 Undecided 9 11 10 9 Part A A newspaper reporter will randomly select a Grade 11 student from this survey to interview What is the probability that the student selected is opposed to lengthening the school day Part B The newspaper reporter would also like to interview a student in favor of lengthening the school day If a student in favor is randomly selected what is the probability that this student is also from Grade 11

8 a 9 10 Are the following points collinear QNM circle one Yes No b Are the following points coplanar Q NP circle one Yes No Name line a in two other ways Name one pair of opposite rays N M a

For Exercises 13 15 find the measure of the angle formed by the hands at each time 13 3 00 14 4 00 19 15 3 30 10 9 8 12

P is the weighted average of A and B on the number line Find the coordinate of P under the given conditions 5 4 3 2 1 0 1 2 4 1 A has a weight of 6 and B has a weight of 3 2 The weight of A is one third the weight of B 3 The weight of B is 0 and the weight of A is greater than 0

7 2 3 7 7 9 5 9 7 7 11 10 7 8 1

Suppose f z y tan z y and u is the unit vector in the direction of 3 2 Then a f z y b f 0 5 9 sec x 2vtanx y 2vtanx y c fu 0 5 9 Du f 0 5 9 0 0311 A

or the following exercise evaluate the expression writing the result as a simplified complex number 5 4i 5 3i 3 2i

Find the slope of a line parallel to each given line 7x 2y 4 x y 2 3x 5y 0 x y 4

6 1 point B C F E S D A If chord AB is congruent to chord CD then what must be true about EF and EG They are different lengths They have no relationship They are parallel They are the same length

7 5 9 13 2 8 1 16 15 18 Write the slope intercept form of the equation of each line I 10 9

46 Which coordinate point is in the solution set for the system of inequalities shown in the accompanying graph 1 3 1 2 2 2 3 1 1 4 0 1 2 1 3 2 1 y 2 X

Find the midpoint of each line segment 1 5 2 3 154 43 AY M x x yfy 2 2 M 1 S 2 M 62 2 1 20 M 3 1 2 3 4 2 2 4 AY AY Y

On a reality show contestants had to spin two wheels of fate Spinning the first wheel determined the remote location where contestants would reside for the duration of the season Spinning the second wheel determined which bonus survival tool they would be allowed to bring along with a few other necessary items A tent Matches A rope Desert Rainforest 3 7 9 4 4 3 What is the probability that a randomly selected participant spun the second wheel and landed on matches or a tent Simplify any fractions

61 66 Right triangle relationships Draw a right triangle to simplify the given expressions Assume x Q 62 cos sin x 3 61 cos sin x 63 sin cos x 2 64 sin cos e for 0 0 2 65 sin 2 cos x Hint Use sin 20 2 sin 0 cos 0 cos 0 sin 0 66 cos 2 sin x Hint Use cos 20

7 The endpoints of line segment AB are located at 5 2 and 3 10 What is the equation of the line that is perpendicular to AB and passes through the midpoint of AB A y 4 2 1 B y 4 x 1 C y 6 x 4 D y 2 2 3

8 Get Fit Power House and Fitness Frenzy are competing gyms that are trying to recruit new members They all have new deals to attract customers Get Fit 35 one time registration fee and 5 for every time you visit Power House 40 one time registration fee and 4 for every time you visit Fitness Frenzy No sign up fee Pay 15 a month Consider the graphs that represent the cost of attending a gym for the first month if you visit times for each gym a Which gym s graph if any would represent a horizontal line Explain b Which gyms graphs if any would represent perpendicular lines Explain c Come up with a pricing scheme for a new gym Run Around the Clock so that the graph of monthly cost of attending the gym a times is parallel to that of Power House

5 Which of the following equations does NOT represent the line shown in the graph A 3x 5y 15 3 B y 3 x I Y 5 3 1 D y x 5 3 6 5 4 3 2 2 1 0 2 6 7 8 9 10

a Find a parametric equation for the line through the point 1 4 6 and in the direction of ai bj ck F t b Find conditions on a b c so that the line you found in part a goes through the origin Be sure you can give a reason for your answer Then use your work to give two distinct triples a b c tham result in the line passing through the origin Choice 1 a b Choice 2 a b 1 c

Exercise 6 two phase method Solve the following linear programming problem using the two phase simplex method minimize x x2 x3 subject to X1 X2 x3 3 x 2x2 7x3 4 X1 X2 X3 0 Start by adding slack variables and note that the problem was to minimize rather than maximize In Phase 1 set up an auxiliary LP problem that either proves the original problem is infeasible or provides a basic feasible solution to the original problem If Phase 1 yields a basic feasible solution then proceed to Phase 2 solve the original LP problem starting from this basic feasible solution

Let ro xo yo zo be a fixed point r x y z be a variable point and a b c be a vector V If r ro tv is a vector equation for the line through ro co yo zo in the direction of v a b c then we can conclude that Select all that apply robus x xo a AXIN x x0 at y yo bt z 20 ct are parametric equations for the line y Yo b CAPANS If r x y z is on the line then the displacement vector r ro x xo y yo z zo is parallel to the vector v 2 20 C HAVYNS Masin The equation v r ro 0 that is a x xo b y yo c z zo 0 is an equation for the plane containing the line a b c are symmetric equations for the line

The point P co yo zo is in a plane for which n a b c is a normal vector Which of the following equations must every other point Q x y z in the plane satisfy Select all that apply n PQ 0 nx PQ 0 O ax by cz d where d axo byo czo a b c x xo y yo z zo 0 O a x xo b y yo c z zo 0

For the following matrix in reduced row echelon form give the set of solutions to the corresponding system of equations Let any free variables be r s or t For example if the solution is 12r 1 22 r you would enter 2 r 1 r 1 0 2 5 013 0 1 0 2 0 5 000 0 16

Q 3 show that there exists a projective transformation r A B C S A2 B2 C A A3 P B3 B C3 C A4 A R B B4 C C4 S

The accompanying figure shows a surveyor collecting GIS data at point B on top of a building AB that is 50m high He observes two potential streetlight locations C and D The angle of elevation of B from D is 55 and the angle of elevation of B from C is 48 11 50m 0 52 42 DB 55 y 48 11 3 1 Calculate the length of BD and BC 3 2 Calculate the distance between the two streetlight locations C and D 3 3 Calculate the area of ABCD

Equations of lines a 4 points Find the equation of the line which passes through the points 3 7 and 5 2 b 3 points Find the equation of the line which passes through 3 4 and is perpendicular

2 10 8 6 2 6 3x 3y 12 8 10

in a public park a triangular region of grass is bounded by walkways Sprinkder heads are placed at the vertices of the triangle as shown in the figure Each sprinkler head can be set to limit its angle of rotation For each sprinkler head how large should the angle of rotation be set so as to keep the walkways dry and to conserve water Round to the nearest degree 93 ft 118 116 8 A The angles of rotation are 2428 01 40 0 x

What is the most specific name for the figure A 0 0 B 3a 0 C 3a b D 0 b B A Rhombus D A B Rectangle C Square Darallelogram

Type either or in the blank X y x l v 45 54

4 What are the horizontal shift and vertical shift for the function below Use complete sentences and explain your reasoning y x 2 3

What is the most specific name for the figure A 0 b B 8a b C 8a b D 0 b B A Rectangle B Rhombus C Square D A

The figure below is a rhombus y 63 X r 21

What is the most specific name for the figure R P 0 0 Q 2b 2c R 2b 2d 2c S 2d 0 P S A Rectangle B Parallelogram C Rhombus D Square

What is the most specific name for the figure A a 0 B 3a b C 2a 2b D 0 b B A A Rectangle B Square C Rhombus D

A parabolically shaped bookshelf has a width of 10 feet 1 inches at the top and height 9 ft 5 in Their are 7 rows of shelves with the same height 10 ft 1 in 9 ft 5 in How tall is each shelf How long is the board needed for the bottom of the shelf that is the seventh row of shelves from the bottom feet inches

Click here for long description Which of the following graphs represent x OA OB O C D E A Click here for long description B M 4 7 V 5 4 4 3 2 J Click here for long description C D E Click here for long description Click here for long description

If a right circular cone must have a volume of 12 cubic meters then a function that gives the possible radii as a function of the height is The volume of a right circular cone is given by the formula V r h 36 O A r Th B h C r D r 12 Th 36 Th E r 36 36

Polygons or multi sided figures have many shapes Please match the name with its description A polygon in which one or more interior angle has a measure greater than 180 A polygon in which all interior angles have a measure less than 180 A polygon in which all interior angles have the same measure A polygon in which all sides have the same length Choose Choose Choose Choose

There are many types of quadrilaterals a polygon with 4 sides Please match the name to its best description Two pairs of opposite sides parallel All of the angles have a measure of 90 All of the sides have the same length All of the angles have the same measure and all of the sides have the same length One pair of opposite sides are parallel Choose Square Parallelogram Rectangle Trapezoid Rhombus Choose Choose Choose

5 One of the following equations is graphed in the standard x y coordinate plane below Which one A y B y 5 1 1 2 y 54 O 5 x 1 X x 1 2 C y x 1 D y 2x 1 X E y 2x 2 X 5

Suppose that cota 1 2 a Find the exact values of sin sin 11 TL and Vann 2 0 and tan a 2 8 Undefined X

A triangular pyramid is formed from three right triangles as shown below Use the information given in the figure to find the length SU If applicable round your answer to the nearest whole number The lengths on the figure are not drawn accurately R 28 1 1 S U 1 I I 53 I I 117

y 2 cot 3x Drag the movable red point to set the asymptotes for one period of the given function Also place the blue point at the correct set of coordinates You may click on a point to verify its coordinates Provide your answer below TT 3 7 6 5 4 3 2 14 0 1 2 3 4 5 6 TT 3 ZTT 3 4TT 3

Each part below contains one triangle and one figure that can be adjusted to make a triangle The markings indicate congruence a Adjust the figure on the right to explore the different triangles that can be formed Then answer the question Note that the figure will not be graded Which of the following is true O The two triangles must be congruent Reason Choose one O The two triangles do not have to be congruent b Adjust the figure on the right to explore the different triangles that can be formed Then answer the question Note that the figure will not be graded U Which of the following is true O The two triangles must be congruent Reason Choose one O The two triangles do not have to be congruent

Determine the affine transformation which maps the points 1 1 3 2 and 4 1 to the points 0 1 1 2 and 3 7 respectively