Vectors Questions and Answers

Find the scalar and vector projections of b onto a a 3 6 2 b 3 2 1 comp b proj b

Wire 1 41 34 ft 38 Wire 2 Based on the given information answer the questions below Round each answer to the nearest tenth Part A How tall is the pole Show your work Part B How far from the base of the pole does Wire 2 attach to the ground Show your work Part C How long is Wire 1 Show your work

If b 15 7 then 1 6 9 8 7 5 6 5 LG

Vectors can be Select one or more a scaled b subtracted c inverted Od squared

The poin L A m O A LU B C D E F B in the graph below represents 4 5 25 O E 3 N D

If A JHI AJLK then what does JH OZK OLK KJ

Match each statement with its symbolic notation G A q P B pq C pv q D p q E q p F p q G 4 Conjunction 5 Disjunction 6 Conditional 7 Inverse 8 Converse 9 Contrapositive 10 Riconditional n a

b B M D C a In the above diagram OA a and OB b C lies on 04 where OC the midpoint of AB BC and OD intersect at M i Express the following vectors in terms of a and b A AD B OM Hence evaluate BM MC OA D is 3 marks 3 marks 4 marks

3 For independent random creams produced in two different factories the amount of fat was measured and summary statistics are given below Assume that the fat content is normally distributed Factory Factory B n Y S 13 31 2 2 5 11 30 8 3 4 a It is suspected that the creams produced in factory A are higher than the fat content of creams produced in factory B a 0 05 Write Ho and Ha take the test and interpret 20 points b Calculate the significance level of the test 10 points

Solve for x Round to the nearest tenth when necessary 1 5 1 14 5

Let 2 X 1 3 1 Y 1 11 2 5 0 31 V 2 13 x 1 U 1 W 2 02 a 3 marks XYT T b 2 marks 2Y I3 c 4 marks tr W V 2 1 2 1 0 1 0 Evaluate each of the following if possible If it is not possible justify your answer Show all your work

Writing Linear and Exponential Equations An investment is initially worth 11 600 Write an equation representing the value of this investment V after t years in each of the following situations a The value decreases by 6 per year b The value decreases by 800 per year c The value increases by 633 per year d The value increases by 12 per year NY1 V V V V

Based on the information given can you determine that the quadrilateral must be a parallelogram Explain Given XN NZ and NY NW Y W X N 2 Yes opposite sides are congruent Yes two opposite sides are both parallel and congruent No you cannot determine that the quadrilateral is a parallelogram Yes diagonals of a parallelogram bisect each other

Joanna needs two spools of ribbon but there are 13 different choices In how many ways can she choose 2 different spools of ribbon

Find the angle between vectors 2 5 and 3 1 Select one a 130 2 b 49 8 OC Do not have enough information d 54 04

a and fb are orthogonal If a 4 5 and b x y then the ratio 0 is

If a 1 4 b 3 6 what is a b Choose the correct vector Select one a b O C 22 00 16 14 12 10

Because 3i 2j 2 5j and 27 5j 3i 2j i i we can conclude that vector addition is

Given the vector with magnitude 12 and directional angle 60 Write the vector in unit vector form JI 49 S

3 5 The vector above has a magnitude of 1 18 O

Given the vector 4 8 4 8 with a directional angle of

her the equation y 9 x is linear Find the

Consider the vectors in 3 space a b c such that 35 2b 4c 0 then it is necessarily true that O a a 0 b 3x b c c ax b d a b c 0 c 0

Siven polynomial is below f x x 4x 6x 36 a 2 is a zero List all the zeros of the function Enter your answers as a comma separated list X b Write the polynomial as the product of linear factors f x

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

Given the graph of two vectors choose the image which best represents the difference of u Hint Graph the vectors on graph paper then draw the resultant vector Select one a 4 4 4 k

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

Next question You can retry this question below Points A and B are separated by a lake To find the distance between them a surveyor locates a point C on land such than ZCAB 44 3 Find the distance across the lake from A to B C Get a similar question 459 yd distance B 315 yd NOTE The triangle is NOT drawn to scale yd 1 44 3 Enter your answer as a number your answer should be accurate to 2 decimal places Question Help Worked Example 1 A

Find a constant h for which the vectors 3 and h are orthogonal 6 pts

Find the measure of ZPQR List in sequence with reasons the angles you had to find along the wa o determine the required angle M 50 N S 17 P 80 R O

3 Estimate a polynomial for the sine function using the points sin0 0 sin 1 2 1 and sin 0 Hint rewrite as points in x y form to look more like the last problem Use your result to estimate sin 7 3

The graph of a linear function f is shown a Identify the slope y intercept and x intercept b Write the equation that defines f The slope is Type an integer or a simplified fraction Ay 61 10 8 64 2 44 6 B E

For problems 8 10 solve the triangles Round to the nearest tenth 67 V 49 50ft

Match each symbol to the corresponding vocab words from set theory CCB a Intersection An B AUB AC b Union c Subset d Complement

Find the angle between the vectors u 6i 6j v i 3j 5k The angle between the vectors is 0 Round to the nearest hundredth as needed radian s

Sunflower oil is a cooking ingredient that can be used as a substitute for olive oil The density of sunflower oil is 0 925 grams per cubic centimeter A farmer would like to sell bottles of sunflower oil that contain 370 grams of oil What is the volume of the smallest container that holds 370 grams of oil O 0 0025 cubic centimeters O 27 75 cubic centimeters O342 25 cubic centimeters O 400 cubic centimeters

Enjoys playing video games Does not enjoy playing video Plays an organized sport 31 22 Does not play an organized sport 32 15 games One of these 100 students is selected at random to give more detailed answers to some follow up questions A What is the probability that the chosen student enjoys playing video games or plays an organized sport B What does P Enjoys playing video gamesldoes not play an organized sport represent for this survey C Calculate the value of P Enjoys playing video gamesldoes not play an organized sport

10 Which theorem compares two sides and the included angle of two triangles F Hinge Theorem G Converse of the Hinge Theorem H Exterior Angle Inequality Theorem I Triangle Inequality Theorem

he blade of a creu r saw rotales at a rate of 4000 revolubons per minute What is the inear velocity in miles per hour of a point on on the 5p of the outer edpe of a 7 t 4 inch diameter blade The linear velocily as approximately triles per hour Round to the at tanth ded 7

Right triangle ABC is shown A 3 m G 50 C a B Which equation can be used to solve for c sin 50 3 sin 50 O cos 50 O cos 50

Copy vectors u v and w head to tail as needed to sketch the indicated vectors a u v b u v w C U V d u w Choose the correct sketch for u v OA OB 4 Q O C Q W Q OD

Find an equation of the hyperbola having foci at 6 1 and 10 1 and vertices at 7 1 and 9 1 0

The number of cars waiting at a bank for 60 minutes is as follows Cars Frequency 0 2 1 9 2 3 4 16 12 8 P 5 5 6 Find the probability of 5 cars waiting in line Probability 6 7 8 4 2 1

Find a vector equation and parametric equations for the line Use the parameter t the line through the point 4 6 1 and perpendicular to the plane 2x 4y 4z r t x t y t z t

What is the value of x in Clue 11 Enter the numeric value for x only rounded to the nearest tenth 6x 15 4x

Warm Up 3 Area of Regular Polygons Words to Know polygon radius of a regular polygon in a plane a closed figure formed from three or more line segments such that each segment exactly two other segments one at each and no segments with a common endpoint are collinear a segment that extends from the regular polygon to a of the polygon a polygon that is both equiangular and

4 Solve for the values of x y and z yx N 76

Find the area of a circle with a diameter of 14 meters Round your answer to the nearest hundredth of a square meter The area of the circle is about square meters

7 Convert to fractions 23 0 330 700

Question 16 Points 1 Quadrilateral ABCD is reflected over y axis Which of the following is true about the quadrilaterals 2 B 1 1 A DE 4 0 D AO 1 Quadrilaterals are similar B D Quadrilaterals are congruent None of the choices To C Quadrilaterals are not congruent