Coordinate system Questions and Answers

y csc 2x x 2 111 111 111 111 2 020 14 12 337588 U 111 111 111 III

A A camper wants to protect her bag of food from bears She decides to tightly stretch a rope between two trees and hang her bag from a point exactly halfway along the length of the rope The first tree is 10 feet east and 6 feet north of her firepit The second tree is 5 feet west and 8 feet north of her firepit The rope is attached at a height of 8 feet to the first tree and a height of 9 feet to the second tree Let the firepit represent the origin movement east of the firepit represent movement in the direction of positive x movement west of the firepit represent movement in the direction of negative x movement north of the firepit represent movement in the direction of positive y and movement above the firepit represent movement in the direction of positive z 1 Write the coordinates of the points on the trees where the rope is attached 2 Find the distance between the points in part a Use sqrt to indicate a square root For example 3 would be written sqrt 3 3 Find the coordinates of the point where the food bag is hung 4 If the food bag is 1 2 feet long when hung and bears can reach a height of 7 5 feet when standing is the camper s food safe from bears Explain why or why not U pointol

5 tan 6 6 09

AB A 8 BE 6 ED B C DC 2 AC 8 6 4 2 02 4 2 P 4 E D A 6

3 Prime factorization a Find the prime factorization of each of these integers Show all your steps 1 108 2 1188 3 10 b Consider two positive integers a 22 x 32 x 52 x 76 and b 24 x 54 x 72 Using the GCD formula not the Euclid algorithm find the greatest common divisor of a and b No need to justifu

Strong Induction Prove the following statement by strong induction There exist non negative integers x y such that n 3x 7y for all n 1

Calculate the lengths of the 2 unlabeled sides JG 6 5 45 G 6 5 H

The given point is reflected across the line indicated Find the coordinates of the image U across x 2 If the given point U is reflected across the line x 2 the image is Type an ordered pair

5 x y 115 6 w 122 74 x NO Wo 152 70 81 N

x y z 0 3 2 x 4 2 1 1 x y 2 1 2 Y 2 1 3 x y 2 1 2 Y Z 1 3 3 2x y 2 1 x y 2 5

hombus 2 3 mZ1 21 Kite mz2 429 m21 mz2 2 mz3 m23 3 46

3 Rhombus H 1 3 I 2 7 J 2 6 K 3 2 HJ IK Slope HJ Slope IK

Look at the graph 5 10 5 0 5 10 What is the equation of the horizontal asymptote

5 The equation of a circle is x y2 8x 6y 9 0 Graph the circle Identify the domain and range x bx b x x2 8x1y 16y a Ex

5 22 cm 36 A 6 15 m x 18 m

Find the missing measures of Rhombus TUWV Round to the nearest tenth W TU T 5 X V U 8 WU TX TV

pulverized in a ball mill and the resulting powder was digested with various strong resulting solution was evaporated to dryness dissolved in dilute hydrochloric acid and separated from interferents by ion exchange chromatography The resulting solution containing an unknown amount of Pd II was then diluted to 50 00 mL with pH 3 5 buffer Ten milliliter aliquots of this analyte solution were then transferred to six 50 mL volumetric flasks A standard solution was then prepared that was 1 00 10 5M in Pd 11 Volumes of the standard solution shown in the table were then pipetted into the volumetric flasks along with 10 00 mL of 0 01 M arsenazo III Each solution was then diluted to 50 00 mL and the absorbance of each solution was measured at 660 nm in 1 00 cm cells Volume Standard Solution mL 0 00 5 00 10 00 15 00 20 00 25 00 A660 0 216 0 338 0 471 0 596 0 764 0 850 a Enter the data into a spreadsheet and construct a standard additions plot of the data b Determine the slope and intercept of the line J G Sen Gupta Anal Chem 1967 39 18 DOI 10 1021 ac60245a029

Your Turn Find the probability using permutation with repetition 1 There are 2 mystery books 2 romance books 2 poetry books to be randomly placed on a shelf What is the probability that the mystery books are next to each other the romance books are next to each other and the poetry books are next to each other For example MMRRPP 2 The school jazz band has 4 boys and 4 girls and are randomly lined up for a yearbook photo Find the probability of getting all of the boys grouped together

8 Find the value of x in the figure below Lesson 15 4 0 5 point 21 14 27 9 In the circle mBC B E x 38 and mAD 146 What is mzAED Lesson 15 5 1 point 10 Answer the following about the given circle Lesson 15 4 15 5 a If mQR 80 and mQS 150 what is m P 0 5 point

H 5 ve for x and y N 2y 6x 9 3y 4x 11 F G om your textbook on separate lined paper for

10 Use the diagram to the right to find the total height of the flagpole 5 5 ft 23 30 ft Will

Lesson 15 2 Checkpoint Once you have completed the above problems and checked your solutions complete the Lesson Checkpoint below Complete the Lesson Reflection above by circling your current understanding of the Learning Goal 1 Find the following angle measures of the inscribed quadrilateral mzRQP mzPSR m SRQ m2QPS 5x 20 10x R 7x 8

Find mcDAB DAB DEB mzDAB 63 3 Find mX2 108 18 126 43 mDE mEB Arc Addition Postulate For 2 3 use Circle C 2 Find mWX Inscribed Angle Theorem Your Turn Use the Inscribed Angle Theorem to find missing angle measures 1 Find the arc measure of CE Substitution Simplify X W Y SA C 9 106 Z

Guided Exanie 4 Name three points on the line y 2 4x

Find the slope of the line through each pair of points X X X Y 3 2 10 8 16 1 26 X X X ya 4 17 5 15 13 13 5 15 17 1

7 17

9

1 Graph y 1 2 cos x TI TT V TT 2 1 5 1 0 5 0 0 5 TT 2 TT 3TT 2 2TT x

9 Identify the midline period amplitude domain and range of the function shown in the graph V 0 14 2 2TT 4TT N

2 Is the point 5 0 on the graph of y sin x Explain

Using graph paper In the Q2 quadrant make a PRE IMAGE of a picture using 8 points or more if need be but not much more List all your points on a separate piece of paper in one column NEXT In quadrant Q1 on the graph paper TRANSLATE the pre image using any translation rule List the points on the separate piece of paper including your translation rule Draw an arrow from the pre image quadrant to the one where you translated on the graph paper NEXT In quadrant Q4 on the graph paper ROTATE one of your other images 90 degrees Again list your points on that separate sheet of paper including your rotation rule Draw an arrow from the image you used to the one where you rotated on the graph paper NEXT In quadrant Q3 on the graph paper REFLECT one of your other images Again list your pionts on that separate sheet of paper including your reflection rule Draw an arrow from the image you used to the one where you reflected on the graph paper FINALLY Dilate the image enlarge or shrink in the Q3 quadrant State what your dilation is then list your new points based on your dilation If you decide to do a different order of transformations for Q1 Q4 and Q3 that s fine just make sure you track what you are doing and notate it on your coordinate lists www daisypaper com

15 3x 2y 2 Find the slope a 2 3 c 2 3 b 3 2 d 3 2

tionalize each denominator answer in simplest radical form 5 12 11 6 3 12

Completely simplify each radical expression 1 63 2 112

A scale model of an oil tanker truck can hold 1 gallon of oil If a trucking company wants the full size truck to hold 8 000 gallons of oil what scale factor must they apply to the mode