Coordinate system Questions and Answers

z 2x 5y 3y 4x 3y 2x Subject to 2y 2x Minimize X 24 16 14 0 0 Y Solve this using the graphical method Be sure to clearly show all steps Sketch the feasible region Determine the corner points n

In this problem we will use the line segment PQ where P 1 3 and Q 3 7 a Find the length of the line segment PQ using i the distance formula ii integration with respect to z iii integration with respect to y b Create a frustum of a cone by rotating the line segment PQ about the z axis Find the surface area of the resulting frustum of a cone by using i the surface area formula for a frustrum of a cone ii integration with respect to z iii integration with respect to y c We now create a frustum of a cone by rotating the line segement PQ about the line y 1 Find the area of the resulting frustum using i the surface area formula for a frustrum of a cone Explain what changes compared to b i and what stays the same ii integration with respect to z iii integration with respect to y Hint draw the frustum and find its dimensions

5 Compute the curvature of f x x 3x 4 at x 0 1 2 3 Curvature X X AN

33 46 Horizontal Shifts Find the amplitude period and hori zontal shift of the function and graph one complete period cos x 1 2 20 34 y 2 sin x x 7 7 x 7 36 y 3 cos x 33 y cos 2 sin x 6 35 y 2 sin x F m F

Extra Proplem 7 Ptolemy s theorem Let ABCD be a cyclic quadrilateral a quadri lateral whose vertices lie on a common circle Show that AC BD AB CD BC AD Hint After you draw the diagonals you should see a lot of triangles and many pairs of congruent inscribed angles There are many ways to proceed here The sine theorem should be useful along with some trig identities Have patience with this one B As we have seen many special triplets of lines in a triangle are concurrent The

7 Given Rectangle ABCD AD CD PERIMETER AREA A 0 0 O B 2 2 D 5 5 C 7

Part 1 of 2 Error Analysis For the dilation with center 0 0 shown on the graph your friend says the scale factor is friend likely make The correct scale factor is What is the correct scale factor What mistake did your

Question 1 143 points Consider the following measures of the segments shown in the diagram BF 12 cm CF 6 cm DF 5 cm Determine the length of the segment EF 10 cm 12 5 cm 013 144 mm 543 D Figure may not be drawn to scale

ompute 5 6 4 1 6 4 5 6 4 1 6 4 Simplify your answer

C Note Figure not drawn to scale The circle above has center C and has a radius of 2 If the length of arc PQ shown in bold is between and 16 what is one possible integer value of y 36 A toy store keeps marbles in the closet of its stock room In the closet 230 marbles are blue and 370 marbles are red If 110 red marbles are added how many blue marbles must be added to the closet so that 2 of the marbles in the closet

Which angle measure is equivalent to A 20 B 140 C 280 D 70 14T 9 radians

The parent function of a quadratic f x x 2 is vertically compressed by a factor of 2 3 and translated 9 units left and 16 units up Write the equation of the transformed quadratic function g x in vertex form g x

2 points Recall a quadratic function has the form f x ax bx c Show that any space curve C parametrized by r t x t y t z t where each of x y and z is a quadratic function of t lies in a single plane in R Try graphing a few examples if you re not convinced

circle with radius 15 corresponding to an angle of 220 Answer 52 56 Find the coordinates of the point on a arde with radius 8 corresponding to an angle of 4

GEOMETRY Identifying corresponding a Give a pair of alternate interior and

r 2 7 sine chart and graph

Describe the cross section O triangle O rhombus 1 I O Rectangular prism O rectangle

8 Given PQRS PX bisects LQPR RY bisects LSRP Prove RYPX is a S Y P R X O

Find b and c so that y 7x bx c has vertex 9 5 b 126 c 395 X OT

E 16404 Let the cube ABCD A B C D On the edges BB and CC we consider the points and such that the sum AM MN ND is minimum If MN 2 10 cm calculate the sine of the angle determined by the lines MN and AD

v W Describe the bearing shown in three different ways Bearing of v S v 55

Show that the point is on the unit circle We need to show that the point satisfies the equation of the unit circle that is x y x y 11 11 25 Hence the poir Select on the unit circle

A point is chosen randomly on AD Identify the probability that the point is on BD 3 7 A B 3 8 O 5 8 6 C D

Identify the probability to the nearest hundredth that a point chosen randomly inside the rectangle is in the regular hexagon 0 04 0 06 0 02 0 98 26 2 in 1 8 in 2 in 13 in

What are the coordinates of D 2 x for x 1 1 Y 2 2 and Z 3 0

Insurance Plan Summary Deductible Wellness Exams Premium monthly Individual Individual Spouse 5 000 00 No deductible Using this plan what is the out of pocket cost for a medical treatment that costs 600 100 covered A 45 00 B 0 45 00 400 00 C 600 00 D 400 00

Find the distance across the pond Type your answer as a number only Example 10 not h 10 16 m pond 9 m B

13 Graph Triangle PTR with P 5 2 T 1 4 and R 2 3 Apply the rule x y x 7 y 6

9 1 747Oms Use a graphing utility to graph the function Include two full periods Identify the amplitude and period of the graph y 2 2 sin 2 x 4 6 4 amplitude 2 0 2 4 6 6 14 2 2 0 2 0 2 2 X X 4 4 6 6

1 Using the origin as the center of dilation and a scale factor of k 1 2 find the coordinates of the vertices of the image of the polygon below 4 points B 6 5 4 3 2 1 A 4 3 B 4 3 C 2 3 D 2 3 A 6 5 321 2 O 123456 6 C 2 3 4 5 6 X D A 2 3 2 B 2 3 2 C 1 3 2 D 1 3 2

3 Find the exact value of the real number y Do not use a calculator Show supporting steps and or diagrams like those discussed in class y arccsc 2

y 1 x 8 64 9 1 Distance from the center to each focus is

10 8 6 4 2 9 6 5 3 6 9 y X 4 6 8 10 Write the standard equation for the hyperbola graphed above

5 Compositions of FU Directions Given f x 2x 9x 2 g x 1 6x and h x x2 4 find each function Indicate any restrictions in the domain 1 f g x 2 4 x 3 g f x 7 fog x using 4 f h x 6 g h x 8 hof x Directions Using the functions above find each function value h g 7 10 foh 2

olve the following applied problems 1 A rectangular sign is being designed so that the length of its base in feet is 4 feet less than 4 times the height Express the area of the sign as a function of h

36 In 2000 tuition and fees for an undergrad resident to attend the University of Washington was 3 761 Since 2000 tuition and fees have been growing exponentially at a rate of 8 per year a Label the variables x b Complete the table y 0 1 2 3 d Draw the graph for this situation y 4 y c Write the equation in the form y ab e Based on this model what will the tuition and fees at UW be in 2025 f What year will tuition and fees at UW go over 40 000

Draw quadrilateral A 2 1 B 4 2 C 5 5 D 1 3 Use a scale facto of 2 to draw a dilation of the quadrilateral

Enter the value for x that makes the equation 12x 2 34x 212 true

Problem No 5 ABCD is an isosceles trapezoid with median XY If the measurement of vec AB is 5x 12 inches and bar DC is 8x 14 inches what is the measurement of its median

10 8 6 4 2 6 5 4 3 2 1 2 6 8 10 1 2 3 4 5 6 The function graphed above is Concave up on the interval s Concave down on the interval s There is an inflection point at

Question Given the graph of f x select the 1 graph of f 514 5 5

13 In the figure below G is the center of the circle LK is a diameter H lies on the circle J lies outside the circle on LK and JM is tangent to the circle at M Which of the following angles or minor arcs has the greatest degree measure L A LM B MK C ZJMG D ZLHK E ZMIL G M H K

Question 11 8 2 5 shading to show the following set on the Venn gram A nB the graphing tool to shade the region s Click to enlarge graph HW Score 16 O Points 0 c

Given the measures provided in the diagram shown find the area of trapezoid ABCD Figure may not be drawn to scale 26 cm 34 cm 36 cm 40 cm 4 cm 7cm 10 cm D

22 points Find the exact volume of a sphere that has a radius of 3 cm Figure may not be drawn to scale 81x cm 36 cm 27x cm 9x cm

Question 7 13 points A cone is shown with the following measures A radius of 8 cm A height of 15 cm A slant height of 17 cm Determine the approximate surface area of the cone 307 9 cm 542 8 cm 628 3 cm Figure may not be drawn to scale 17 cm 8 cm

s diagram lines AC and DE are parallel and line DC is perpendicular to each of them What is a reasonable estimate for the length of side BE A B 1 C 3 2 D 5 A AC DE DC 1 DE DC 1 AC 5 D B 4 C 11

21 Use the graph of the hyperbola to determine its equation in standard form Vertices Foci 1 312 1 3 Center 1 0 1 3 1 3 2 Foci

E H G Given mGH 40 degrees and mEF 111 Find m J

Use the method of tubes also known as the method cylindrical shells to determine the volume of the solid generated by rotating function f x 64 7 about the y axis on 4 8 Volume