Coordinate system Questions and Answers

Graph the image of square EFGH after the following glide reflection Translation 19 units left Reflection across the line y 1 14 12 10 8 6 4 2 12 10 B 6 4 2 2 4 6 8 10 12 2 4 6 E 8 H 10 12 14

Consider the following planes 2x 5y z 7 4x 4y 3 z 10 Find their line of intersection by finding two points that are on the line and write it in parametric form Use t for the parameter and denote vectors using the notation x y z Do not evaluate any fractions that mig appear in your answers enter the exact fractions Note Please do not rescale simplify the direction vector of the line

6 For a signal x as shown in figure 5 a Write the mathematical function for x using step and ramp function b Plot 2x 0 51 2 2 x 1 A

What are the coordinates D 24 2 14 E B F G

1 Find an equation for the set of points whose distance from the plane z 2 is the same as the distance to the point 5 2 0 Write your answer in one of the forms of quadric surfaces listed in Section 12 6 and identify this surface You do not have to sketch this surface

Use the following graph of y f x to graph each function g a g x f x 1 b g x f x 1 2 c g x f x d g x f x 1

b At time t let D t and D t denote the distance from the particle to the solution planes of the equations 3x 4y z 9 and x 5z 8 Determine if there is a time t 0 such that D t D t If there is find it together with the common distance from the planes

witch two triangles are congruent 10 65 45 Q Q S 45 70 S 10 60 10 45 45 R 10 65 T igles

K 6 5 is the image of K after a reflection in the line y 2 What are the coordinates of K

A heavy rope 30 ft long weighs 0 7 lb ft and hangs over the edge of a building 80 ft high a How much work W is done in pulling the rope to the top of the building W ft lb b How much work W is done in pulling half the rope to the top of the building W ft lb

a To define the inverse sine function we restrict the domain of sine to the interval For example sin sin x y sin sin b To define the inverse cosine function we restrict the domain of cosine to the interval cos by cos x y cos Need Help Read It 2 2 Points DETAILS SPRECALC7 5 5 002 For example cos On this interval the sine function is one to one and its inverse function sin 1 is defined by because sin On this interval the cosine function is one to one and its inverse function cos 1 is defined cos because cos MY NOTES PRACTICE ANOTHER

Triangle EFG with vertices E 2 3 F 2 4 and G 1 1 is reflected over the line x 3 What are the new coordinates E

Rewrite the expression in terms of the given angle s reference angle then evaluate the result Write the exact answer Do not round 16 Answer sin

E 19 is this graph eve Odd Even or odd

Consider the following quadratic equations given Imaginary or real Quadratic Equations Imaginary roots z 2x 5 0 z 62 7 0 z 5x 6 0 Real roots

Find the measure of the each angle to the nearest degre sin 14 7

Vertex Form of Parabolas Use the information 1 y x 16x 71 8 7 Y a x h f k provided to write the vertex form equation of each parabola 16 71 0 162264 71 71 y x 14x 59 59 14x 1959 7 144x 4 Ma 64 1671 64 10 C 75 Y CX 7J HO y x 12x 460 46 46 0 termouth 636 12 4616 6 6 10 x 6 HO x YX 61 10 y x 6x 5 x 8 7 2 x 8 7 X 14 49 2 36 2 y x 2x 5 x 2x 5 0 5 5 x 1215 1 x 1 6 X x 8 7 Date 6 y x 4x 4 y 2x 36x 170 8 y x 5 x 4 10 2 12x 1 6 32 22 1 1 Pe 13 0

A quadrilateral has vertices at 1 4 1 2 4 1 and 2 5 What kind of quadrilateral is it Explain

Graph each function over the interval 29 2 Identify the characteristics of each function as well S cxc x 1 2 x 2 sec2 x 1 x cot x 7 2 Amplitude None Period 2TT Phase Shift T to the higjet Vertical Shift Midline Amplitude Period Phase Shift Vertical Shift Midline Amplitude Period Phase Shift Vertical Shift Midline

0 1 pt 399 Details A maintenance worker fills a swimming pool with water 3 at a rate of 8 m minute Suppose at t 0 the swimming pool is filled with 95 m of water A function giving the volume V of water in the swimming pool after t minutes is V t How much water will be in the swimming pool at t 20 minutes m 3 When will the swimming pool contain 359 m of water minutes

What is the length of QU O 30 12 pony U 12 12 V 30 R T

Directions Identify the key characteristics of each graph then write the equation that best represents the graph Keep in mind more than one answer can be true for the equation Amplitude Vertical Shift SE 2 If 2 Period Equation Amplitude Period Equation Amplitude Period Equation Amplitude Period Equation Phase Shift Vertical Shift Midline Vertical Shift Phase Shift Midline Vertical Shift Midline Phase Shift Midline Phase Shift

The parametric curve x 5 sint y 2cost sts 5m represents an ellipse traced once in the anti clockwise direction starting at 0 2 an ellipse traced 3 times in the clockwise direction starting at 0 2 an ellipse traced 3 times in the anti clockwise direction an ellipse traced 3 times in the clockwise direction an ellipse traced 2 times in the anti clockwise direction starting at 0 2

find equation that hits the points 4 25 59 8 75 41 13 25 59 and 17 75 41

2 21 and 22 are a linear pair and 21 and 23 are ve the value of x A 12 5 B 62 C 26 5

Find the interior angle measures of each inscribed quadrilateral 5 B 3y 16 A D 6y 2 2x 3 T 3y 5 S C skais 4y 6 Q 4y 3 R 3x 23 7 6 8 adam Platge 2x 3 Z 3a H 10 G Y 3x 5 W 4b 8 F 4x 9 6b 12 4a 5

Type the correct answer in each box Spell all the words correctly and use numerals instead of words for numbers If necessary use for the fraction bar s 10 8 6 4 We can show that AABC is congruent to AABC by a translation of 2 Y 10 8 6 C 21 10 unit s 4 07 and a 8 B 10 B across the axis

What is the x coordinate of the center of the circle in the following equation x 9 2 y 8 2 74 Round your answer to the nearest hundredth if necessary Typo your answer

2 10 pts Use the graph of f x given below to answer all the p Please pay attention to scaling in both the x axis and y axis a What is the domain of f x Please write answer in interva b What are the x intercepts of f x If value is not on the gra Please write your answer as an ordered pair s c What is the y intercept of f x Please write your answer a d Find f 2 e Find where f x 1 3 2 1 2 y 3 0 1 3 1

1 In right triangle ABC shown in the diagram below altitude BD is drawn to hypotenuse AC AD 6 cm and AC 30 cm B Heartbeat or Boomerang Proportion a Determine the length of BD A D b Determine the area of AABD C

Find the point W that is on the directed segment that is the distance from U to V given u 4 3 and point 2 3 41 9 O 1 1 0 1 2 1 3 2 2 4 R 3 4 e U A

What is the midpoint of the segment AB given point 4 6 1 and point 8 3 7 2 8 1 4 14 6 7 3

The endpoints of a diameter of a circle are A 1 1 and B 3 3 What is the length of the radius 2 20 3 2 K 3 A 1 1 B 3 3 4

Determine the point x y on the unit circle associated with the following real number s Write the exact answer as an ordered pair Do not round S 1 46

The vertices of AJKL are J 3 2

3 7 points Find the value of each variable Round any radical to the tenths place 3 1 7 X 60 25 3 y x type your answer y type your answer

Directions Graph each function over the interval 2 0 2 Identify the characteristics of each function as well x csc x 2 CSC Six 2 sec2 x 3 1 f x cot x 4 2 r Amplitude Period Phase Shift Vertical Shift Midline Amplitude Period Phase Shift Vertical Shift Midline Amplitude Period Phase Shift Vertical Shift Midline

A boat travels on a course of bearing N 53 50 W for 81 4 miles How many miles north and how many miles west has the boat traveled Round at least to the nearest tenth of a mile Miles North Miles West miles miles

The given function models the displacement of an object moving in simple harmonic motion y 2 cos 16 t a Find the amplitude period and frequency of the motion amplitude period frequency

c A system of 3 equations in 5 variables whose general solution involves 3 paramete 101002 010113

16 Consider the function f x x 16x 60 Find the axis of symmetry of this function Type a response 17 Consider the function f x x 16x 60 Find the vertex of this function

Consider the following graph Step 2 of 2 Determine the domain and range of the graph 10 S Enable Zoom Pa

Geometry U7 Assessment Name Period I can find the missing side of a right triangle using Pythagorean Theorem and its Converse score 21 1 Find x the height of the water tower 3pts 31 feet 45 feet 7 ft 3 Solve for x in the diagram below 24 X X Water Tower 4 11 ft 6 5 Use Pythagorean theorem to determine if the triangle below is right obtuse or acute triangle Show work 3pts 15 ft 3pts Date 2 What is the length of a diagonal brace that could be used for a wall 9 feet high and 12 feet long 3pts 4 The side measures of a triangle are 5 12 and 15 Use Pythagorean theorem to determine whether the triangle is right obtuse or acute triangle 3pts 6 Two airplanes leave the same airport One heads north and the other heads east After some time the northbound airplane has traveled 40 miles If the two airplanes are 55 miles apart how far has the eastbound airplane traveled 3pts 7 A flying squirrel s nest is 8 feet high in a tree From its nest the flying squirrel glides 10 feet to reach an acorn that is on the ground How far is the acorn from the base of the tree 3pts

5x 42x c What does c need to be in the equation above to complete the square Round your answer to the nearest hundredth Type your answer

5 2 09 Review Write the equation of the line that is the perpendicular bisector of the line segment having endpoints 9 0 and 3 4 Write your final answer in slope intercept form Use of the grid is optional

Convert the angle measure 0 35 rads to an approximate degree measure O O 20 05 23 540 61 08 866 140

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