Questions

Expand cos 6u using a double angle identity in terms of sines

Factor each completely 12 marks 1 x 9 3 a x 5 25a 60a 36 7 5x 45y 9 2n 98 11 36b 84b 49 2 9x 25 4 x 16x 64 6 9x 6x 1 8 81 18x x 10 4y 20y 25 12 36a 121

A graph of a transformed logarithm f x a log x b c appears below a 3 2 b 2 2 C Question Help Message instructor a

Question What trigonometric substitution should be used to find the arc length of f x 2 ln 2x over 1 4 The arc length is 1 da Leave a out of your answer and give the answer in terms of 0 For example If the substituti given by is a cos answer cos 0 Provide your answer below

Graph the following function using the techniques of shifting compressing stretching and or reflecting Start with the graph of the basic function y x and show all stages Be sure to identify at least three key points Find the domain and the range of the function f x x 8 Which transformations are needed to graph the function f x x 8 Choose the correct answer below OA The graph of y x should be shifted horizontally to the right by 8 units OB The graph of y x should be shifted vertically up by 8 units OC The graph of y x should be shifted vertically down by 8 units OD The graph of y x should be shifted horizontally to the left by 8 units

where Describe UA and A where A is the collection of sets of the form An Civen the relation r CZ such that me 2 n n TEM

Suppose that f x y is a differentiable function Which of the following are correct statements Select all that apply f x y fz x y O f x y lim h 0 fy x y lim h 0 f x y lim h 0 f x h y f x y h f x y h f x y h f x h y h x y h

b Construct a 2 4 matrix A such that the columns of A are linearly independent or explain why such matrix does not exist

To approximate the area of a lake a surveyor walks around perimeter of the lake taking the measurements shown in illustration Using this technique what is the approximate of the lake Completed in 1902 in New York City the Flatiron Building is triangular shaped and bounded by 22nd Street Broadway 5th Avenue The building measures approximately 87 feet the 22nd Street side 190 feet on the Broadway side and feet on the 5th Avenue side Approximate the ground area covered by the building 8 5 in 35 ft 40 ft 17 in For no 1 80 ft 4511 For no 2 8 5 in 20 ft 100

The graph of a x is shown below let b x 2 x 2 3 Graph 4 x and b x on the same Set of axes a x n 5 5

Question What trigonometric substitution should be used to find the arc length of f x x over 1 4 The arc length is given by out of your answer and give the answer in terms of 0 For example If the substitution is S 1 4x dx Leave x cos 0 answer cos 0 Provide your answer below

Consider a triangle ABC like the one below Suppose that a 57 b 63 and A 29 The figure is not drawn to scale Solve the triangle Carry your intermediate computations to at least four decimal places and round your answers to the nearest tenth If no such triangle exists enter No solution If there is more than one solution use the button labeled or b a B B C c 0 or B 1 C c 0 or X No solution

Write the function whose graph is the graph of y x but is shifted to the right 7 units y Simplify your answer

Drag the function given above into the appropriate area below to match the graph Q

r 1 36x da Include the constant C in your answer Evaluate Sorry that s incorrect Try again 1 36 1 36x 5 1 36x 3 c I

The terms of a particular mortgage are Amount of Mortgage 364000 Monthly Payment 2674 monthly payments Annual Interest Rate 3 9 annual interest rate Term 15 year mortgage Use this information to complete the first three lines of the amortization table below Round to the nearest cent as needed MonthInterest Payment Principal Payment Balance of Loan 123

Synthetic Division of Polynom x4 3x 3x 2x 1 x 4

You invest 15 000 in a bank account that earns 3 4 interest compounded continuously How much is in the account after 20 years Round your answer to the nearest cent POSSIBLE POINTS 2

2 4x 22x 28 0

x 3 Solve 6 2 6 X 1 216

Now label the branches for these groups in your phylogeny with these ages 2 Discuss whether the first appearance data support the Land Plant phylogeny that we are using The plant phylogeny is constructed based on various lines of evidence like fossil record and genet data and so much more

2 6x 12 11x 5 5

Solve 625 m 1252m 2 m 514

Solve 64 162v 3 V 114

the numerator 0 0 if value s make numeratoro factor conjugate Detirmine domain 1 2x x 10x 24 O ex f x x 6 x 4 0 x 6 0 x 6 X 4 0 X 4 Dom IR x 6 4 What do we do if a domain pro 4 9x x28x 33 ex f x x 11 x 3 4 9 X

into water Include states of matter in your answer MgSO s An error has been detected in your answer Check for typos Mg 2 aq SO

Examine the Perch skull Looking at the rear of it notice how there is a small braincase housed within an outer skull Draw a cross section of the Perch skull from this perspective This is the primitive condition for many vertebrates Tetrapods included It is called the anapsid condition a braincase a complete outer skull with a space between them 6 On your drawing label the parts that correspond to the braincase holds the brain and sensory organs

d the x intercepts of the quadratic equations A B 2 1 2n 7n

Find the volume of the solid formed by rotating the region enclosed by about the x axis y e a 2 y 0 x 0 x 0

2 Discuss whether the first appearance data support the Land Plant phylogeny that we are using

1 Do some basic research and find the age of the earliest known fossils for Bryophytes sometimes called Bryopsids Tracheophytes Seed plants Angiosperms Use simple search terms like earliest known Bryophyte or oldest Bryophyte fossil Cite your sources Now label the branches for these groups in your phylogeny with these ages

Directions Calculate the critical points of the quadratic equation and graph the parabola 6 y x 8x 12 X intercepts Vertex min max Y Intercept 10 8 6 101 8 6 4 4 2 2 2 4 6 8 2 4 6 8 1

How many square yards of carpet are needed to cover the floor of a rectangular room 12 feet by 18 feet Submit All Parts yd ft

5 Ground truthing the Land Plant phylogeny Phylogenies are fundamentally just hypotheses For example no one was present during the hundreds of millions of years over which land plant evolution took place No one watched it happen and documented the branching pattern of their evolutionary history The Land Plant phylogeny that we use in this class is a conjecture based on cladistic analysis and other phylogeny reconstruction techniques It is definitely a conjecture that makes sense but did plants really evolve in the exact order that the phylogeny depicts How can we ever know for sure Is there any independent way to assess it Using first appearance data can help evaluate a phylogenetic hypothesis The term first appearance means the age of the oldest known fossil in a given group The branching sequence on a phylogeny proceeds through time from the bottom upward Theoretically then organisms on branches lower on the tree should have appeared first in time and should have an older fossil record compared to organisms to belong to branches higher on the tree

1 Mioplusus and Coelocanthus Mioplusus is a Tertiary ray fin fish Coelocanthus is a living lobe fin fish This is a scale model of Coelocanthus What primary feature distinguishes ray fin fishes from lobe fin fishes Sketch an example of a fin from each to highlight your description

3 What is the slope of the line 2x y 10

Give the exact value of the expression without using a calculator tan 5 COS LLY cos tan 5 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

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

2 What is the y intercept of the line 2x 4y 12

Given A ABC B D A ADE find the length of line segment AC 33 154 3 Picture is not drawn to scale Length of AC E C

e exact real number value of the following expression without using a calcula 24 arccos 25 rccos 24 25 Type an integer or a simplified fraction

d the approximate value of cos sin sin 0 42 und to four decimal places

Given the similar triangles below AEDF A BAC set up an equation that you would need to solve in order to find the missing side z Do not solve the equation LLJ I Faustic 50 LL F B Figure is not drawn to scale 45 A 90 C

156 Slope run Reminder The slope of a line is how steep it is It is calculated as the ratio of Start at the bottom left corner of the graph paper and make a staircase with the indicated rise anc run Then draw a line touching the tips of each stair A rise 1 run 1 slope of 1 C rise 2 run 1 slope of 2 B rise 3 run 2 3 slope of 2 D rise 1 run 2 slope of

4 Find an equation of the line through the first quadrant that cuts off the least area from the first quadrant

h FF h T V F H VE T 3m h 5 m r 6m h 7m 12 m H v

Write the slope intercept form of the equation of 3 15 through 4 1 parallel to y x 4 17 through 2 5 parallel to y x 3 3 19 through 3 3 perp to y x 2 8 21 through 1 3 perp to y x 16 through 4 5 parallel to y x 4 18 through 4 4 parallel to y 3 3 20 through 0 4 perp to y x 1 2 22 through 2 4 perp to y x 5

Graph each linear equation A y 2x 1 B y 3x 2 34 S A

How many square yards of carpet are needed to cover the floor of a rectangular room 18 feet by 9 feet A

One side of a 120 square foot rectangular room is 15 feet long How long is the other side Submit All Parts yd yd ft vd