Quadratic equations Questions and Answers

The power dissipated in an electric circuit is given by the expression P RI2 where R is the resistance of the circuit and I is the current through the circuit For a sinusoidal alternating current the current might be represented by the relation I A sin 27ft where A is the amplitude f is the frequency and t is time Write an expression for P involving the sine function and use a fundamental identity to write P in terms of the cosine function OPRA sin 2 ft P RA RA cos 2 ft OP RA sin 2 ft P RA cos 2 ft OPRA sin 2 ft P RA cos 2nft P RA sin 2 ft P RA RA cos 2uft

T X 14 Find the reference angle and sketch and in standard position 0 155

X 15 The point 8 15 is on the terminal side of an angle in standard position Determine the exact value of cot 0 17 15 O cot e cot 8 cot 0 cot 8 cot 8 15 17 15 17 15 8 15

X 17 Select the graph of the function below Include two full per TCX

X 20 Evaluate the following expression x n where n is a whole number 5 sec x 5 5 sec x 5 cot x O 5 cot x 5 tan x 5 tan x

X 11 Find the period and amplitude y 8 sin x O Period 7 Amplitude 8 O Period 27 Amplitude 1 O 1 Period 7 Amplitude 8 O Period 27 Amplitude 8 Period 27 Amplitude 8

A manufacturer of skis produces two types downhill and cross country Use the following table to determine how many of each kind of ski should be produced to achieve a maximum profit What is the maximum profit What would the maximum profit be if the maximum time available for manufacturing is increased to 60 hours Manufacturing time per ski Finishing time per ski Profit per ski Downhill Cross country 2 hours 1 hour 0 5 hour 60 1 hour 60 Maximum Time Available 48 hours 30 hours How many of each kind of ski should be produced to achieve maximum profit The manufacturer should produce downhill skis and cross country skis Type exact answers Type integers or simplified fractions COXE

Solve the compound inequality and give your answer in interval notation 5x8 22 OR 3x 42 14

Express the inequality m 3 1 using interval notation

e 1 sin 0 1 cose cose

1 1 1 cosx 1 1 cosx 2csec x

1 Solve for x and simplify the answer a 6x 2x 3 0 to no pignus b 2x 4x 5 0 c 2x 2x 3

60 X

Santa s sleigh is flying at a constant height above the ground It drops a present which follows a parabolic path described by the equation h 0 5t 2 5t 10 where h represents the height in meters and t represents the time in seconds How long does it take for the present to hit the ground

What are the x intercept s of the function f x Ox 9 Ox 0 Ox 9 4x 36x2 x 9

x 22 sin x sec x sin

2 5 Solve for y y 5y 6 0 y 5y 6 1 21 3 3 a b C 8 27 d 216 1

Find the domain and range of the relation and determine whether it is a function What is the range of the relation OA 1 y 1 OB 6 y 6 OC 1 y OD o y 200

Make a table of values for the equation Then graph the equation y x 2 1 Complete the table of values below y X 5 3 1 0 1 3 5 Simplify your answers Which graph below is the correct graph of the equation

The domain of the piecewise function is 0 00 a Graph the function b Use your graph to determine the function s range a Choose the correct graph below OA 20 Ay OB f x 2x if x 0 2x if x20 b The range of f x is y20 Type your answer in interval notation O C Q D

For f x 5x 4 and g x 2x 3 find the following functions a fog x b gof x c fog 1 d gof 1 a fog x Simplify your answer b gof x Simplify your answer c fog 1 Simplify your answer d gof 1 Simplify your answer

Simplify the expression Write the final form with no fractions sin x 2sinx 1 sin2x sinx tan sin cos cot Osec

Simplity 3 6x y 144x 3 6x y 144x 2 3

Q 13 A ball is thrown straight up from 3 m above the ground with a velocity of 14 m s This action can be modelled by the quadratic function h t 5t 14t 3 where t represents time in seconds and h t represents height a After how many seconds does the ball hit the ground b What is the maximum height the ball reaches and state the time this happens 3

1 11 A 5m C 5m 13 A C 3m 5m 6 6 5 15 C 14x 56x 66 A x 7 x 8 x 12 B D 5m 12 2 n n n n n 2n 3 n 5n 6 n 5 3 n 3 2 3 n 4 n 2 m B D n 2 n 3 1 x 4 B 19 7x 33 12 14 16 12 A 9 C 14 A B C D 16 10 6 4 8m A 15 8m B D 4 4p 20p 4p 20p p p 6 p 2 p 1 2 P 5 p 1 p 1 P 2 P 3 1 4 p p 72 P 11 P 5 13 C P 20 11 1 m 1 P 8 B D P 9 P 11 P 7 P 9

Find each product 7 4m 4 2m 6m 5 A 8m 16m 4m 20 B 49m 28m 61m 40 C 24m 40m 16m 64 D 16m 18m 28m 49 Simplify each expression 9 5p 29p 42 25p 35 5p 19p 30 7 5p A 4p p 9 p 7 5 p 7 P 5 B C 5 D 3p p 9 10 8 10 8 8b 8 b 6b 5 A 25b 50b 31b 24 B 8b 40b 8b 40 C 14b 36b 19b 20 D 28b 44b 56b 64 10 A C 14m 25m 25 m 10 m 9 m 6 m 4 3 m 2 m 10 3m 6 14m 25m 25 B 8 m 9 7 4 m 9 D

9 Simplify each and state the excluded values x 15x 56 10x 80 17 A B C D x 7 19 8 10 x 8 3x 5x x 3 5x 8 9 5x 9 0 7 3 8 State the excluded values for each 12n 4n 12n 24n Factor each completely 21 5p 10p 18 18 20 22 A B 6x 60 x x 90 20 6 9 x 7 x 3 5 x 2 3 x 3 x 7 D 8 7 x 7 9 10 3 63p 81 27p 27 0 3 22 m 2m 63

7 In the figure below a 8 b 9 and 0 48 Use this information to solve the parallelogram for c The diagonals of the parallelogram are represented by c and d Round your answer to two decimal places 8 b figure not drawn to scale

14 Find a unit vector in the direction of the given vector 0 4 U O 0 0 O 1 0 O 0 1 O 1 0

5 To determine the distance between two aircraft a tracking station continuously determines the distance to each aircraft and the angle A betwe them see figure Determine the distance a between the planes when A 41 b 34 miles and c 19 miles B b

2 Use the Heron s formula to find the area of the triangle Round your answer upto two decimal places a b c 0 08 O 0 12 O 0 06 O 0 10 0 11

J 2 Which of the following is equivalent to the given expression cos x 1J

1 Use the given values to evaluate if possible three trigonometric functions cos sin tan 3 6 2 0 4 seco csc o 3 5 5

7 Convert the angle measure from degrees to radians Round to three decimal places 0 57 O 0 57 1 310 radians O 0 57 0 010 radian O 0 57 0 090 radian 0 57 1 010 radians 0 57 0 310 radian

6 Find u v u 4 5 v 6 0 O 10 10 O 5 5 O 5 10 O 11 6 O 10 5

stwoled all ov 14 If a b and b2 c what is a in terms of c A C 18 B c27 1 C c 2 D co E c2 fees 6

c x x 1 1 3

v x x 6x 8 xx x

8 P k 12 K 6k 40 B 3K 3 5k 2 5k 8 5k 8 5k 2 10 4 91 2 0 5 Factor each completely 9 2x 8x 10x A 2x x 1 x 5 B 2x x 1 x 5 C 2 x 1 x 5 D 2x x 1 x 5

Simplify each expression 2 2 2 m 3 A B C D 2 2m 1 m 3 2m 1 5 m 3m 4 4 2m m 3 2m 1 6m 8 m 3 2m 1 Find each product 4 4p 8 6p p 4 A 32p 24p 44p 12 B 10p 19p 46p 16 C 5p 32p 7p 2 D 24p 44p 24p 32 3 3 2 2 v 1 A C v 1 7 2v 2 v

8 An airplane is flying 700 feet above ground From the plane to the base of the control tower the angle of depression is 47 How far away is ground directly underneath the plane to the control tower Round your answer to the nearest tenth 4 foot above

Solve the right triangle D CD mZD 7 m B Write your answers as integers or as decimals rounded to the nearest tenth O C O 3 B

Find mZU W 5 9 U V Write your answer as an integer or as a decimal rounded to the nearest tenth

3 6x 9x 1 Find

8 A traffic light weighing 15 pounds is suspended by two cables see figure Find the tension in each cable if 0 40 and 0 35 Approximat the answers to one decimal place 0 0

10 Find the component form of v if v 10 and the angle it makes with the x axis is 120 O 10 10 3 5 2 5 2 0 5 3 5 0 5 3 10

9 Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vec Initial Point 9i 5j O 5i 9j O 9i 5j O9i 5j 9 7 Terminal Point 0 2

10 How are the GRAPHS of sin x and cos x different How are they similar Explain in detail your answer U Font Family AA A 3 C D

Use long division to divide Simplify your answer completely 7 x 1 x 1

a Explain how biotic and abiotic factors can impact growth of populations b How does one feeding niche impact others in