Quadratic equations Questions and Answers

1 cot e 2 7 16 Find the value of the six trigonometric functions of 0 where is the angle formed by the positive x axis and the line segment from 0 0 to 2 7 sin 0 cos 0 tan 0 sec 0 csc 0

C 55 A 9 B If angle C measures 55 and BC has length 9 find Angle B in degrees The length of AB The length of AC If you use a calculator to find a decimal approximation your answer must be accurate to at least 3 decimal places

12 A If angle B measures 27 and AC has length 12 find Angle C in degrees The length of AB The length of BC 27 B

Given a right triangle with sin 0 1 cos 0 2 tan 0 3 sec 0 4 csc 0 5 cot 0 5 8 determine the value of the other trigonometric ratios of 0

9 Suppose f x 0 for all x and f x dx 18 Let R be the region in the first quadrant bounded by the coordinates axes y f x and x 3 Find the volume of the solid generated by 0 revolving R around the y axis BELEM Set up the integral that gives the volume of the solid Use increasing limits of integration Select the correct choice below and fill in the answer boxes to complete your choice Type exact answers OA JOf x dx OB SD x dx

weather balloon has a volume of 720 L when filled with helium at C at a pressure of 385 torr Part A What is the new volume of the balloon when the pressure is 0 18 atm the temperature is 45 C and n remains constant Express your answer to two significant figures and include the appropriate units Vnew Value Units

10 10 x B 2 0 10 2 0 10 Find the coordinates of in the ordered basis B a b Hint The preview shows the picture of a with the coordinates you pro

O Points 0 of 1 all fence runs parallel to the wall of a house at a distance of 10 ft Find the length of the shortest ladder that extends from the ground to the house without touching the fen Assume the vertical wall of the house is 20 ft high and the horizontal ground extends 20 ft from the fence PEND The length of the shortest ladder is ft Round the final answer to the nearest tenth as needed Round all intermediate values to the nearest thousandth as needed S

Type the correct answer in the box Tiffany is monitoring the decay of two radioactive compounds in test tubes at her lab Compound A is continuously decaying at a rate of 12 and compound B is continuously decaying at a rate of 18 Tiffany started with 30 grams of compound A and 40 grams of compound B Create a system of inequalities that can be used to determine when both compounds will be less than or equal to the same mass M where t is time in weeks PA is the initial amount of compound A PB is the initial amount of compound B and ris the rate of decay Enter the inequalities in the field by replacing the values of PA PB and r olo O 0 101 0 Vo 0 X TT a B A P sin cos tan sin cos tan 9 PO csc sec cot log log In 0 11 0 L VO A U 00 L00

Select the correct answer from each drop down menu Two different species of deer are housed in two separate areas of a wildlife park The initial population of species A was 300 and the population is increasing by 15 every year The initial population of species B was 400 and the population is increasing by 7 every year Use the given information to determine when the two species will have the same population After years the populations of the two species will be approximately equal with deer of each species

Select the correct answer The height of a pelican as it swoops down to catch a fish in the lake is modeled by this equation where x represents the time in seconds and y represents the height of the pelican in feet y r 6x 8 75 At the same time a second pelican flies in a straight line modeled by this equation y 5 Which statement describes the number and viability of the system s solutions The system has only one solution and it is viable because it results in positive values of time The system has two solutions but only one is viable because the other results in a negative value of time C The system has only one solution but it is not viable because it results in a negative value of time D The system has two solutions and both are viable because they result in positive values of time A B

Use the given conditions to find the exact values of sin 2u cos 2u and tan 2u using the double angle formulas cos u 15 17 2 U sin 2u cos 2u tan 2u

Select the correct answer Using graphing what are the approximate solutions to this equation 2x 1 1 x OA B C OD 0 913 and 1 803 0 761 and 1 217 x 0 761 and 1 803 0 913 and 1 217

Select the correct answer Consider functions fand g 5 2 1 3 Using a table of values what is an approximate solution to the equation f x g x to the nearest quarter of a unit A B C 2 2x 1 D 2 50 1 75 1 50 22 25 Next

A C C If a 8 b 8 and ZC 60 then find the length of side c b B a

An arch shaped monument is often mistaken to be parabolic in shape In fact it is a catenary which has a more complicated formula than a parabola The arch is 614 feet high and 614 feet wide at its base Assume that the x axis represents ground level and that the y axis goes through the center of the arch Complete parts a b and c a Find the equation of a parabola with the same dimensions Let x equal the horizontal distance from the center of the arc Simplify your answer Use integers or fractions for any numbers in the expression

8 58 X 19w 45 5

Suppose that In 5 s and In 11 t Use properties of logarithms to write the logarithm in terms of s and t In 55

Write the following expression as a sum and or difference of logarithms Express powers as factors In e x 7

Use common logarithms or natural logarithms and a calculator to evaluate the expressi log 15 17 Use the change of base property to rewrite the given expression log 17

Provide your answer below 2 0 14 0 6 DC

Given the function C n n 1 n 7 n 4 the coordinates of its C intercept are the coordinates of its n intercepts are

Convert this equation to slope intercep form 2x 3y 6

4 Which expression below is equivalent to 3 2x 4 3 x 5 a 3x 27 3x 27 c 9x 27 d 3x3

3 Which value for x below is a solution to the equation 2x 8x 20 5x a 1 b 2 C 4 d 5

What is the value of x in the equation 3 i 2 B 3 19 2 6 i 34 4 646 2x 6x 52

Convert this equation to slope inte form br 221 0

Convert this equation to slope interce form x y 8 Oy x 8 Oy x 8 Oy x 8 Oy x 8

Solve Check for any extraneous solutions x 2 4 Ono solution x 62 x 64 x 66

Write the sum of the first three terms of the binomial expansion expressing the result in simplified form 13 x 2 The sum of the first three terms of the binomial expansion is Simplify your answer

Find the indicated term of the binomial expansion 6th x y The 6th term is

K Find the sum of the first 53 terms of the arithmetic series 39 43 47 51 53

Use a system of two equations in two variables a and d to write a formula for the general term the nth term of the arithmetic sequence whose third term a3 is 15 and whose eighth term ag is 45 an

If an arithmetic series has a 5 d 1 and n 33 what is Sn S33

Find a when d 2 and ag 10 a1

3 2x X 2 A 11 0 16 x B 1 3 C 11 D 4

Determine which quadratic equation has tw non real solutions A 2x 3x 5 0 B 3x 7x 10 0 4x 8x 4 0 C D x 5x3 0

Write the radical expression for the complex number given 4 160

Select Yes or No to indicate whether each ordered pair is a point of intersection between the line y 2x 4 and the parabola y x 4x 1 Ordered Pair 3 2 1 6 0 4 Yes 2000 No

Simplify each of the following expression Write your answer as a complex number 1

Simplify each of the following expression Write your answer as a complex number Subtract 271 5 3

Which is the value of n in the equation 3n 18n 30

Solve the system of equations x y 34 3x 3y 6

6 Simplify mn 2n m n O O O O 4n 4n8m4 2m 72 no 8m

Simplify 2y 2yx 3 y 2 1 24 1 O O O O 16x8 y 5 K 4 y x 1 32x 2y 5 15 Y 18

9 g x dx such that A expresses the area of the region between the functions y V and 9 Evaluate the integral to find the area of the region Answers should be exact As a suggestion graph the equations so you can see the region for which you are solving for the area Write an integral in the form A a lower limit of integration b upper limit of integration g x Area of region A

2 Find the exact value of the following logarithmic expression logs

Find the exact value of the following logarithmic expression

Select Yes or No to indicate whether each ordered pair is a point of intersection between the line y 3x 1 and the parabola y x 4x 1 Ordered Pair 2 5 1 4 0 1 Yes No

Select Yes or No to indicate whether each ordered pair is a point of intersection between the line x y 6 and the circle y 26 x Ordered Pair 1 5 1 5 5 1 Yes 0 No