Algebra Questions

If csc x 4 for 90 x 180 then sin 2 2 COS cos 2 2 tan 2

12 Given the function f x x2 1 where n is a Natural number using calculus methods determine the intervals of concavity Show all work for full marks

0 10 pts 399 Details Write an expression of the type A log x B or A log x B for the transformed logarithmic function shown below 5 4 3 2 1 6 5 4 3 2 1 1 2 3 A 5 6 1 2 3 4 5 6 f x Hint Use the vertical asymptote to find B To solve for A use a point on the graph and substitute the coordinates into y A log x B or y A log x B as appropriate

Oil leaked from a tank at a rate of r t liters per hour The rate decreased as time passed and values of the rate at two hour time intervals are shown in the table t h 0 2 4 6 8 10 r t L h 8 9 7 5 6 9 6 2 5 7 5 3 Find lower and upper estimates for the total amount of oil in liters that leaked from the tank over the interval 0 10 Use five equal subintervals lower estimate upper estimate

dare Using a national random sample from the NEXT Generation Health Study researchers compared alcohol and drug impaired driving between high school seniors with those one year post high school The sample included 2407 high school seniors and 2178 subjects one year post high school All sub jects in the study completed a questionnaire that in cluded several questions related to recent alcohol and drug use with the following table reporting the inci dence of several of these behaviors for the two groups Binge drinking refers to at least four for females or five for males drinks within two hours 23 Explain why it is not correct to use a chi square test on this table to compare the high school seniors and post high school graduate groups Alcohol drinking at least once last 30 days Binge drinking at least once last 30 days Used marijuana at least once last year Used illicit drugs other than marijuana at least once last year High School Post High School Seniors Graduates 787 402 583 157 1044 583 654 162

Click here to watch the video Given that cos 1 A 5 5 and 0 x 2 determine the exact value of cos a cos 2 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Ratic

V Suppose that the functions g and h are defined for all real numbers x as follows g x 3x 3 h x 6x Write the expressions for g h x and g h x and evaluate g h 2 g h x g h x 8 h 2 X 3

1 point Find an equation for the plane that contains the line 1 Plane equation in general form X Y Z 5 4t 6 t 4 4t and is perpendicular to the plane 5x y 5z 40

A ngle B measures 17 and BC has length 10 find Angle C in degrees The length of AB 18 17

f AC has length 13 9 and BC has length 16 1 find The length of AB The measure of angle B in degrees The measure of angle C in degrees 13 9 A 16 1 B

If AC has length 4 and BC has length 15 find The length of AB The measure of angle B in degrees The measure of angle C in degrees 4 A 15 B

A AB has length 13 9 and BC has length 19 9 find The length of AC The measure of angle B in degrees cor 19 9 13 9 B

If AB has length 9 3 and AC has length 16 3 find The length of BC The measure of angle B in degrees The measure of angle C in degrees 16 3 A 9 3 B

If AB has length 5 and BC has length 14 find The length of AC The measure of angle B in degrees The measure of angle C in degrees A 14 5 B

Test Question 17 of 20 Find the sum of the first 9 terms of the geometric series 4 12 36 The sum of the first 9 terms of the geometric series is Simplify your answer

11 f AB has length 11 and AC has length 11 find The length of BC The measure of angle B in degrees A 11 B

Find the following sum if it exists 4 16 64 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The sum is Type an integer or a simplified fraction OB The sum does not exist

Find the nth or general term for the geometric sequence 6 6 6 6 Which represents the nth term OA 6 n 1 OB 6 1 OC 6 1 OD 6 1 1

Test Find the 18th term of the arithmetic sequence 4 9 14 19 The 18th term is Ques

A B C 4 List the intervals for each section of the function and state whether it is inci decreasing or constant Label them A E starting from left to right on the graph D Distance km 70 60 50 40 30 20 10 0 09 00 10 00 11 00 2 00 13 00 The 14 00

Find the sum of the first 21 terms of the arithmetic series 48 54 60 66 21

Test OA 5n 100 Write a formula for the general term the nth term of the arithmetic sequence a a2 a3 a4 5 0 5 10 B 5n 10 90 C 5n 10 110 O D 5n 100 Question 9

Find the first term and the common difference 5 8 11 14 a 11 d

Find the first 4 terms a10 and a15 of the sequence with the following nth term an 2n 1 a 1 Simplify your answer a2 3 Simplify your answer a3 5 Simplify your answer Simplify your answer Simplify your answer Simplify your answer a4 a10 a15

Find the first 4 terms of the recursively defined sequence 1 a 5 an 1 1 an a2 Simplify your answer Type an integer a fraction or a mixed number a3 Simplify your answer Type an integer a fraction or a mixed number a4 Simplify your answer Type an integer a fraction or a mixed number

omework Question 8 8 5 35 Write the sum of the first three terms of the binomial expansion expressing the result in simplified form 13 The sum of the first three terms of the binomial expansion is Simplify your answer HW x

A ZA LB ZC b 43 33 C degrees C a b C 15 PO B

Homewor Find the indicated term of the binomial expansion 13th c 3 14 What is the 13th term Simplify your answer Question 7 12

Previous Problem BC Use the Pythagorean Theorem to determine the length of the hypotenuse Give the value for each trigonometric ratio using exact form Do not use decimal approximations sin B cos B tan B sec B csc B cot B Problem List 5 A 1 B Next Problem

Find the indicated term of the binomial expansion 7th x y 10 The 7th term is

Without using a calculator state the exact value of the following trig functions for the specified angle 53 0 a sin b sin c sin 27 0 3 d sin e sin f sin g sin h sin 4T 3 5T 3 7T 3 4 3 5T 3 2 23T

Without using a calculator state the exact value of the following trig functions for the specified angle a cos b cos 2 0 c cos 3 d cos T 3 e cos T 0 f cos 3 g cos h cos 4 3 5 3

Without using a calculator state the exact value of the following trig functions for the specified angle T a tan 3 2 b tan 3 4T 3 0 C tan d tan 5 e tan f tan 3 g tan 3 5T 3 h tan

2 27x6 35x 8 0

Exponential Growth and Decay Exponential growth and decay problems follow the model given by the equation A t Pert The model is a function of time t A t is the amount we have after time t P is the initial amount because for t 0 notice how A 0 Pe t Pe P r is the growth or decay rate It is positive for growth and negative for decay Growth and decay problems can deal with money interest compounded continuously bacteria growth radioactive decay population growth etc So A t can represent any of these depending on the problem Practice The growth of a certain bacteria population can be modeled by the function A t 350e0 0796 where A t is the number of bacteria and t represents the time in minutes a What is the initial number of bacteria 6 How long will it take for the number of bacteria to double round to the nearest whole number of bacteria b What is the number of bacteria after 20 minutes round to the nearest whole number of bacteria your answer must be acc

Given a right triangle with tan 0 1 sin 0 2 cos 0 3 sec 0 4 csc 0 5 cot 0 5 7 determine the value of the other trigonometric ratios of 0 Use exact notation not decimal approximations If you need to write a number such as 3 type out sqrt 3

The population of Brazil can be modeled by the function P t 247 1 0 0151 where P t measures the population in millions and t represents the number of years since 2000 1 Using this model what was the population of Brazil in 2014 2 Predict the population of Brazil in 2026 3 If this growth rate continues in what year will the population of Brazil rongill

ng the triangle A C ZA ZB ZC 67 B b degrees degrees a a b C 9 7 C

A ZA LB LC b degrees a degrees degrees 5 b 6 c 9

The angle of elevation to the top of the Empire State Building in New York is found to be 11 degrees from the ground at a distance of 1 mile from the base of the building Using this information find the height of the Empire State Building Your answer is feet

18 s 0 n 0 ec 0 sc 0 cot 0 6 1 10 18 d 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 6 1

hot air balloon is floating above a straight road To calculate their height above the ground the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon The angles of depression are found to be 16 and 19 How high in feet is the ballon

D redit 8 How high can you go using s 2 4 1 1 7 4 2 3 2 1 32 2741 24 2 2 3 7 4 3 4 4 5 7 4 2 5 6 4 2 6 7 7 8 4x2 8 D 9 7 2 9 10 11 7 4 11 12 7 2 17 14 2 12 13 7 4 2 11 2 13 14 7 4 2 28 2 14 15 2x4 7 8 7 15 16 42 16 7x2 4 14 4 10 17 24 7 17 18 72 4 18 19 41 7 2 24 7 17 2 19 20 4 21 22 41 2 24 2 22 23 27 4 23 24 7x4 2 28 2 24 25 7 4 49 24 25 26 41 2 24 2 26 27 27 28 7x4 28 72 49 74 2401 42 16 27 128 47 16384 2 4 4 14 2 47 74 42 42 312 29 24 42 27 72 7 5040 4 24 21 2 16384 128 2401 49 149 7

You approach a hill on top of which there is a tall radio antenna You know from your map that your horizontal distance from the bottom of the radio antenna is 600 feet The angle of elevation to the bottom of the antenna is 10 and the angle of elevation to the top of the antenna is 25 You figur that the height of the hill is feet and the height of the antenna is feet Enter your answers rounded to the nearest foot Hint Draw a picture Figure out the height of the hill Figure out the combined height of the antenna and the hill Compute the difference

A plane is flying at an elevation of 21000 feet It is within sight of the airport and the pilot finds that the angle of depression to the airport is 26 Find the distance between the plane and the airport Find the distance between a point on the ground directly below the plane and the airport

A 20 ft ladder leans against a building so that the angle between the ground and the ladder is 72 degrees How high does the ladder reach on the building Your answer is feet

18 0 0 4 3 d 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 4 3

Show Transcribed Text 2 so Calculate the angle delta theta using cosine law The triangle to be considered is A BC Given that A C 23 98 A B 40 91 RC 221

Rewrite the following logarithms in expanded form by applying the properties of logarithms a log ry b log H Y c log x

First determine the quadrant for 0 then find x y and r and finally give all six trigonometric ratios for given the following information tan 0 and sin 0 0 e lives in quadrant I K 11 11 1 sin 0 2 cos 0 3 tan 0 4 sec 0 5 csc 0 6 cot 0