Math - Others Questions

Verity the identity cos x cos x tan x secx Choose the sequence of steps below that verifies the identity O A O B O C cos x cos x tan x cos x tan x 1 cos x cos x tan x cos x 1 tan x cos x cos x tan x cos x 1 tan x OD cos x cos x tan x 1 tan x secx 1 sec x 1 2 sec x 1 sec x secx sec x secx sec x sec x sec x

Simplify the given expression Express the answer with positive exponents 3 x 4 1 2 3x 5 24 x 4 1 1 2 B 3 x 4 3x 5 24 x 3x 5 24 x 4 Simplify your answer Type your answer using exponential notation Use integers or fractions for any numbers in the expression

Choose the sequence of steps below that verifies the identity O A csc t 1 cott csct 1 B O C D csct 1 csct 1 csct 1 cott cott csct 1 csct 1 cott csct 1 cott csct 1 cott csct 1 csct 1 cott csct 1 csct 1 cott csct 1 cott csct 1 csct 1 csct 1 csct 1 csc t 1 cott csct 1 csc 1 1 cott csct 1 csc t 1 cott csct 1 cot t cott csct 1 cot t cott csct 1 cot t cott csct 1 cot t cott csct 1 cott csct 1 cott csc t 1 cott csct 1 cott csct 1

Solve the given equation log 5x 1 log x 2 1 X Type an integer or a decimal Round to two decimal places as needed Use a comma to separate answers as need

Use logarithms to solve the equation symbolically Inx Inx 3 X Round to the nearest thousandth

Simplify by taking roots of the numerator and denominator Assume that all expressions under the radicals represent positive numbers 81y5 5 81y 6

tan x sec x csc x cot x Choose the correct proof below A E tan x sec X CSC X sin x COS X COS X sin x cos X 1 sin x X sin x cos X 2 COS cot x X OC tan x sec xcsc x sin x COS X sin x cos X 1 sin X sin x cos x 2 COS x cot x 1 sin x OB tan x sec X CSC X sin x 1 cos X COS X 2 1 sin x sin x cos x 2 cos X sin x cos x cot x OD tan x sec xcsc x sin x COS X 1 sin X sin x cos x 2 COS X sin x cos X cot x 1 sin x

1 Solve the following equations Round your answers to 3 decimal places 10 pts ea a 9 531 441 I b 400 600 600 e 0 5x Give exact answers do not round 10 pts ea

Full Solutions be sure to show all your work 6 Write the quadratic y 2 x 3 7 written in standard form

3 The total cost for a certain business is given by C x 3000 In 20 x 10 17 000 a b Find the total cost of producing 50 units 5 pts C

The following table shows the daily cost data and demand schedule for a typical firm producing board games in a monopolistically competitive market in the short run Fill in the values in the Marginal Cost Total Revenue and Marginal Revenue columns in the following table and then answer the questions that follow Total Cost Marginal Cost Dollars Average Total Cost Dollars Quantity Price Board games Dollars per game Dollars 1 10 00 2 3 4 5 6 7 8 9 00 8 00 6 00 4 00 3 00 2 00 1 00 17 Based on your calculations the firm will 20 27 32 35 48 56 64 Under monopolistic competition a typical firm will produce Fill in the Average Total Cost column in the previous table Total Revenue Dollars board games at a price of itu in this monopolistically competitive market is Marginal Revenue Dollars A per board game in the short run

6 A restaurant is building a new addition that has a rectangular seating area with a semi circular windowed alcove as shown below SHOW YOUR WORK 10 marks 14 ft 9 in 3 45 m 2 84 m 38 ft 4 in a Find the floor area of the shape in square feet b The ceiling height will be 12 feet Find the volume of the space in cubic feet c The design requires 11 air changes per hour Calculate the total CFM needed for the space d The designed air speed in the duct work is 275 ft min Calculate the cross sectional area of the duct work needed for this air speed e If a circular duct is used to supply this air specify the diameter of the duct to be used

7 Which statements BEST describe the key features of the Law of April 6 1830 Select TWO correct answers It outlawed immigration from the United States It encouraged an influx of new American empresarios It slowed the economic development of ranching in Texas It imposed taxes on trade between foreign nations and Texas It relocated the settlers in Nacogdoches to new land near San 1 O D

9 Why is the Battle of Goliad referred to as the other Alamo O Both were brutal losses for the Texian Army Both were valiant victories for the Texian Army Both were brutal losses for the Mexican Army Both took place in the same area

Find the measure of the bigger arc 5x 10 3x 4 30

If the measure of arc QP is 76 degrees and angle 3 is 92 degrees what is the measure of arc SR P 1 3 R S

tlook 42 K D2 Homepage 23F Technology Mathemati Prove the given identity tan x sec x csc x cot x Choose the correct proof below O A tan x sec xcsc x sin x cos x sin x cos x 2 1 sin x sin x cos x cot x cos x OC tan x sec xcsc x sin x the C COS X 1 sin x 2 sin x cos x cos x sin x cos x cot x mylab pearson com Pearson MyLab and Mastering Question 7 of 10 OB tan x sec xcsc x sin x 1 1 cos x cos x sin x 1 sin x cot x are b Dat sin x cos x cos x sin x cos x P In class Quiz 2 2 1 sinx sin x cos x COS X This quiz 25 point s pos This question 3 point s OD tan x sec xcsc x sin x 1 1 cOS X sin x cos x cot x cos x sin x

s Campus smoking areas Outlook iz 2 K DZL Homepage 23F Technology Mathemati tan r r t v mylab pearson com P Pearson MyLab and Mastering Question 8 of 10 Simplify the given expression The result will be one of sin x cos x tan x cotx secx or csc x tan x cot x CSC X

Verify the following identity sin 2x 1 cos2x tan x O Which of the following three statements verifies the given equation O 2 T C sin 2x 1 cos2x sin 2x 1 cos2x sin 24 L nical 1 2 cos x 1 2 sinx cos x 1 2 sin x 1 2 cos2x 2 sinx cos x 2 sin x ng Ques 51

Prove the given identity csc 0 sin 0 cos 0 cot 0 Choose the correct proof below OA csc 0 sin 0 OB csc 0 sin 0 OC csc 0 sin 0 OD csc 0 sin 0 1 sin e 1 sin 0 1 sin 0 sin 0 1 sin e sin 0 sec 0 sin 0 sin 0 1 sin 0 1 sin 20 sin 0 1 sin 0 2 sin 0 sin 0 1 sin 0 2 sin 0 2 cos 0 sin 0 sin e cos 0 2 sin e s20 cos 2 Question cos 0 cot 0 cos 20 sin 0 cos 0 cot 0 cos 0 cot 0 cos 0 cot 0

Verify the identity cos 0 tan 0 sin 0 Which of the following four statements verifies the identity OA cos 0 tan 0 1 sin 0 OB cos 0 tan 0 cos 0 OC cos 0 tan 0 cos e sin 0 OD cos 0 tan 0 sin 0 cos 0 sin 0 cos e cos e sin e cos 0 sin e cos sin 0 sin 0 cos sin 0 cose cos sin e sin 0 cos 0 sin 0 cos e sin 0 sin 0 sin 0 sin 0

ches om wearing using such products in this building Outlook 2 K Homepage 23F Technology Mathemati 2 cos attacks respirator 1 Amylab pearson com Use a double angle formula to find the exact value of the given expression 2 8 P Pearson MyLab and Mastering Question 2 of 10 In class Qui This quiz 25 This questic 2 2 cos 1 8 Simplify your answer Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression

Prove the given identity Choose the correct proof below cos 0 cot 0 csc 0 sin 0 OA cos 0 cot 0 csc 0 cos 0 OB O C cos 8 cot 0 csc 0 cos 0 cos 8 cot 8 csc 0 cos 0 OD cos 0 cot 8 csc 0 cos 0 cos 0 sin 8 cos 0 sin 8 cos e sin 0 cos 0 sin 0 1 sin 8 1 sin 0 sec 0 1 sin 0 1 sin 0 sin 8 cos 0 1 cos 0 1 sin 8 cos 0 1 sin 0 Question 3 of 10 cos 0 1 sin 0 sin 0 sin 8 sin 8 sin 0 sin 0 sin 0 sin 0 sin 20 sin 8 sin 8 sin 8 sin 8

Verify the identity csct 1 cott OB Choose the sequence of steps below that verifies the identity O A O C O D csct 1 csct 1 csct 1 cott cott csct 1 csct 1 cott cott csct 1 csct 1 cott csct 1 cott csct 1 cott csct 1 csct 1 cott csct 1 csct 1 csct 1 csc t 1 csct 1 cott csct 1 csct 1 cott csct 1 csc t 1 cott csct 1 csc t 1 cott csct 1 Question 10 of 10 cot t cott csct 1 cot t cott csct 1 cot t cott csct 1 csc t 1 cot t cott csct 1 cott csct 1 cott csct 1 cott csct 1 cott csct 1 cott csct 1 cott csct 1

Prove the given identity sec xcsc x sin xsec x cos x csc x Choose the correct proof below OA sec xcsc x sin xsec x 1 cos x sin x sin x cos x 1 sin X sin x cos x cos x cos xcsc x 1 COS X sin x OC sec xcsc x sin xsec x 1 1 cos x sin x sin x cos x 1 sin x sin x cos x 2 COS X cos X CSC X Question 8 of 10 O B sec xcsc x sin xsec x 1 1 This quiz 25 This questia cos x sin x 1 sin 2 sin x cos x 2 COS X X sin x cos x cos x csc x OD sec xcsc x sin xsec x 1 1 sin x cos x sin x 1 sin x sin x cos x cos 2x sin x cos x cos xcsc X 1 COS

Find the exact value of 1 2 sin x cos x 2 sin x cos 2x Question 9 a 1 2 sin x cos x 2 sin 4x cos 2x Simplify your answer

Verify the identity tan 0 cos 0 sin 0 Which of the following four statements verifies the identity A tan 8 cos 0 cos 0 sin 0 OB tan 8 cos 0 sin 0 OC tan 8 cos 8 OD tan 0 cos 8 sin 8 cos sin 8 cos cos 0 sin 0 sin 0 cos 0 cos sin 0 sin 9 cos 0 sin sin 0 0 sin 8 cos 0 cos 0 sin 0 cos cos 9 0 sin 9 sin 8 sin 8 sin 8

Use a double angle formula to find the exact value of the given expression 2 3 2 cos Question 6 of 10 H This question 2 cos Simplify your answer Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression

Simplify the given expression The result will be one of sin x cos x tan x cotx sec x or csc x cos x sec x tan x cos x sec x tan x Question 5 of 10

Factor and simplify csc x csc x sec 2 X Choose the correct simplification below D A tan x sec x B 1 C sin x sin 2 X

Activity 7 Mathematical Induction Part 2 Solve the following problems 1 Expand the following sums 10 a 3 b i 3 5 i 5 ST 2i i 2 NI c 1 1 Pre Calculus

10 Give the general solution to the Cauchy Euler equation 4x y 16xy 9y 0

4 10 Suppose that the third order homogeneous linear differential equation ay by cy dy 0 has solutions y ex y2 e2x and y3 ex Is S y Y2 Y3 a fundamental solution set for the differential equation Answer yes or no and justify your answer

5 20 Give the general solutions to the following equations a y 5y 6y 0

10 Use the method of separation of variables find the general explicit solution to the differential equation dy 5 ln x dx xy

3 10 Is the differential equation 2 e y dx 2 y dy 0 exact Answer yes or no and justify your answer DO NOT SOLVE THE DIFFERENTIAL EQUATION

2 15 Find the solution to the initial value problem dy 2 esin x cos x y y 0 t by finding an appropriate integrating factor No credit for any other method dx

Assign 1 point If x 2 0 4 and 7 5 find tan 0 where is the angle between 7 and w tan 0

Assignment 10 Problem 3 1 point A triangle is defined by the points A 7 7 9 B 10 4 5 and C 3 k 9 The area of the triangle is 16390 Determine the value of k k 0 or k 0 this problem

1 point 4 Calculate the cross product assuming that u xw 3 4 w 0 00 3u 2w x w

1 point Let P 0 0 0 Q 1 1 1 R 2 1 1 Find the area of the triangle PQR area Let T 2 4 4 U 2 7 2 V 8 9 7 Find the area of the triangle TUV area

Assignment 10 Problem 1 1 point Find the area of the parallelogram with vertices A 1 1 4 B 0 3 9 C 1 0 7 and D 2 2 12 Area 0

1 point Find the area of the triangle with vertices 0 0 0 1 2 5 and 1 3 3

Prove the given identity sec x csc X sin xsec X cos XCSC X Choose the correct proof below OA sec xcsc x sin xsec x 1 COS X sin x 2 1 sin x sin x cos x 2 COS X sin x cos x cos X CSC X OC sec xcsc x sin xsec x sin x cOS X sin x cos x 2 1 sin x sin x cos x 2 COS X cos x CSC X Question 10 of 10 D OB sec xcsc x sin xsec x 1 This quiz 25 poll This question 3 COS X sin x 1 sin X sin x cos x cos x sin x cos x cos xcsc x K sin x OD sec xcsc x sin x sec x 1 1 cos x sin x sin x cos x 1 sin x sin x cos x 2 COS x COS XCSC X sin x 1 COS X 1 cos x

Prove the given identity sec x csc X sin x sec x cos XCSC X Choose the correct proof below OA sec xcsc x sin xsec x 1 cos x sin x 2 1 sinx sin x cos x COS2 X sin x cos x cos X CSC X OC sec xcsc x sin xsec x 1 COS X sin x sin x cos x 2 1 sin x sin x cos x 2 COS X cos X CSC X Question 10 of 10 OB sec xcsc x sin xsec x 1 sin x cos X sin x sin X This quiz 25 This question sin x cos x 2 COS X sin x cos x cos XCSC X OD sec xcsc x sin xsec x 1 COS X sin x sin x cos x 1 sin X sin x cos x 2 COS X cos X CSC X 1 sin x cos 1 cos x

3 Find the exact value of 2 sin x cos x 2 sinx cos x sin 2x Questio 2 sin x cos x 2 sin x cos x sin 2x Simplify your answer

Prove the given identity csc 0 1 CSC 0 Choose the correct proof below OA osc 0 OB csc 0 OC csc 0 cos 0 cot 0 OD csc 0 1 csc 0 1 csc 1 csc 0 1 csc 0 sin 0 sin 0 sin sin 0 sin 0 1 sin 0 sin 0 sec 0 sin 0 1 sin 0 in 0 sin 0 1 sin 0 sin 0 1 sin 0 sin 0 cos 0 sin 0 cos sin 0 sin 0 cos 0 sin 0 cos 0 cos Ocot O cos Ocot O cos Ocot 0 cos Ocot 0

Verify the identity sec 0 sin 0 tan 0 Which of the following four statements verifies the identity OA sec 0 sin 0 1 cos 0 OC sec 0 sin 0 cos 0 OD sec 0 sin 0 OB sec 0 sin 0 sin 0 sec 0 sec 0 cos 0 sin 0 cos 0 sin 0 sin 0 cos 0 cos 0 sin 0 cos 0 sin 0 sin 0 cos 0 tan 0 tan 0 tan 0 tan 0

Verify the identity csct 1 cott OB Choose the sequence of steps below that verifies the identity O A csct 1 csct 1 csct 1 csc 1 1 cott csct 1 cott cott csct 1 O C O D cott csct 1 csct 1 cott csct 1 cott csct 1 cott csct 1 cott csct 1 cott csct 1 cott csct 1 csc 1 1 csct 1 cott csct 1 cott csct 1 csct 1 csct 1 csct 1 csct 1 csc 1 1 cott csct 1 csc 1 1 cott csct 1 BE cot t cott csct 1 cot t cott csct 1 cot t cott csct 1 cott csct 1 cott csct 1 cott cot t cott csct 1 csct 1 cott csct 1

Question 3 of 10 Simplify the given expression The result will be one of sin x cos x tan x cotx secx or csc X tan x cot x sin x tan x cot x sin x