Calculus Questions

Solve sin 5x cos 8x cos 5x sin 8x 0 8 for the smallest positive solution X Give your answer accurate to two decimal places

Simplify the lefthandside so that LHS sin a sin a 1 cos a 1 cos a RHS 2 tan a

2 2TT in terms of sin x and cos x 3 Rewrite cos x

Write the sum as a product cos 18 7v cos 11 7v Note coefficients inside of the trigonometric functions should be entered as simplified decimal value do not enter fractions inside of the trig functions else they will be marked incorrect by the system F 11 example if your answer is enter 5 5 instead of 11 2

Rewrite sin x 5T 6 in terms of sin x and cos x

Write the product as a sum or difference 18 cos 14r cos 12r

Simplify sin t cos t cos t sin t 2 sin 2t csc t to a single trig function

Use the spinner shown It is equally probable that the pointer will land on any one of the regions If the pointer lands on a borderline spin again If the pointer is spun twice find the probability that it will land on a color other than yellow for each spin 2 4 Type an integer or a simplified fraction Find the probability that the spinner will land on a color other than yellow for each spin green red yellow blue blue yellow red green

Which of the following is equivalent to tan x 2 Select the correct answer below O tan x O tan x 1 O tan x 1 1 tan x 1 tan x O 1 tan x 1 tan x 1 tan x tan x

Simplify the following expression Select the correct answer below O tan tan a tan a tan 01 tan a tan p O 1 tan a tan tan a tan B 1 sin a b cos a cos p

1 point Solve y sin x if y 0 0 and y 0 3 y x help formulas

Simplify the following expression using the sum and difference identities 5 Cos 7 COS Select the correct answer below cos 3 O sin 3 COS 11 O sin 1 4 O sin 4 COS COS sin 5 57 sin 7

a Set up an integral for solving y x y x dy x x when y 4 10 dx t b Evaluate your answer to the previous part to find y x help formulas

Previ 1 point A spaceship is traveling directly away from earth with speed 412 4 km s At time t 0 s it is 500 km from earth How far is it from earth on minute after time t 0 s Include units in your answer Distance help units

You are given that tan A and tan B 2 Find tan A B Give your answer as a fraction

dy 1 point Find a solution to dx xy 9x 5y 45 If necessary use k to denote an arbitrary constant help equations

You are given that sin A 7 with A in Quadrant II and cos B 3 with B in Quadrant I Find sin A B Give your 17 answer as a fraction

x 3 y 0 east one of the answers above is NOT correct the questions remains unanswered point Solve the differential equation dy X dx 9y a Find an implicit solution and put your answer in the following form x 2 2 9y 2 2 constant help formulas b Find the equation of the solution through the point x y 3 1 x 3y help equations N x 3y 0 of the colution through the point x y 0 7 Your answer should be of the form y f x correc incorre

1 Cars arrive at a one bay car wash facility where the interarrival time is exponential with mean of 10 minutes Arriving cars line up in a single line It takes between 10 and 15 minutes uniformly distributed to wash a car Assume first arrival occurs at time 0 T 0 and system is empty initially Simulate the system for first 7 customers and calculate the following performance measures a What is the average queue length 20p b What is server utilization 20p c What is the average time that a customer waits in the queue 20p X Ln R Table 1 Random numbers x 9 a 6 a R Random Numbers for Interarrival times Random Numbers for Service times 0 3397 0 1351 0 2677 0 8762 0 9912 0 8176 0 2236 0 8422 0 8820 0 8471 0 4249 0 9113 0 9387 0 3456 2 Using multiplicative congruential method generate 10 random numbers for following input parameters 20p

A population is modeled by the differential equation dP P 1 5P 1 4500 dt a For what values of P is the population increasing Enter your answer in interval notation PE b For what values of P is the population decreasing Enter your answer in interval notation PE c What are the equilibrium solutions Enter your answers as a comma separated list P

a For what values of r does the function y e satisfy the differential equation 5y 34y 7y 0 Enter your answers as a comma separated list r b If r and r are the values of r that you found in part a show that every member of the family of functions y ae 1 be 2 is also a solution Let 1 be the larger value and r be the smaller value We need to show that every member of the family of functions y ae 1 be 2 is a solution of the differential equation 5y 34y 7y 0 We must decide whether 5f x 34f x 7f x 0 for f x ae 1X be 2x Substitute your values for r and r into f x then find f x and f x We have f x and f x Substituting and combining like terms we get the following C De x Therefore f x ae1 be 2 is a solution to the differential equation 5y 34y 7y 0 5f x 34f x 7f x

Solve the differential equation t sec 0 8 de dt Bet

You are given that cos A your answer as a fraction 13 with A in Quadrant III and sin B 13 with B in Quadrant I Find sin A B Give

You are given that cos A with A in Quadrant II and sin B 2 with B in Quadrant II Find cos A B Give your answer as a fraction

The population of deer in a forest can be modeled with the sinusoidal function p 6000cos 1 51000 where t is the number of years after 1976 To the nearest whole number what was the population in the year 1994 NOTE The angle is in radians Provide your answer below

You are given that sin A with A in Quadrant IV and sin B with B in Quadrant III Find cos A B Give 13 your answer as a fraction Provide your appr

The equation p 5000cos t 54000 describes the number of deer in a forest where t is the number of years af 1972 What was the population in the year 1991 to the nearest whole number NOTE The angle is in radians Provide your answer below

19 2sin t 8 where t is the The temperature in a room of a nearby library can be modeled with the equation T number of hours past midnight Marie measures the temperature when t 22 To the nearest degree what does she find NOTE The angle is in radians Provide your answer below

Question You are given that cos A 3 with A in Quadrant I and sin B answer as a fraction answer below 2 with B in Quadrant I Find sin A 1

Question You are given that sin A with A in Quadrant I and sin B with B in Quadrant IV Find sin A B Give your answer as a fraction aquer below

y 3 cos 2 Drag the black dot to shift your graph in the desired direction Use the blue draggable dot to change the period Drag the orange dot to change the amplitude and or reflect with respect to the x axis The horizontal distance between the vertical dotted green lines corresponds to one period Provide your answer below 2TT 6 5 4 3 2 0 2 0 1 0 13 2 2 4TT 6TT 8TT 10TT

You are given that tan A 4 and tan B 7 Find tan A B Give your answer as a fraction

You are given that cos A with A in Quadrant II and sin B 13 your answer as a fraction with B in Quadrant II Find cos A B Give

Provide your answer below Drag either of the movable red points to set the asymptotes for one period of the given function Also place the blue point at the correct set of coordinates You may click on a point to verify its coordinates 21T 31 2 IT T2 6 3 2 6 1 1 2 2 tan x IT y 2 tan 311 2 2m

Considering only the values of for which sec B 1 cos 1 cos B is defined which of the following expressions is equivalent to see 1 cos B 1 cos Select the correct answer below 1 sec tan cos B sec sin tan

Graph the following function y sin 1 Drag the black dot to shift your graph in the desired direction Use the blue draggable dot to change the period Drag the orange dot to change the amplitude and or reflect with respect to the x axis The horizontal distance between the vertica dotted green lines corresponds to one period Note reference the sinusoidal function A sin Bx C D Provide your answer below 211 41 3 2 2 2 1 0 0 2 0 TT

Considering only the values of a for which 1 sec a tan a Select the correct answer below O sin a sec a tan a tan a 1 sec atan a is defined which of the following expressions is equivalent to

Which of the following is equivalent to for all values of a for which Select the correct answer below see a tan a sec atan a sce a 1 sin a is defined

Considering only the values of 0 for which cos 0 sec 0 1 is defined which of the following expressions is equivalent to cos 0 sec 0 1 Select the correct answer below sec 0 sin Otan 0 sin 0 sin 0 FEEDRACK MORE INSTRUCTION SUBMIT

Which of the following is equivalent to csc 0 sec 0 1 sec 0 1 for all values of 0 for which csc 0 sec 0 1 sec 0 1 is defined Select the correct answer below Otan 0 Osec 0 O cot 0

Considering only the values of 0 for which I cos 0 is defined which of the following expressions is equivalent to I cos 07 Cos 0 Select the correct answer below cos sin 0 sin Otan 0

Which expression is equivalent to Select the correct answer below O cot B O cos B sec O tan 01 cos B sin B 1 cos B for all values of B for which sin 1 cos B is defined FEEDBACK MORE IN

Considering only the values of a for which the expression is defined which of the following is equivalent to the expression below Select the correct answer below cot a cse a sec a cos a csc a sec a cos C cot a cos a tan a cse a cot a

Given that csc 0 5 and 0 is in Quadrant IV what is tan 0 Write your answer in exact form Do not round Provide your answer below

Given that tan 0 and 0 is in Quadrant II what is cos 0 Write your answer in exact form Do not round Provide your answer below

raph the following function Drag the black dot to shift your graph in the desired direction Use the blue draggable dot to change the period Drag the orange dot to change the amplitude and or reflect with respect to the x axis The horizontal distance between the vertica dotted green lines corresponds to one period Provide your answer below 6 5 4 3 2 2 1 0 0 y 3 sin 2x in 2x 2 2 TT 2n 0 21 3TT

Write the following function in terms of its cofunction Make sure to include the degree symbol in your answer csc 20

A Use an indirect proof to prove the following GIVEN A ABC is not isosceles ADB CDB 6 PROVE AD DC D B C

onsider the given function and the given interval f x x 6 5 8 a Find the average value fave of fon the given interval fave b Find c such that fave f c C C c Sketch the graph of f and a rectangle whose area is the same as the area under the graph of f f x f x 4 3 smaller value larger value 2 2

The graph shows the function y h t 1 5 4 3 2 1 X 1 2 3 4 5 a I We define a new function r x h t dt 0 2 Complete the table of values for the function r 1 5 r x te