Application of derivatives Questions and Answers

Question 7 Divide and simplify 126 41i 9 4i Question Help Video Messago inc

Simplify 562 5 6i

Question 8 2 Find a formula for the exponential function passing through the points 3 27 and 1 6 y

Find the size of the permanent endowment needed to generate an annual 25 000 forever at a continuous interest rate of 5

x 2 x 7 0 Give your answer in interval notation

x 2 x 7 Try again 2 7 0 Give your answer in interval notation

TT VE vo 4x 5 3X 8 x 2 x 2 Use the piecewise function to ans Find f 2 Submit

The table shows the numbers x of absences in a school year and the final exam scores y of several students Absences X Final Exam Score y Absences 1 7 0 5 0 94 69 98 77 97 6 1 4 2 6 Final Exam 73 93 81 89 72 Score y a Use a graphing calculator to find an equation of the line of best fit Round the slope and y intercept to the nearest integer b Interpret the slope and y intercept of the line of best fit c Approximate the final exam score of a student who has 3 absences a The line of best fit is b The slope is and the y intercept is So a student with 0 absences is expected to earn a points per absence decreases by about on the final exam and the score

When a certain medical drug is administered to a patient the number of milligrams remaining in the patient s bloodstream after t hours is modeled by D t 60e 0 5t How many milligrams of the drug remain in the patient s bloodstream after 2 hours Round your answer to one decimal place mg

An investment of 6000 is deposited into an account in which interest is compounded continuously Complete the table by filling in the amounts to which the investment grows at the indicated interest rates Round your answers to the nearest cent t 6 years Rate per year 1 2 3 4 5 6 Need Help Read It Amount

Use a calculator to evaluate the function at the indicated values Round your answers to three decimals 5x g x 5 g 6 g 3 65

pts Use tra lations to sketch the graph of domain off What is the range What is the equation of the asymptote 4 6 pts Rewrite each log equation as an exponential equation a log 3x 5 b log x 2 3 c In x 4 2 5 6 pts Rewrite each exponential equation as a log equation a 2 47 b 10x 450 80 now the asymptote What is the

Simplify the following trigonometric expression as much as possible 1 cos x sin x O sin x O cos x O 2 csc x O 2 sin x sin x 1 cos x

On one ranch the farmer decided not to randomize the order of treatments and instead chose which cows received each treatment A researcher reminds the farmer that randomization helps minimize the influence of confounding variables in an experiment Which of the following could be a confounding variable in this setting Explain to the farmer how the cofounding variable could create a false perception of a relationship between markings and predator attacks if treatments are not randomized Gender of each Cow Age of each Cow Explain your thinking Size of the Number of Cows on the Farm

A twenty story hospital building with a 200 ft x 270 ft footprint is to be built on a site underlain by fill over glacial sands The building will have a 25 ft deep basement and will probably be supported on either a mat foundation located 5 ft below the bottom of the basement or a deep foundation extending about 100 ft below the bottom of the basement The groundwater table is about 30 ft below the ground surface and bedrock is about 165 ft below the ground surface There are no accessibility problems at this site a How many exploratory borings will be required as per NYC Code and to what depths should they be drilled b How would you obtain groundwater data Explain your answer

28 fx x 2 dx

s 6x 4x 6 dx Do not include the constant C in your answer For example if you found the antiderivative was 2x C you would enter 2x What is

In summarizing the results the researchers in the article state Ambush predators were less likely to kill cattle painted with artificial eyespots than unmarked and cross marked cattle The differences between the groups were statistically significant Would it be valid to claim that the painting of eyespots caused a reduction in attacks by predators Explain your choice Yes The claim is appropriate Explain your thinking No The claim is not appropriate

An object moves with velocity as given in the graph below in ft sec How far did the object travel from t 0 to t 15 velocity f sec 9 8 7 6 5 4 3 2 1 5 10 15 20 25 30 time sec feet 35 40 45 a

9 54 Evaluate the indefinite integral 2 9 fx 1 x dx 11 ft e di 13 sin t 3 dt dx 4x 7 15 Sz 17 S cos e 1 sin 0 19 cos 0 sine de 21 eu de 4 2 du 10 5 3x dx 12 f sint 1 cost dt 14 f sec 20 de 16 y 4 y dy z 18 1 5r 20 fer dr 22 dz sin 1 x dx

your answer Note When entering natural log in your answer enter lowercase LN as In There is no natural log button on the Alta keyboard Sorry that s incorrect Try again

Suppose an object moves along a straight line The graph below shows the velocity of the object from t 0 seconds to t 10 seconds S 4 3 2 Velocity 1 2 3 5 Time 2 3 4 5 6 7 8 9 10 O Determine the intervals over which the object is moving forward moving backward or is stationary Report solutions using interval notation Over what interval s if any is the object moving forward Over what interval s if any is the object moving backward Over what interval s if any is the object stationary

The velocity of a particle moving along the x axis is given by f t 4 4t cm sec Use the graph of f t to find the exact change in position of the particle from time t 0 to t 4 seconds including units Change in Position

The velocity of a car is f t 10t meters per second Use a graph of f t to find the exact distance travelled by the car in meters from t 0 to t 8 seconds Distance m

An airplane is traveling in the direction 30 west of north at 700 km hr Find the component form of the velocity of the airplane assuming that the positive x axis represents due east and the positive y axis represents due north What is the component form of the velocity of the airplane Round the final answer to one decimal place as needed

If AB i 7j 2k and B is the point 7 5 6 find A The point A is

If f x determine the antiderivative of f x Do not include the constant Cin 8 x 4 your answer Note When entering natural log in your answer enter lowercase LN as In There is no natural log button on the Alta keyboard

Let u 7 4 and v 5 3 Find the a component form and b magnitude length of the vector 8 15 u 17u 17 v 8 15 17 17 Tyne integers a VE simplified fractions

3 y x 3x 5 Find an equation of all the horizontal tan

lim X 1 5 4 3 x 3x 2x 1 1 X 1

2 3 Write an equation for a rational function with Vertical asymptotes at x 4 and x 2 x intercepts at x 6 and x 5 y intercept at 9 y Write an equation for a rational function with Vertical asymptotes at x 4 and x 2 x intercepts at x 1 and x 1 Horizontal asymptote at y 7 y Write an equation for the function graphed below 7 6 5

Write the equation for the graph below 40 y 3 7 6 Write an equation for the function graphed below 4 3 3 20 4 34 2 2 3 6 7 2 Write the equation for the graph below 10 y 10 9

1 Nyx is in the middle of a crafts project For this portion of their project they are designing stylized bird feathers They construct the feathers in the following way First they glue two concentric circles made of construction paper together a 10 diameter one made of white paper placed on top of a 12 5 diameter one made of black paper Next they cut the circles into twelve equal wedges I 12 5 10 Nyx wants to finish the feathers by adding a strip of tinsel along the border of the dark region of each feather How much tinsel will they need for one feather Write your answer below Show all work including any assumptions you make

Question 6 24x 57x 3x 6 Find the equation of the vertical asymptote and the equation of the slant asymptote of the rational function f x 1 Question Help 5 23 The equation of the vertical asymptote is x The equation of the slant asymptote is y

Find the arc length parameter along the curve from the point where t 0 by evaluating the integral s v T dt T 0 Then find the length of the indicated portion of the curve r t 8 4t i 3 7t j 9 2t k 1st 0 The arc length parameter is s t Type an exact answer using radicals as needed

A E Match each of the following graphs with the correct function by placing the letter of the graph on the line provided Each letter can only be used once Do not use a calculator or desmos to draw the graph 3 f x x 1 2 4 f x x 1 1 0 5 f x x 2x 1 6 f x x 2x 1 7 f x x 8 f x x 2x 9 f x x 2x 3 10 f x x 2x 2 2x 2 3 2 0 1 B F 1 1 2 2 1 0 2 0 1 2 2 1 1 3 x D V 2 3 1 1 1

Use Newton s method to approximate all the intersection points of the following pair of curves Some preliminary graphing or analysis may help choosing good initial approximations y 4 sin x and y 9x 7

Find the most general antiderivative of f x F x tvt vt 2t

cot 6 Select the correct choice below and if necessary fill in the answer box to complete your choice O A K 6 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression B The expression is undefined cot 42 1 0 7x 4 1 42 42 45 3x 5x 4 6 65x 2x 4x 3 K2 0 1 3x 2 0 x y 1

Determine the values of the trigonometric functions of a tan Type a simplified fraction 25

sin 5 4121 0 7650 Round to four decimal places cos 5 4121 Round to four decimal places

The conect expression is 3 Type an equation using as the

51 The complement of the angle is 39 Simplify your answer The supplement of the angle is Simplify your answer

Question 3 60 points 3 Integrate each of the given expressions a 21 3 2 5 x 5 x 7 dx b 2 1 21 1 1 dt t2 c 2 x da d z 3 4z dx

Question 1 20 points 1 Determine the value of a that makes F x an antiderivative function of the given function f x a f x 5x F x ax5 b f x 10x 4 F x ax5 4 Paragraph V BI U A A v

Question 2 20 points 2 Find antiderivatives F x of the given functions a f x 2x x b f x x x x 3 Paragraph V B I U A E E O 40 GE

Find the area of the region inside the lemniscate r 6 cos 20 and outside the circle r 3 Points will be awarded based on uploaded work 71 6 21 3 411 3 2 11 2 3m 2 11 3 5m 3 71 6 11 6 0 1

Find the length of the spiral curve 0 0 T

a Replace the polar equation 8rsine with the equivalent Cartesian equation t

a Find the tangent to the curve x t and y t 4 at the point 2 3 where t 4 b Find as a function of t for the given x and y d y dx