Application of derivatives Questions and Answers

Consider the following piecewise defined function if x 4 if 4 x 4 3 4 if x 24 Step 2 of 3 Evaluate this function at x 4 Write the exact answer Do not round If the answer is undefined write Und as your answer Answer 2 Points f x 2 x 2 f 4 Ke Keyboard She

Consider the following piecewise defined function ifx 4 if 4 x 4 2 1 4 if x 24 Step 1 of 3 Evaluate this function at x 6 Write the exact answer Do not round If the answer is undefined write Und as your answer Answer 2 Points Keypad Keyboard Shortcut

What type of polar curve is the polar equation 7 4 cos 29 O cardiod lemniscate

Given the vector u defined by the points 2 7 5 10 Step 1 of 2 Find the component form of the vector Assume the first point is the initial point and the second point is the terminal point Answer 6

What is the period of the trigonometric equation f 1 3 cos z 2 Enter your answer as a simplified fraction in the box

tan 1 sin cos Enter your answer as a simplified fraction in the b What is the exact value of cos tan 1 co COS

What angles are coterminal to an angle measuring 7 and 4 Drag the choices into the boxes to correctly complete the table Coterminal with Coterminal

individually 2 The sum and difference identities can be used to find the exact value of trig functions whose ratios we 54 memorized like cos 75

Determine the equation of the tangent to the curve y 1 x 1 which passes through the point 1 1 2

Does the rock cycle always follow a certain path In other words is it a one way process

Find the equation of the following ellipse Express your answer in standard form 8 4 Enable Zoom Pan 4 4 8 XA

Find the area of the region between the curves a f x x and g x x 4

10 Find the average velocity the function for the given interval Then find the instantaneous velocity at the time given Assume time t is in seconds and position s t is in meters a s t t 3t 2 Avg 0 3 Inst at t 2

A volleyball was hit into the air at a speed of 31 miles per hour at an angle of 35 from the horizontal Express this velocity in vector form Round your answer to four decimals Answer Keypad Kowboard Shortcuts

Statistics show that the fractional part of a pair of flashlight batteries P that is still good after t hours of use is given by P 4 0 021 What fractional part of the batteries is still operating after 50 hours of use Express your answer as a fraction or as a decimal rounded to six decimal places AnswerHow to enter your answer opens in new window 2 Points of the batteries Keypac Keyboard Shortcu

and the x coordinates of the absolute extremum points if any of f x cos x sin x on the interval 2

Velocity 7 given 7 0 2 sin 7 27 2 cost Answer format a b c Check Answer Save Find att 3 4 Answer format Enter a number Check Answer Save Acceleration a t mm Answer format a b c Step By Step Example 2 cost 2 2 sin f Find a 2 cos fi 2 sin k Step By Step Example f find a 1 Congratulations your answer is correct and saved Check Answer Save Step By Step Example Live Help Live Help Live Help ONG 12

Let F e cosy i e siny be a vector field determine whether is conservative if Fis conservative then find the potential function To show that F Pi Qi is a conservative field we need to show that Answer format Enter the value X OP 20 dy dx Find OP

x y xy 2x 64 y 0 Show Transcribed Text

4 A rectangular storage container with a square base and an open top is to have a volume of 36 cubic meters Material for the base costs 8 dollars per square meter Material for the sides costs 3 dollars per square meter Find the dimensions for the cheapest such container 15 points

3h where h Distance to the horizon can be approximated by the function D h represents the height of the observer above the earth in feet and D represents distance to the horizon in miles Write your answers using complete sentences Round answers to two decimal places as needed a Determine the distance to the horizon from the top of your car estimate 5 feet the top of a 100 foot building and the top of an 8000 foot mountain b If the horizon is 50 miles away determine the height observer above the car

b The graph of L t given below represents the drip rate in liters per day of a pipe tha is leaking in a house Assuming 25 liters of water had already leaked from the pipe how many liters are lost in a week Provide evidence to support your solution

17 A hot air balloon rises vertically as a rope attached to the base of the balloon is released at a rate of 5 feet per second The pulley that releases the rope is 20 feet from the platform where passengers board At what rate is the balloon rising when 500 feet of rose has been played out 20

Simplify the expressions given Use exact values Hint Using the change base formula might make these problems quite easy log 27 log 27 logg

16 A 5 000 gallon tank which holds water will drain in 40 minutes The volume remaining aft minutes is given by the formula below v t 5 000 1 t a Find 20 5 Write a sentence interpreting the meaning of your answer 20 5 b Find v 30 Write a sentence interpreting the meaning of your answer

12 A local apple farmer needs to enclose a 10 acre 435 600 square feet rectangular plot of land with fencing to keep out ATVs and snowmobiles The land borders a deep relatively straight ditch so fencing is only needed on 3 sides If the cost of the fencing is 5 per foot find the minimum cost

8 8 8 10 Suppose f f x dx 16 ff x dx 24 and g x dx 3 5 3 5 Calculate the value of the definite integrals that follow Clearly illustrate each step 8 a f g x 6 f x dx 5

List all the rules that we need to use to find the derivative of f x x sin x

Consider the following Venn diagram A Q

For each of the following sequences find tn and t5 a 2 14 98 686 b 160 80 40 20 c 7 21 63 189 Enter your responses in the space provided Be sure to include a b and c in your responses to indicate the answer for each For the too proce F10 RC

The general term of a sequence is tn n 5 a Find the first 3 terms of the sequence b Identify if this sequence is an arithmetic one a geometric one or neither Type your responses in the space provided

8 At the same time Tom and Alice measured the angle of elevation to the moon while standing exactly 300 km apart The angle of elevation to the moon for Tom was 49 8974 and the angle of elevation to the moon for Alice was 49 9312 To the nearest 1000 km how far was the moon from the Earth when the measurement was observed 7 pts 49 8974 Tom 300 km 49 9312 Alice Moon

7 Determine the remaining sides and angles for the given triangle 7 pts Shainb 2 20 C 5 b

3 Graph f x 3x3x The 2 3 is an exponent on the x Compute the first derivative Make a sign chart as demonstrated in lecture to indicate the intervals of increase and decrease Find any local maximum and minimum values b Compute the second derivative Make a sign chart as demonstrated in lecture to indicate the intervals of concavity Find any inflection points c Sketch a neat and accurate graph using your sign charts from parts a and b Use graph paper or a ruler to make axes Be sure to mark the scale on the axes Neatness and accuracy count for points

N 4 A model used for the yield Y of a crop as a function of soil nitrogen level N is Y 1 9N where N 0 What nitrogen level gives the maximum yield and what nitrogen level gives the minimum yield Remember that not all critical numbers give max mins Your work must clearly show how you know where the absolute max and absolute min occur

1 The temperature T of a patient at time t is modeled by T t 2 os t 98 6 Find the instantaneous rate of change of the temperature at any time t

3 Air is being pumped into a balloon at a rate of r t 6t grams per minute How much air is pumped into the balloon during the time from time t 2 to time t 4

5 Find dy dx using implicit differentiation 2x x y y 2

2 Find the derivative of f x e x In 4x

nd the sum S of the first 40 terms of the arithmetic sequence 4 10 16 22

Let A 3 5 B 2 1 and C 1 4 Find the component form of the vector 2C Select one O a 1 2 O b 2 8 c 4 2 O d 6 10 Find the magnitude of the vector 3A Select one O a 24 O b 306

In how many ways can a group of five nurses be chosen from a hospital nurses advisory board consisting of 15 members Select one O a 3 O b 360 360 O c 3003 O d 1 09x 1010

A jar contains 6 blue balls and 4 yellow balls If 2 balls are drawn without replacement what is the probability that neither ball is yellow Select one O a 2 3 O b 1 5 O c 11 45 O d 1 3 A

What is the area of this figure 3 mi 6 mi r 6 mi 7 mi 5 mi 3 mi Write your answer using decimals if necessary 4 square miles

pute the volume of the solid whose base is the region in the first quadrant bounded by y 5 y 1 and the y axis and whose cross sections perpendicular to the x axis are squares 16 15 V

3 10 points A particle moves on a straight line with velocity v t 9 t m sec Find the total distance travelled by the particle over the time interval 0 t 4 Please express your final answer as a single number not a sum or difference of numbers

5 10 points Compute the following definite integral 1 S t 1 In t You can write the answer in a simplified form or up to 3 decimal places dt

6 10 points Using integration by parts calculate the following indefinite integral xsin sin 2x dx

Damon is saving up money for a down payment on a condominium He currently has 5094 but knows he can get a loan at a lower interest rate if he can put down 6038 If he invests the 5094 in an account that earns 4 9 annually compounded quarterly how long will it take Damon to accumulate the 6038 Round your answer to two decimal places if necessary Answer Keyp

ind the general solution given that y e satisfies the complementary equation Use c and c fo he two constants xy 4x 1 2x 1 y 3x e