Application of derivatives Questions and Answers

4 Select the correct choice below and if necessary fill in the answer box within your choice O A The square root is a real number 4 OB The square root is not a real number

A large waterfall is managed so that a minimum of 130 000 cubic feet of water per second ft sec flow over the falls Find the minimum amount of water that will flow over the falls in a 24 hour period durin tourist season Write your answer in scientific notation www A minimum of cubic feet of water flow over the falls in a 24 hour period Use scientific notation Use the multiplication symbol in the math palette as needed

The distance from a planet to its moon is approximately 249 000 mi If a spacecraft travels at a speed how many hours would the spacecraft need to travel from the planet to the moon Use distance rate x time The spacecraft would need Type an integer or a decimal hours to travel from the planet to the moon

In June 2010 the population of a large country was about 308 5 million people about 6 960 billion people Determine the ratio of the country s population to the world s population by the country s population by the world s population Write your answer as a decimal number and round to the nearest thousandth The ratio of the country s population to the world s population is Type an integer or a decimal rounded to the nearest thousandth as needed

45 678 9 10 11 12 13 14 15 Without using a calculator indicate between which two adjacent ruler marks the following irrational number will fa 68 in The number 68 falls between Simplify your answers and on the ruler

6 5 4 3 2 1 90 1 y 7 659 5 126 t 2 3 4 5 6 7 1 2 4 Write an equation for the function graphed above

Express the number in decimal notation 8 21 10 21 1 10

L T X a L T system defined by the following table Answer parts a through g T X Q Q T Q L T X L T Q X Q L T XLT XO 2000 BUCH Now determine the inverse element of Q Select the correct choice below and if necessary fill in the answer box to complete your choice The inverse element that corresponds to Q is T B Q has no inverse element d Evaluate the following expression T L L T Evaluate the following expression T LOL L e Does the associative property hold for the system Yes No Clear all

Show that the point is on the unit circle 2 1 7 4 We need to show that the point satisfies the equation of the unit circle that is x2 y 1 x y 3 4 9 19 1 Hence the point is Need Help Read It 7 x 1 6 on the unit circle

Perform the indicated op 210 000 0 0007 210 000 0 0007 3 0 x 108 Use scientific notation Use the multiplication symbol in the math palette as needed

Perform the indicated operation Express the answer in 210 000 0 0007 210 000 0 0007 Use scientific notation Use the multiplication symbol in the math palette as needed

Perform the indicated operation Express the answer in scientific 0 00004 0 0000024 0 00004 0 0000024 9 6 x 10 11 Use scientific notation Use the multiplication symbol in the math palette as needed

30 000 2 300 calculator and express the answer in scientific notation The answer is Use scientific notation Use the multiplication symbol in the math palette as needed

Find the formula for a function of the form w x points between these two points w x Check your result by making a plot not submitted A sin Bx C with i a maximum at 0 5 1 ii a minimum at 1 5 5 and iii no critica

Express the number in decimal form without exponents 2 3 104

Consider the mathematical system defined by the following L G M L M L NG M L GM L IZ N a Is the system closed No Yes NMING N L G L NGM N b Is there an identity element in the set If so what is it Select the correct choice below and if necessary fill in answer box to complete your choice OA There is an identity element It is OB There is no identity element

Consider the function B x x 1 x on 0 x 1 with a b 0 Absolute Maximum value Hint Your answer may depend on a and or b

Let f x x 6x 1 Fill in the values or intervals below If there is nothing applicable for a given category enter NONE For use infinity For use infinity To indicate a union of intervals use U interval s on which f is increasing interval s on which f is decreasing x coordinates of all local maxima x coordinates of local minima interval s on which f is concave up interval s on which f is concave down Use your results as recorded above to sketch the graph of f Check by making a plot not submitted

Consider the function w x 2x 15x 144x 10 on the interval 8 x 4 On the given interval this function has absolute minimum at the point maximum at the point Enter the coordinates of points as ordered pairs with parentheses

A graphing calculator is recommended A rectangular beam is to be cut from a cylindrical log of diameter d 30 cm The figures show different ways this can be done depth a Express the cross sectional area of the beam as a function of the angle 8 in the figures A 8 b Graph the function you found in part a A 6 800 600 400 200 O width A 8 800 0 5 1 0 1 5 0 A 8 30 25 20 15 10 5 A 6 800 0 5 1 0 1 5 U

Find the area of the shaded region in the figure Round your answer to two decimal places 120 6

Determine f x 1 for the following function Answer 2 Points f x x 3 3

In the following exercises compute each indefinite integral e x 320 2x dx

Consider the following function Answer 2 Points Step 3 of 3 Identify the correct graph of this piecewise defined function 4 87 ak 3 x5 Enable Zoom Pan o A 5 Enable Zoom Pan if x 1 if x 1 7 Enable Zoom O 8 Enable Zoom

Eify the correct graph of the following piecewise defined function ver 2 Points 4 4 3 2x O X Enable Zoom Pan Enable Zoom Pan if x 3 if x 3 4 41 Enable Zoom Pan lo 4 a Enable Zoom Pan KA

Step 2 of 2 Find two points on the line to graph the function Answer 2 Points Any lines or curves will be drawn once all required points are plotted A B 10 5 5 Enable Zoom Pan 19 10 Key

Consider the following function a x x 11 6 3x Step 1 of 2 Find the slope and the y intercept Express the intercept as an ordered pair Simplify your answer Answer 2 Points Slope y intercept

Find the minimum or maximum value of the function f x 10x x 7 Give your answer as a fraction

1 3 7 3 Graph of y f x 2 A graph of f x x is shown The numbers shown represent the geometric area of the regions above 0 1 and 1 2 Evaluate the following definite integrals a b C 22 22x dx numbers z 0 4 2 x 6 dx 6 x 4 dx help 6 d x 4 6 dx

h the blank with the appropriate word ng generalizations or predictions fro

ll in the blank with an appropriate word or phrase sample that consists of a random selection of groups or units is sample that consists of a random selection of groups or units i

Identify y a pair of corresponding angles in the diagram Nar

utions and Use the frequency distribution to co through e a Determine the total number of o b Determine the width of each cla c Determine the midpoint of the s d Determine the modal class or c e Determine the class limits of the additional class were to be added

Given the function f x 2x 6x 18x 4 determine the intervals where the function is increasing and decreasing and the intervals of concavity Write the intervals using inequalities f x is increasing for f x is decreasing for f x is concave up for f x is concave down for

Find the discriminant a x 4xy 10y 2y 5 0 b x 4xy 3x 25y 6 0 c 9x 6xy y 7x 5y 0 d xy 3y 4x 2y 8 0 I a b C d

Determine the eccentricity type of conic and directrix r 5 7 14 sin 0 The eccentricity is

Qu ve the equation Give a general formula for all the solutions List

Designing a Flashlight Mirror The mirror of a flash light is a paraboloid of revolution Its diameter is 6 cm and its depth is 2 cm How far from the vertex should the filament of the lightbulb be placed for the flashlight to have its beam run parallel to the axis of its mirror 6 cm 2 cm

Question 15 Part 1 of e equation Give a general formula for all the solutions List six solutions 2 e

Question 14 8 Part 1 of 2 ation Give a general formula for all the solutions List six solutions

4 a At a price of 58 per ticket a musical theatre group can fill every seat in the theatre which has a capacity of 1500 For every additional dollar charged the number of people buying the ticket decreases by 75 Use calculus to find what ticket price maximizes revenue Be sure to check your second order condition a concert was N P3 2P where N is the attendance and P is the price Now suppose that price is b Suppose that the number of people coming dependent on the cost of putting the concert together P 5 C where C is the cost Find dN dC by the chain rule please note that this question is separate froth part a

gure to evaluate the function given that g

solutions of the following equation 3x 2 2 0

exact values of the following expressions 7t 6 20 3 and sin

2 COS exact value of tan 2 cos

he figure to evaluate the function given th 2x

Question 3 of 15 1 point Graph the polar equation r 6 cos 0 Part 0 2 Part 1 of 2 Attempt 2 of Unlimited View Plot six points satisfying the polar equation r

Which point do all conics of the form x 4py have in common Select one O a 1 1 O b 0 1 O c 1 1 O d 0 0 O e 1 0

o is the initial height D Question 4 2 pts A soccer ball is kicked across a field at an angle of 60 with an initial speed of 69 ft s Determine when the soccer ball reached its maximum height

x x 2 and k 3 which of the following represents a vertical shift