Calculus Questions

12 Using the disk method determine the volume of the solid obtained by rotating the region bounded by y x 4x 5 x 1 x 4 and the x axis about the x axis

3 e Bonus 1 35 x 10 14 mm to m

2 Convert the following numbers to decimal notation 2 points a 3 66 x 105 b 1 06 x 10 7

10 A spring has a natural length of 15 in A 900 lb force stretches the spring to 20 inches a b C Find the force constant How much work is done in stretching the spring from 15 in to 18 in How far beyond its natural length will a 2000 lb force stretch the spring

4 Perform the following operations Assume all numbers are measured unless otherwise indicated Give all answers in scientific notation and with the correct number of significant figures 4 points a 7 83 x 10 5 5 x 10 3 915 108 b 4 6 x 108 8 38 x 197 5 5 48 92601 431 98 102

3 For the years 1995to 2002 the number N of cellular phone subscribers in millions can be modeled by the equation N 17 4x 36 1x 83 8 where x 0 represents the year 1995 If this trend continued in what year did the number of subscribers reach or surpass 3750 million

Identify the radicand x y y 5 The radicand is

Use a calculator to approximate the square root 209 49 209 49 Round to the nearest thousa

The graph below is the function f x 5 4 3 2 1 3 2 1 2 4 5 Determine which one of the following rules for continuity is violated first at x 2 Of a is defined Olim f x exists xia Olim f x f a HIP

The graph below is the function f x 5 4 3 2 1 5 4 3 2 1 1 N 3 4 5 ON Select all statements below that you agree with Note You may be checking more than one box No partial credi Of 2 is defined lim f x exists x 2 4 5 Olim f x f 2 x 2 The function is continuous at x 2 The function is not continuous at x

Submit Answer DETAILS SCALCET9 6 1 004 3 1 Points Set up an integral for the area of the shaded region Evaluate the integral to find the area of the shaded region 10 5 5 x 4y y x y 6 y y 5 5 5

2 A small cube of palladium measures 65 36mm on each side The mass of the cube is 3 36kg Calculate the density of platinum in g cm and report your answer to the correct number of significant figures

The electric charge q in C passing a given point in a circuit is given by q t sec 0 21 t 0 60 s idq dt A Thon round to two decimal places as needed 1 where t is the time in s Find the current i in A for

The displacement d in mm of a piano wire as a function of the time t in s is given by d 2 0 sin 178t cos 178t How fast is the displacement changing when t 3 0 ms The change in displacement is mm s when t 3 0 ms Do not round until the final answer Then round to the nearest whole number as needed

Power P is the time rate of change of work W Find the equation for the power in a circuit for which W 6 sin 7t

For a certain electric circuit the current in A is given by i 1 68e 66 1t sin 194t where t is the time in s Find di dt the expression for b E m

9 Consider the following hypothetical data on the occurrence of hepatitis in two cities a Calculate the cumulative incidence of hepatitis in each city b Which city has the higher cumulative incidence City City A City B New cases Observation period 85 90 Total January December 2017 January December 2017 10 The table below displays hypothetical data of 1 year diarrheal disease risks for 1 900 adults working in daycare centers in Georgia Treat their job duties as a way of understanding their exposure Remember risk is another way of saying cumulative incidence Certified childcare providers for children ages 0 3 years exposed Office staff not exposed Disease 50 9 59 No Disease 950 891 Starting population at risk 85 000 150 000 1 841 Total 1000 900 1 900 Risk Re Risk among the exposed Ru Risk among the unexposed a What is the 1 year risk cumulative incidence of disease for the exposed per 1 000 population Hint you will not need a calculator to got

1 point Rebecca has 45 coins all nickels and dimes The total value of the coins is 3 60 How many of each type of coin does Rebecca have 13 dimes and 32 nickels 10 nickels and 35 dimes 18 nickels and 27 dimes 27 dimes and 18 nickels

1 point 5 3 is a solution to the system of equations 2a y 7 x y 2 True False

Find the general expression for the slope of a line tangent to the curve of y x 2x at the point P x y Then find the slopes for x 2 and x 0 5 Sk the curve and the tangent lines What is the general expression for the slope of a line tangent to the curve of the function y x 2x at the point P x y mtan The slope for x 2 is The slope for x 0 5 is Sketch the curve of y x 2x and the line tangent to it at x 2 Choose the correct graph below A O B O C Ay tongent to the curve of y x 2x at x 0 5 Choose the correct graph below O D G

Suppose that x and y are related by the equation 4x 3y 5 and use implicit differentiation to determine dy dx 11 dy dx

A 5 2 resistor and a variable resistor of resistance R are placed in parallel The expression for the resulting resistance R is given by R Determine the limiting value of R as R The limiting value of R is 1 Simplify your answer 5R 5 R

The energy E in J dissipated by a certain resistor after t seconds is given by E In t 1 0 5t At what time is the energy dissipated the greatest t second s

Find the derivative of the given function dR dt 8 R 4 tan 3t

Integrate the given function 5 3 dy y y Simo dy Then round to two decimal places as n

Find the area bounded by the following curves y 9 x y 0 x 1 x 2 The area is plify your answer

Suppose that x and y are related by the equation 3x 4y 2 and use implicit differentiation to determine dy dy

Integrate the given function dx 5 4x dx 5 4x

The displacement s in m of an object is given by the following function of time t in s s t 2t 4t Find the object s acceleration when t 2 When t 2 the acceleration is m s Simplify your answer

Use the shell method to find the volume of the solid generated by revolving the shaded region about the y axis The volume is Type an exact answer using as needed 6 2 y 21x 1 18

Evaluate the following indefinite integral 4x 3 3 dx 4x dx 3 3

Let s represents the displacement and let t represents the time for an object moving with rectilinear motion according to the given function Find the instantaneous velocity for the given time s 60 180t 60t t 1 5 The instantaneous velocity is Simplify your answer

What is the velocity in ft s of a sandbag 2 5 s after it is released from a hot air balloon that is stationary in the The velocity is ft s

Find the radius of gyration of a plate covering the region bounded by y 2x x 2 and the x axis with respect to the y axis R

ind the coordinates of the centroid of the region bounded by y 49x and 1 The region is covered by a thin flat plate What are the coordinates of the centroid Type an ordered pair

The electric current i in A as a function of the time t in s for a certain circuit is given by i 5t t Find the average value of the current with respect to time for the first 5 0 s The average value of the current with respect to time is Type an integer or decimal rounded to one decimal place as needed

The electric current in a microprocessor circuit is 0 370 A How many coulombs pass a given point in the circuit in 2 30 ms

b The length of arc s of a curve from x a to x b is given by the formula s a 3 2 described by the equation y 0 16x 1 dx 2 dx The cable of a bridge can be from x 0 to x 100 ft Find the length of the cable S feet Round the final answer to the nearest integer as needed Round all intermediate values to the nearest ten thousandth as needed 100 ft

A hoist mechanism raises a crate with an acceleration in m s a 1 0 25t where t is the time in seconds Find the displacement of the crate as function of time if v 0 m s and s 3 m for t 0 s The displacement of the crate is given by s Type an expression using t as the variable

The voltage across a 4 5 F capacitor in a copying machine is zero What is the voltage after 19 ms if a current of 45 mA charges the capacit The voltage at t 19 ms is V Type an integer or a decimal

What is the velocity in ft s of a sandbag 2 25 s after it is released from a hot air balloon that is stationary in the ai The velocity is ft s

Find the area bounded by the following curves 3 y x x 2 x 1 y 0 The area is Simplify your answer

59 60 Using right triangles Use a right triangle sketch to complete the following exercises 59 Suppose cos 5 13 Find sin 0 and tan 0

27 32 Graphing inverse functions Find the inverse function on the given interval if specified and graph both f and f on the same set of axes Check your work by looking for the required symmetry in the graphs 27 f x 8 4x 29 f x x 2 for x 2 30 f x 3 x for x 3 31 f x x 2 1 for x 2 32 f x x 4 for x 0 28 f x 3x 5

Parking fees Suppose that it costs 5 per minute to park at the air port with the rate dropping to 3 per minute after 9 P M Find and graph the cost function c t for values of t satisfying 0 t 120 Assume that t is the number of minutes after 8 P M

a The graph of y f x is shown Draw the graph of y f x b The graph of y g x is shown Draw the graph of y g x

The graph of fis translated a whole number of units horizontally and vertically to obtain the graph of g The function fis defined by f x x Write down the expression for g x g x 0 2 0101 X G E

Below is the graph of y x Transform it to make it the graph of y 3 x 1 4 VN X

61 Explain why or why not Determine whether the following state ments are true and give an explanation or counterexample a The range of f x 2x 38 is all real numbers b The relation y x 1 is not a function because y 2 for both x 1 and x 1 c If f x x then f 1 x 1 f x d In general f f x f x e In general f g x g f x f By definition f g x fog x g If f x is an even function then cf ax is an even function where a and c are nonzero real numbers h If f x is an odd function then f x d is an odd function where d is a nonzero real number i If f is both even and odd then f x 0 for all x 62 68 Working with diff

Verify that the indicated function is a solution of the given differential equation 1 2y y 0 y e x 2 2 y 25 y y 5 tan 5x 3 y 2xy y y y c x dP 4 P a bP P dt ac eat 1 bc eat 5 x y dx x xy dy 0 c x y xey x 6 y y y cosha sinh r 7 y 3y 3y y 0 y x e