Calculus Questions

33 42 Composite functions and notation Let f x x 4 g x x and F x 1 x 3 Simplify or evaluate the following expressions 33 g 1 z 35 F g y 34 F y 36 f g w f 2 h f 2

Find the moment of inertia with respect to the y axis for a flat plate covering the region bounded by y 1 x The moment of inertia is approximately Round to two decimal places as needed 1 6 the x axis x 0 and x

Use integration by parts to evaluate the integral x x 4 dx x x 4 dx

For a voltage V 270 sin 100 t find the root mean square voltage for one period Vrms V

TU Find the volume generated by revolving the region bounded by y sec x x 0 x and y 0 about the x ax V Type an exact answer using as needed

Evaluate the integral S dx 2 25 x dx fx2 0 25 x

Evaluate the integral 14e7x 1dx

A mountain climber is about to haul up a 60 m length of hanging rope How much work will it take if the rope weighs 0 45 N m The amount of work required is Type an integer or a decimal J

A force of 16 N will stretch a rubber band 8 cm 0 08 m Assuming that Hooke s law applies how far will a 4 N force stretch the rubber band How much work does it take to stretch the rubber band this far How far will a 4 N force stretch the rubber band m Simplify your answer

When a particle of mass m is at x 0 it is attracted toward the origin with a force whose k magnitude is If the particle starts from rest at x b and is acted upon by no 2 X other forces find the work done on it by the time it reaches x a 0 a b Set up the integral that gives the work required Use limits of integration in increasing order dx Type exact answers

It takes 1100 J of work to stretch a spring from its natural length of 1 m to a length of 2 m Find the force constant of the spring The spring s force constant is N m Type an integer or a simplified fraction

Find the first quadrant area under the curve of y The area is units Round to three decimal places as needed 3 4 In x X from x 1 to x 5

Evaluate the integral integral 488x 3 dx 0 48e x 3 48 3x 3 dx

Integrate the given function dx 7 2x dx 17 2x 0 7 2x

Integrate the given function 5 5 1 X 18x 9x dx 1 x 18x 9x Tung an integer or a decimal Round to the nearest thousandth as nee dx

Approximate the value of the given integral by completing parts a and b below a Use Simpson s rule using n 2 b Check by direct integration 2 S 6 x dx 0 a Use Simpson s rule using n 2 2 Sco 31

After an electric power interruption the current i in a circuit is given by the equation shown below where t is the time Find the expression for the total electric charge q to pass a point in the circuit if q 0 for t 0 i 21 1 e e

Integrate the function Sco 5 cos x sin x dx 5 cos x sin x dx

Evaluate the following definite integral T 36 T 36 0 cos 6x CSC 6x cos 6x dx dx

Integrate the function 13 tan xsec xdx

Find the equation of the curve that passes through 3 4 if its slope is given by the following equation dy dx 3x 7 y x 0

Evaluate 16 16 1 4t 1 2 1 4t 1 1 2 t dt dt Simplify your answer

Evaluate the following indefinite integral 30x dx 2 3 2 30x dx

Evaluate the given definite integral 2x 6 x dx 3 3 1 3 x 6 x dx 3 Type an integer or a simplified fractic

Evaluate the following indefinite integral 120x dx 2 0 dx X

Find the area under the curve y 5x that is between the lines x 1 and x 4 The area under the curve y 5x that is between the lines x 1 and x 4 is Simplify your answer

Determine the following 12x dx 12x dx

Evaluate the following indefinite integral S 8x 7 8x 7 7 X 7 7 X dx dx

Find an antiderivative of the given function f t 6t 12 What is a possible antiderivative of the given function Select the correct choice belo 3 4 t 12t O A F t 2 OB F t 6t4 12t O C F t 6t4 12 OD F t t4 6t

Exam Type Question Big Bang Dimensional Analysis When Sheldon s barber becomes ill he complains about his hair growing at an astonishing rate of 4 6 yoctometers ym per femtosecond fs What is this in inches month Note 1 month 30 days 1 ym 10 24 m 1 in 2 54 cm exact 4

Find the length of the following curve 312 y 2x from x 0 to x 4 The length of the curve is Type an exact answer using radicals as needed

Find the length of the following curve 3 2 y 2 X y from y 7 to y 9 3 3 N W 2 1 2 y The length of the curve x 3 Tyne an exact answer using radiolo from y 7 to y 9 is

The graph of the equation x2 3 y2 3 102 3 is one of a family of curves called astroids because of their starlike appearance as shown in the accompanying figure Find the length of this particular astroid by finding the length of half the first quadrant portion y 102 3 2 3 3 2 3 2 5 2 2 x 10 and multiplying by 8 The length of the given astroid is Simplify your answer Type an exact answer using radicals as needed 10 10 10 10

y Find the length of the curve x 4 1 2 8y The length of the curve is Type an integer or a simplified fraction from y 1 to y 3

Find the length of the following curve If you have a grapher you may want to graph the curve to see what it looks like 32 y 27 9x 6 from x 3 to x 9 The length of the curve is Type an exact answer using radicals as needed

to see the correlation between test scores and homework The homework grade x and test grade y are given in the accompanying table Write the linear regression equation that represents this set of data rounding all coefficients to he nearest tenth Using this equation estimate the homework grade to the nearest integer for a student with a test grade of 38 Answer Attempt 1 out of 2 Homework Grade x Test Grade y 46 55 50 59 76 87 87 90 Copy Values for Calculator Open Statistics Calculator 55 46 74 90 80 89 12520

4 3 U9 Carbon dioxide is produced by combustion of biomass and fossilized organic matter Define combustion State the products of a combustion reaction State sources of fuel for a combustion reaction 4 3 A2 Analysis of data from air monitoring stations to explain annual fluctuations Sketch a graph of the annual fluctuation in atmospheric carbon dioxide concentration Paste here Explain the annual fluctuation in atmospheric carbon dioxide concentration in the northern hemisphere

The sum of the interior angles of a polygon with n sides is given by the formula 180 n 2 To solve for n we set up the equation 180 n 2 2340 and solve for n The correct answer is option C sides

I Y 2 1 5 Select Select Not a function Function O 2 3 2 1 5 7

When Abdoulaye commutes to work the amount of time it takes him to arrive is normally distributed with a mean of 45 minutes and a standard deviation of 5 minutes Using the empirical rule what percentage of his commutes will be between 35 and 55 minutes

Find the surface area of the rectangular prism 2 in 4 in

e table displays the scores of students on a recent exam Find the mean of the scores to the nearest 10th Score Number of Students 60 9 65 8 70 4 75 1 80 6 85 3 90 6

On a standardized exam the scores are normally distributed with a mean of 300 and a standard deviation of 40 Find the z score of a person who scored 400 on the exam

The box plot below represents some data set What is the range of the data T

Find the surface area of a square pyramid with side length 3 m and slant height 4 m 2 m m 3 m

Kayla is organizing textbooks on her bookshelf She has an English textbook a biology textbook and a history textbook How ma different ways can she line the textbooks up on her bookshelf

The graph below represents data that was collected by students on the number of social media posts they made the previous day SOCIAL MEDIA POSTS Frequency Number of Students 1 2 3 4 5 6 7 Number of Social Media Posts Made 8 9 What s the most common number of posts students in this class made

Determine the amplitude of the following graph 27 5 4 3 2 1 2 3 4 5 T 27 5 37 47

What is the volume in cubic centimeters of a cylinder with a height of 12 centimeters and a base radius of 6 centimeters to the nearest tenths place Answer Attempt 1 out of 2

Which equation represents a line which is perpendicular to the line y 2 Answer 5x 4y 28 4 5 12 4x5y 25 4x 5y 30