Mathematics Questions and Answers July 08, 2020

Plot the complex number 1 2i 5 4 3 2 1 3 24 7 2 3 4 5 Clear All Draw Dot 1 2 3 4 15

Question 8 Given f x Domain 1 x 4 V and g x 16 x 3 find the domain of f g x

The length of the curve defined by the equation cy f x 16 from x a to x b is given by L f f x dx wher

You are given that cos A your answer as a fraction 13 with A in Quadrant III and sin B 13 with B in Quadrant I Find sin A B Give

Find k such that the function is a probability density function over the given interval. Then write the probability density function.f(x)=k, [6,9]k= (Type an exact answer.)The probability density function is f(x) = (Type an exact answer.)...

*(d)r cos(x)drHint: Rewrite the integrand as rr cos(x). Now experiment as to what to set u and duequal to. Do not use online resources!

Evaluate the integral using the following values L x dx x3 dx 1020 8 L 11 dx 8 8 x dx 30 dx 6

H Find the length of the curve corresponding to r t 2t e e over the interval 0 t 1 Note the first component is 2t not 2t integor

Consider the function f x whose second derivative is f x 5x 4 sin x If f 0 2 and f 0 4 what is f x f x

7 Find the number of cm3 in 2 0 2 54 cm 1 00 in 11

7. Find the number of cm3 in 2. (2.54 cm 1.00 in I

Find f s if we know that s 12s s 1 2 3 and C

Find f (s) if we know that and f I

1 Evaluate fx cos x dx os x dx as an infinite series

1. Evaluate f as an infinite series.

aluez 2 Pedz dz avec u avec une erreur inf rieure 10 2

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin Foci 7 0 major axis of length 18

K Evaluate the following integral Sx 6 x 6x x

Evaluate the integral.

10pts Section 16 2 Evaluate J Laye x y 2 Include a sketch of the region of integration in your solution xy dA where R is the region bounded by the lines y x y 2x and

1 point Fill in the following table of values for X I x 0 0 5 f 1 d I x 1 1 5 2

8 Convert from general form to standard form for 2x 2y 16x 8y 10 0 x 4 2 2 1 a 15 15 b x 2 y 4 1 15 15 C x 4 y 2 d 30 30 x 2 y 4 30 30 1 1 I

(Coding) In this problem we will find the exponential of best fit (y = c1ec2t) through the points(1, 2), (2, 2), (3, 7), (4, 10), (5. 17).(a) Find the vector of equations r and the Jacobian Dr.(b) Determine (with justification) some initial guess x0

If y = cos x, how many periodswill there be between-5T and 9??[?]

If y cos x, how many periods will there be between 5T and 97T

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

Evaluate the following indefinite integral. 3 30x dx o

Let f t be the temperature of a cup of coffee t minutes after it has been poured Interpret f 5 190 and f 5 8 Estimate the temperature of the coffee after 5 minutes and 36 seconds that is after 5 6 minutes What does f 5 190 imply EXOD OA 190 minutes after the coffee has been poured the temperature of the cup of coffee is rising at a rate of 5

The following is the graph of a function f x 5 4 3 2 1 Clear All Draw 4 3 2 1 1 2 3 4 5 7 21 3 4 a On the same axes sketch a graph of the inverse function f x b Use the graph of the inverse to evaluate f 2

Hint try the substitution u x O A arcsin x C OB B arcsin u C c arcsin x C O C D x arcsin x C O E 2 arcsin z C

Find the area of the shaded region below Area y y x 2 y 1 x 1 x 2 X

Evaluate f x y z dV for the function f and region W specified 12 x y dV f x y z 12 x y W y z x 0 y x 0 x 1

Evaluate the definite integral 0 Sy4 5y5 6 dy 1 0 y sy 6 dy Simplify your answer Type an exac 2

Evaluate the difference quotient for the given function Rationalize the numerator and simplify your answer f x f 1 x 1 f x x 4

Find the remaining sides of a 45 45 90 triangle if 49 The shorter sides are each 1 51 The shorter sides are each 4 53 The longest side is 8 2 55 The longest side is 4 50 The shorter sides are each 5 52 The shorter sides are each 54 The longest side is 5V 2 56 The longest side is 12

K A 30 m long chain hangs vertically from a cylinder attached to a winch Assume there is no friction in the system and that the chain has a density of 6 kg m Use 9 8 m s for the acceleration due to gravity a How much work is required to wind the entire chain onto the cylinder using the winch b How much work is required to wind the chain onto the

y MuetsUGNAREmpt 1 of 3 10 11 00 12 13 the murder of Alexander Litvinenko a Russian dissident was though The half life of 210 Po is 138 4 yr If 0 8 mg of 210Po is present in a sam the function for the given values of I and interpret the meaning in co 38 4 76 8

Solve the given equation for x 52x6 32 X Basic Funcs Trig

Solve the given equation for c. 32 asic Funcs Trig

Reverse the order of integration for the integral Then evaluate the integral with the order reversed 4 16 S S 0 4x 1 y dy dx 11 0 4x dx dy 2 1 y

Let the region R be the area enclosed by the function f x ln x and 1 Find the volume of the when the region Ris g x x solid generated 6 You may use a calculator and round to the nearest thousandth revolved about the line y A 2 i I 1 14 12 10 8 10 6 4 2 y I 1 3 I 4 I 5 16 1 7 1 I i 1 8 9 10 X

Find the flux of F 3x 2zj 3yk out of the closed cone x i y 2 with 0 x 1 flux

Show that the integral is independent of path and evaluate r 2 2 In 3 Ja 1 1 In 3 ez dx 3y dy 2xe z dz

Question 5 20 points 5 Find the moment of inertia in terms of its mass of a right circular cone of radius r and height h with respect to its axis h Axis

1 Use Simpson s rule with m n 2 to estimate f f x y2 dy dx

I. Use Simpsons rule with m 2 to estimate JK (2 V 2) dy du.

4 Find a parametrization for the curve The line through the points 3 3 and 5 1

4. Vind a parametrization for the curve The line through the points ond (5,

The graphs of two functions f and g are given below 2 7 3 1 2 f Evaluate each limit if the limit does not exist say why a lim f x g x b lim f x g x c lim f x g x d lim f x g x 3 2 g x x 1 f x h lim e lim f x g x f lim g x g lim f x cos x 4 0 2 14 2 2

Using the Midpoint Rule In Exercises 13 18 use the Midpoint Rule with n 4 to approximate the area of the region bounded by the graph of f and the x axis over the interval Sketch the region See Examples 2 and 3 Function 13 f x 2x Interval 1 3

3 16 points Find the volume of revolution resulting from the region bounded by x y 2 and y x being revolved around the x axis Use the shell 3x y 2 0 method

If you know that f x f x f x and that f 9 9 while f 7 9e then 7 2 f x f x dx

2 In x 2 4 2 X X 1 dx

Calculate the definite integral. 7e dx

Given a b c 0 use Green s theorem find the area of the region D given by ax by c

1 2 Find the area of the shaded region 2 1 YA y 5x r2 y x 4 4 X

41 For the function f whose graph is shown list the following quantities in increasing order from smallest to largest and explain your reasoning A fo f x dx B f f x dx C f f x dx D f x dx E f 1 YA 2 0 5 x

te S x y z dS where S is the part of the cone 2 x y that lies between the planes Evaluate z 1 and z 4

Calculate the definite integral 2 2 S 7 0 7e5x 7 5x dx C

Calculate the definite integral. 7e dx

Question Given that a particle travels according to the velocity function v t 4t 8 m sec what is the total distanced traveled by the particle over the time interval 0 7 Enter your answer as an exact fraction if necessary and do not include units in your answer Provide your answer below I

A box company makes a variety of boxes all with volume given by the formula x 12x 45x 50 If the height is given by x 5 what is the formula for the area of the base 1 Keyp

A point on a line and its slope are given Find the point slope form of the equation of the line P 4 1 m 0 The point slope form of the equation of the line is Do not simplify Use integers or fractions for any numbers in the equation

Find two unit vectors orthogonal to both (9, 8, 1) and (-1, 1, 0).(smaller i-value)____(larger i-value) ___

Find two unit vectors orthogonal to both (9, 8, I) and (1, 1, O). (smaller ivalue) (larger ivalue)

Evaluate the integral using an appropriate substitution x x8 5 dx C

Evaluate the integral using an appropriate substitution.

Use the given triangle to evaluate the expression If necessary express the value without a square root in the denominator by rationalizing the denominator 4 COS COS R 4 T COS COS 4 4 2 450 459 Simplify your answer Type an exact answer using radicals as needed Use integers or fractions for any numb the expression Rationalize all denominators

1 It is important to note that not all functions will have an inverse function Since the inverse f z takes an output of f and returns an input of f in order for f to itself be a function then each output of f input to f must correspond to exactly one input of f output of f in order for f to be a function You might recall that this is the

Find the indefinite integral f 2x 9 x 9x 12 5 dx 02 x 9x 12 5 C 26 O O 25 x 9x x 9x 12 6 c 21 x 9x 12 26 0

R is the region bounded by the functions f(x) = 1 - 2cos(x) and g(x) = 4sin(x). Find the area of the region bounded by the functions on the interval [0, ?/2].Enter an exact answer.Provide your answer below:A = ________units^2.

(a) Evaluate the following indefinite integrals. Show complete working. In particular: if you use substitution, write down the substitution that you used. Show the full working needed to make that substitution. Write your final answer in terms of a. if you use partial fraction decomposition, show the complete working that is needed to find

xin x3 A In In x3 C B In x C in 0 D in inx 3

B)tnx3C C)4nx3C

Compute ?c F .dr where F(x, y) = (-y, x) and C is the counterclockwise oriented unit circle.

5. (19 points) Compute Jc P dFwhere F (x, y) (y3,x3) and C is the counterclockwise oriented unit circle.

We also must make a substitution for the limits of integration in the definite integral Since x sec 8 we note that when x 2 0 then a 1 Step 2 We have determined that if we let x sec 0 then dx sec 8 tan 8 de on the interval sec 4 sec 0 tan 0 1 3 tan 0 Step 3 So far we have the following rsec 4 sec 8 tan 8 tan 0 dx 1 x x 173 2 1500 Jn 3 To evaluate

1 Fill in the missing statements for the following two column proof Given C is the midpoint of AD Prove x 2 Statements 1 C is the midpoint of AD 2 AC CD 3 AC CD 4 9x 5x 8 5 6 x 2 Statements 1 C is the midpoint of AD Reasons A 1 a 9x 1 a 2 b 3 4 c 5 d Subtraction property of 6 e Reasons C segments have equal Definition of mic Transitive prope

3 Compute the value of the iterated integral 1 f dxf dye

3. Compute the value of the iterated integral dye

T 9 Use the comparison theorem for improper integrals to prove that 2 points cos x x7 dx converges

Use the comparison theorem for improper integrals to prove that 9. 1 (2 points) cos x I (lx converges. 7

Find f Use C for the constant of the first antiderivative and D for the constant of the second antiderivative f x 25 6

mutations to solve udent activity club at the college has 22 members In how many different ways can the president a treasurer and a secretary ute values into the formula for Pr

Compute? ? ? z(x + y2) d V, where E is a solid that lies within the cone z = -r +6 (in the cylindrical coordinates),below the plane z = 6/2and above the plane z = 0 when A = 6.

Express 4 58585858586 as a rational number in the form P 9 where p and q are positive integers with no common factors and a n

46 A steady wind blows a kite due west The kite s height above ground from horizontal position z 0 to 50 Find the distance traveled by the kite z 80 ft is given by y 150 40

Consider the function y 4 sin 2x x Give exact answers using fractions and multiples of Determine the following information a Amplitude 4 b Period T c Phase shift Direction Left Number of units enter a positive number using fractions and multiples of d The point 0 0 transformed into e The point 1 transformed into f Graph the function 57 8 2 37 8 7

14 58 four red cars and three gray ctures on the graph to show as they counted Blue Gray comparison symbol or 3 69 3 Colors of Cars 29 10 18 would use to measure how much water is in a b easuring cup balance

44 Describe the graph of the equation 8 80 A a circle of radius 1 with center at the point 1 80 B a line passing through the pole making an angle of 80 with the polar axis OC a circle of radius 99 with center at the pole D a line perpendicular to the polar axis passing through the point 1 80

2This figure shows segments of the graphs of y =2??daO?10dx?f ?10dx10So ?dx3These line segments are congruent; their lengths are equal.Which TWO integral expressions can be used to calculate the length of the line segments?3x and y =3x and y = x.

If cos 0 sin 0 1 and is in the 4th quadrant find the exact value for sin 0 5

Replace the polar equation with an equivalent Cartesian equation 1 2 cos 0 3 sin e O 2y 3x 1 2x 3y 1 1 2x 3y 0 1 1

Graph of a function y f x is shown Evaluate 2 S 4 f x dx Show your solution co y f x 2 1 3 2 0 1 2 3 Selected Answer None Given Response Feedback None Given 3 4 E

An object travels through two dimensional space in accordance with the parametric curve r t 1 1 2 where time t is measured in seconds and distance is measured in meters a Sketch the trajectory of the object Then give a description in plain English of how the object travels along this trajectory Include in your description information about the

Use these rental pricing data to answer the questions below City 2009 Rent 2015 Rent Boise 583 745 Boston 1 577 2 150 Seattle 958 1 600 What is the rate of change of rent with respect to time for Boise Round to the nearest penny a specify units in the question below Answer What are the proper units for this rate of change years per dollar years

Question Find the total distance traveled by a particle according to the velocity function v t 4t 4 m sec over the time interval 0 4 Enter your answer as an exact fraction if necessary and do not include units in your answer Provide your answer below

Use partial fractions to find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)?1/x-4 dx

For the demand equation express the total revenue R as a function of the price p per item q 10p 1000 R P Sketch the graph of the resulting function C No Solution Help 20 90000 80000 70000 60000 60000 40000 30000 20000 10000 20 1000 4 40 60 80 120 140 160 180 200 220 240 260 280 100 120 Ch Fill WebAssign Graphing Tool Graph Layers After you add an

Evaluate the integral sinx from 0 to pi/2 by 1) using trapezoidal rule 2) Simpson rule Using 11 ordinates. Also estimate the errors by finding the value of the integral

Why must integration be used to find the work required to pump water out of a tank OA Integration is necessary because the acceleration of gravity changes at each level B Integration is necessary because W mgy O C Water from the same horizontal planes is lifted different distances D Different volumes of water are moved different distances

O A e 3 C Fe O B e C OC 255 22 C O D e 3 C O E Fe C

domain 4 4 that satisfies the hypotheses of the Mean Value Theorem and the conclusion of the Mean Value Theorem at and x 2 graph x 3 M5b Sketch the graph of a function on domain 4 4 that fails at least one of the hypotheses of the Mean Value Theorem resulting in a graph that does not satisfy the conclusion of the Mean Value Theorem

2 3 4 5 6 7 8 19 20 21 A E b For each of the following functions use your work in a to help you determine the general antiderivative of the function Recall that the general antiderivative of a function includes C to reflect the entire family of functions that share the same derivative Label each antiderivative by name e g the antiderivative of m

where b is a real constant Use Desmos to graph this function with a slider for b Guiding Questions 1 What do you notice about how the slope of the function changes with b What does this tell us about how addition or subtraction of constants impact the behavior of functions How does this related to the graph transformations you reviewed in week 1

12 Find the volume of the solid generated by rotating the region bounded by y sin x and y 0 between 0 and about the x axis

Social animals that live in groups can spend less time scanning for predators than solitary individuals However they waste time fighting with the other group members over the available food There is some group size at which the net benefit is greatest because the animals spend least time on these unproductive activities and thus can spend time on

Find the area of the region bounded by the curves 3 y sin x y csc x x 4 and x You get O A 2 2 OB 2 2 O c 2 2 OD 2 2 OE 2 2

K Graph the equation using the x an x 2y 4

Graph the equation using the x a x 2y

Find the volume of the region D bounded above by the spher x y z 360 and below by the paraboloid 2z x y

4 Find a formula for the exponential function passing through the points 2 and and 2 36 y Question Help Video Message instructor

Find the center of mass of the solid S bounded by the paraboloid z 3x 3y and the plane z 11 Assume the density is constant Hint Think about the shape before calculating you can greatly reduce the number of calculations to be

he region is formed by the graphs of y 3 x and y 4 x Find the volume of the solid obtained by revolving the region about the x axis The volume of the solid obtained by revolving the region about the x axis is PREURE

Find the average value of f x on the interval 3 6

Find the average value of f(r) on the intetval 13, 61.

Does the inverse relation represent a function If yes list the ordered pairs of th f 1 1 9 9 2 7 7 2

Question 8 Instructor created question suming that b is positive solve the following equation for b 30 3x 10 dx 16 Round your final answer to 4 decimal places Give the positive answer only

Watch the video that describes determining the equation for graph Click here to watch the video The function graphed to the right is of the form ya tan bx or y a cot bx for some a 0 b 0 Determine the equation of the function Half and quarter points are identified by dots