Mathematics Questions and Answers September 24, 2019

How is A right-tailed hypothesis test is a statistical method that uses a greater than symbol to indicate an inequality. For instance, a small business owner might find that their purse price should be more than $50, as the right side is greater than the left

Use the percent formula, Upper A equals PB: A is P percent of B, to answer the following question. What is 5 % of 800? Question content area bottom Part 1 5 % of 800 is enter your response here

Here is a codebook to help you understand what each variable represents. GENDER*: 0 = Male 1 = Female AGE: Ranges between 18 and 45 and represents actual age MARITAL STATUS: 1 = Single 2 = Married 3 = Other FINANCIAL STATUS: 1 = Overextended 2 = Making ends meet 3 = Comfortable PHYSICAL HEALTH: 1 = Poor 2 = Fair 3 = Good 4 = Very good 5 =

For X Normal(, 225), and P (X 50) = 0.9871, find

in a class of 20 students there are 8 men and 12 women four students are selected to present a demonstration on the us eof graphing calculations find the probality that the group consits of all women round your answer to five decimal places

5163What type of setting is most appropriate for the students in Mrs. Chang's class who are receiving basic Tier I instruction on new information

10. I have the results of 1,500 glucose samples. I randomly select 40 of the samples, and the sample mean glucose level has a distribution that is skewed to the right. According to the Central Limit Theorem, if I continue to calculate the mean glucose levels of 40 random samples 100 times, what will the distribution of the sample means look like?

Question: (15 points) Use the direct method of standardization to compute the crude mortality rate and age-adjusted mortality rate for North Carolina in 2000. Use the U.S. population (also in table) as your standardizing population. Age (years) NC population NC deaths NC Age-specific rate (per 10,000) US population US expected deaths per age group

8. Let lim f(x) = 16 and lim g(x) = 42. Use the limit rules to find each limit. a) lim If(x)+g(x)] b) lim If (x) . g(x)] c) lim f(x) -g(x) 2f(x)

Triple Integration A region is bounded by a parabolic cylinder x = y, and the planes x + z = 1 and z =0. Let the density of this region is uniform. Determine the center of mass of this region

Question 1. Let f be a differentiable function in the xy-plane, (x0, y0) be a point in the xy-plane and P be the tangent plane to the graph of f at (x0, y0). Which of the following statements are always true?Question 2. Let f be a differentiable function in the xy-plane, (x0, y0) be a point in the xy-plane. Which of the following statements are

An artifact originally had 16 grams of carbon-14 present. The decay model A = 16 0:002" describes the amount of carbon-14 present after t years. Use the model to determine how many grams of carbon-14 will be present in 6223 years. The amount of carbon-14 present in 6223 years will be approximately grams. (Round to the nearest whole number.)

V2 Limits Introduction 2.1 A Preview of Calculus 2.2 The Limit of a Function 2.3 The Limit Laws 2.4 Continuity 2.5 The Precise Definition of a Limit ' Chapter Review D 3 Derivatives b 4 Applications of Derivatives In the following exercises, use direct substitution to evaluate each limit. 88. lim (4x2 1) xrZ 90. 11me2xx2 x>2

Find the length of the curve r (t) - (3 cos(2t), 3 sin(2t), 2t) for -4

Find the length of the curve F(t) (3 cos(2t), 3 sin(2t), 2t) for 4 t Give your answer to two decimal places

Use the pair of functions to find f (g (x) ) and g (f (@)). Simplify your answers. f (I) = c-3 : 9 (3) = + +3 f (g (I)) = 9 (f (I)) =

5) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Section 2.4., # 6) Give a parameterization (a) for the graph of f (ac) = a2 (b) for the ellipse given by + 25 = 1 6) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Section 4.1., # 20) Show that, at a local maximum or minimum of ||r(t) ||, the vector r (t) is

13. [-/1 Points] DETAILS TANAPCALC10 3.2.004. Find the derivative of the function. F( x ) - (5x + 6)(6x - 7) Fi ( X ) : Need Help? Read It 14. [-/3 Points] DETAILS TANAPCALC10 3.2.004.EP. Consider the following functions. 9 (x) - 4x + 5 h (x ) = 5x - 6 F( x ) - (4x + 5) (5x - 6) Find the derivative of each function. g '( x ) = 1' ( x ) f' ( x ) =

Can someone help me with these questions: Question 1: Find the exact area of the surface obtained by rotating the curve about the x-axia. y=x3, x3 E Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V6 -X, 45x56Find the exact area of the surface obtained by rotating the curve about the x-axis. V = V 1tex,

Consider the function : A(x) = -9x (3x - 5)(x + 5)3 The zero/root corresponding to x is: x = The multiplicity of this zero/root is: This multiplicity is -- |so the graph of f(x) the x - axis. The zero/root corresponding to (3x - 5) is: x = The multiplicity of this zero/root is: This multiplicity is odd v so the graph of f(x) -- the x - axis. The

15) If z 2x2y 31 where 1 12 2rs and y 2r 45, then by means of the chain rule, (a) find g (b) evaluate when r 1 and s O. as 15)

Find all local maximum and minimum values of the function whose graph is shown. local maximum (0,2) at x = 2 X local minimum (-2,-1) at x = -2 (smaller x-value) local minimum (2,0) at x = 0 X (larger x-value) 0

Evaluate the integral by making the given substitution. x2 x3 + 39 dx, u = x3 + 39 + C

Can you please answer this question for my exam prep!! Thank you so much!! 4. Sketch y = 2 cos(x-45) +1 for one cycle. 45 90 135 180 225 270 315 360 405 450 495 540 585 630 675 720 13 5. The diameter of a car's tire is 54 cm. While the car is being driven, the tire picks up a nail. a) Model (find an equation) for the height of the nail above the

lnfectious diseases. such as influenza' can spread according to the autonomous differential equation % : BI (N I) .u,I. I denotes the number of infected people' Ndenotes the total size of the population being modeled' ,6 is a raterofrtransmission constant. and p. is the recovery rate from infection (20m Find all equilibria if B : 0.01, N : 1000,

7. Suppose f(x) = 241 and g(I) = Find f(g(x)) and g(f(r)) Simplify. 1 - I What is the relationship between f(x) and g(x)? Explain

I need the formula please A rm produces 500 units of a good which cost an average of ti 10 each to produce and sells the at a price of ti 15. What is its prot? When the price of a product is lowered from tl 150 to II 100 quantity demanded increases frc 500 to 750 units. Calculate the elasticity of demand over this section of its demand schedule.

solve the two following questions: 1. Calculate the integrals shown below 2. Evaluate the integrals below using the Right Endpoint Reimann sum a) 5 1x 2 - 4 x/dx -3 b) s ( 1 7 + 1 ) ( x - 1) dx 5 (272 +2- 3) da 4 - 2

Will give a thumbs up for correct answers. Thanks! 18. Let POR be a triangle in which M is the midpoint of PO and N is the midpoint of PR. If PM = a and PN = b, find vector expressions for MN and OR in terms of a and b. What conclusions can be drawn about MN and OR? Explain. P N M R

Please help. Many engineering applications of differential calculus involve second derivatives. For example. Newton's second law Fzma can be written in the form where "r" represents position and "a" represents acceleration. But what if the position cannot be expressed as a polynomial, exponential. logarithmic. or trigonometric function? For

1. When the " a" value is a fraction between 0 and 1, then the graph is compressed. y = a ( x h ) 2 + k False True 2. Given the equation y = a ( x p ) 2 + q what does the " a" represent? 3. Without graphing, identify the key features of the given function. -vertex -axis of symmetry -direction of opening -number of x-intercepts

Write an iterated integral of a continuous function f over the region R shown in the figure. + 15 10- y= 2 x 5 - R X . . Write an iterated integral of a continuous function f. f(x,y) dx dy\fEvaluate the following integral, where R is bounded by x = 3, y = 3x + 6, and y = - x - 2. dA R SS 12 dA = (Simplify your answer.) RReverse the order of

Find the exact area between the graphs of f(x) =2-x and g(x) =x

Find the exact area between the graphs of f(x) 2 x and g(x) x.

2. Compute derivatives of implicit functions. e.g. Use implicit differentiation to find Oz/Ox and Oz/dy where z = f(x, y) is implicitly defined by x3 ty' + 2' + 6xyz +4=0. 3. Find tangent planes and linear approximations. e.g. Find the tangent plane to the elliptic paraboloid z = 2x2 + y at (1, 1, 3). e.g. Find the linearization of f(x, y) = xery

A force in Newtons represented by the vector [3, 4, 4] results in a displacement, in metres, represented by the vector [13, 2, 7]. The work done, in Joules, is: C 80 O 8.94 8.66 O 75

The derivative of a function f(x) is defined by f' (x) = lim h-0 Now consider the function f(x) = By definition of the derivative, we have: x2 + 17 f' (x) = lim h -0 This limit is of type: (No answer given) We perform algebraic manipulations to evaluate the limit, and obtain that the derivative f' (x) is: f' (x ) = Check

Question 18 Consider the function f(x) = 2x3 - 3x2 - 36x + 54 Answer the questions below, If you have to enter more than one number or interval, separate your answers with commas. Find the first derivative. f (x) List any critical values Identify intervals of increase. Identify intervals of decrease Find the second derivaitve. f"(x) Use the

Show all work for full credit. Remember to cite any relevant theorems or tests used in your work. 1. Determine whether the following series are absolutely convergent, conditionally convergent, or divergent. 00 (-1)" cos (n) a. n2 + tan-1(n) n= 1 (-1)" Vn + 1 b. n + 10 n=1 en tan '(n) C. (2n)! n= 1 d. sin(n) 2n n+ 3 n=1 2. Find the radius of

Use the alternative curvature formula k = laxv 1v / 3 to find the curvature of the following parameterized curve. r(t) = (4 +3+2, 2t,0)

(b) Let X = {x1, ...,*N} be a finite domain set of some N elements. For a fixed k {0, 1} such that h(xi) = k i=1 as the set of binary classifiers on A that assign 1 to exactly k elements of A'. Show that dvc ( Hk) = k. [12]

Question 3 Factor each of these polynomials: a) 6x + 47x + 71x- 70 b) 12x - 56X + 100x - 80x + 20x' + 8x-4

calculus 1 course help The Heaviside function is used in engineering applications to model flipping a switch. It is defined below. H(x)= 0 ifx

Given the infinite sequence (an], answer the following. an = sin (nit) Part 1. This sequence is a function. Choose the letter of the correct domain. A all real numbers B {1, 2, 3, 4, . . ., n} C the set of positive integers D undefined Part 2. Write the first 3 terms of the sequence. first term second term third term Part 3. Based on the results

3problem19 (1 point) The position s of a body moving on a coordinate line is given by s = 4 - 513 + 2212, with s in meters and t in seconds. Find the body's displacement and average velocity over the interval 0

#1 f(x)= 3x2+4x-1 Point (1, 6) find f'(x) and the equation of the tangent line

Point (1 find f(x) and the equation of the tangent line

The number of liver transplants performed in a particular country in year x is approximated by {(x) = - 245.5 + 2347 In x where x 2 5 and X = 5 corresponds\") the Year 1995- l a) Estimate the number of transplants in 2023. I!) Find H33). 3) According to this model, there should be approximately D liver transplants in 2023, (Round to the nearest

Please write in Maple Software incommand line for solving this All questionotherwise answer won't be collectedthank you. Note [use only Maple softwarefor wiring the problems] Please write inMaple Software in command line forsolving this All question otherwise answerwon't be collected thank you. Note [use only Maple software for wiring theproblems]

Mathematics 3-4 11. A vector v of length 6 makes a 150-degree angle with the vector [1, 0], when they are placed tail-to-tail. Find the components of v

\fCalculus 2 Dashboard I My courses .I MATH61D3 .-' Week14: Final Exams _:' Final Exam The area bounded by x = y3; x = l}; y = 1 revolves about the x-axis. Find the volume generated. stion 38 The area bounded by y2 = x; x = 4; and the x-axis revolves about the x-axis. yet vered volume generated.

4. A rectangular swimming pool is 5 feet deep at one end and 10 feet deep at the other end, and the bottom is an inclined plane. The length and the width of the pool are respectively 40 ft and 20 ft. If the pool is full of water, what is the fluid force on the vertical wall of the pool along a length of the pool? Assume the deep end is along a

96 Consider the function at) 2 6:6 + ?' 0

96 Consider the function f(c) 6c l 00. This function has an absolute value equal to Submit Question at

6. [-/1 Points] DETAILS LARCALCET7 1.6.026. Solve for x. (Enter your answers as a comma-separated list.) esx + 1 _ e X = Need Help? Read It

find the unit tangent. r( t )=( t cos t -sin t )i+( t sin t +cos t )j+ t 2k, t >0

Find an antiderivative with F (x) f(x) and F(l) O . f(x) x8

have a horizontal tangent? Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining

Identify the following as descriptive or inferential: A survey conducted at a local college indicates that most people prefer having cafeteria's on campus. A Inferential B Descriptive

no explanation needed, just answers Rates of Change Unit 1 Test 14 14 11 18 Name: K/U Comm T/I App Date: Knowledge/Understanding (14 marks) Identify the choice that best completes the statement or answers the question. Multiple Choice: 1. Evaluate the limit, if it exists: lim- 25 - x2 * +5 x - 5 a. 10 b. -10 C. 0 d. does not exist 2. Evaluate the

. Question 3 0, f" > 0 Of' 0 Of' > 0 , f" The function graphed above has: Positive derivative on the interval(s) ' Negative derivative on the interval(s) ' Check Answer Test 2 (2.4 -2.6) Score: 0/100 0/13 answered Question 3 0, f">0 Of' 0 Of's of"

2. For a > 0, a smooth function f : R\" )- R is a-conoez'c if for all 3:, y E R", M) 2 ms) + + Elly 3H5. In this exercise we will show a better bound on convergence rate of gradient descent (GD) for such functions. Let f : R\" ) R be a cr-convex iii-smooth function. Let 33'\" be an optimal minimizer for j. Consider the GD algorithm with starting

O O 8 https://www.webassign.net/web/Student/Assignment-Responses/submit?dep=30145920&tags=autosave#question4815715_3 D -/5 Points] DETAILS SCALC9 1.4.008. MY NOTES PRACTICE ANOTHER A graphing calculator is recommended. The displacement (in centimeters) of a particle s moving back and forth along a straight line is given by the equation s = 3

Complete the table below09esure to simplify yoUr

Find the length of the following two-dimensional curve. r(t) = (3 cost+ 3t sint,3 sint - 3t cost) , for 0 Ets L= (Type an exact answer, using it as needed.)\fQuestion 4, 12.1.13 HW Score: 22.22%, 2 of 9 Part 1 of 4 points O Points: 0 of 1 Save Consider the following parametric equations, x= - t+ 2, y=9t+9; -5sts5. Complete parts (a) through (d)

(1 point) Evaluate lim f (4 + h) - f(4) h- h where f(x) = |x - 71 - 1. If the limit does not exist enter -1000. Limit = (1 point) Let f(x) = -1 - x2. Find each of the following: (2 (A) f(6) - f(2) = 6-2 -8 ( B) f( 2 + h) - f(2) h (C) lim f (2 + h) - f(2) = h - 0 h (1 point) Let f(x) = 7x2 + 4. Evaluate lim f(1 + h) - f(1) h -0 h (If the limit does

Please read the question and leave notes on the answer where appropriate. Please DO NOT skip any steps. Please double check your answer. DO NOT SUBMIT A TYPED RESPONSE . Please use a hand written response that is LEGABLE. Please review your answer to make sure all steps are clearly visible. Please double check your work. Thank you. Show all your

Find the Taylor polynomials , ..., P4 centered at a 0 for f(x) 2 cos ( 5x).

Show that 4112 1 and deduce the value of 4n2 1

(a) Let f(x) = (x + 3) , x > 0. Find a formula for f (x) . Answer: (b) For what values of a is f defined

Find an equation of the ellipse to the right. An equation of the ellipse is

Find an equation of the ellipse to the right. An equation of the ellipse is x

1. A farmer wants to fence in an area of 1.5 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. How can he do this so as to minimize the cost of the fence? 2. Without using a calculator, sketch the graphs of the functions defined below. a) f(x) = 3x3- 212 +5 b) f (x) =

Inventory. ABC Auto sells 400 new automobiles a year. It costs $100 to store one automobile for a year. To reorder automobiles there is a fixed cost of $60 and a cost per automobile of $50. How many automobiles must be ordered each time to minimize inventory costs

Find the horizontal and vertical asymptotes of the graph of the function. (You need not sketch the graph. If an answer does not exist, enter DNE.) g(t) = t+ 5 6t - 5 horizontal asymptote y = vertical asymptote t =

Find the absolute maximum value and the absolute minimum value, if any, of the function. (Round your answers to the nearest integer. If an answer does not exist, enter DNE.) f(x) = x2/3(x2 - 4) on [-1, 5] maximum minimum

1. Evaluate the limit, if it exists; otherwise give the reason why the limit does not exist. (a) lim cos x (b) lim V4x' + x - 2x) 2. (a) Find the horizontal and vertical asymptotes of the graph of the function V5x- +7 f ( x ) = 2x -3 aX (b) Find the values of a and b for a rational function of the form y - with a x + b vertical asymptote at x = 2

Can some please solve this I'm having problems with it:(

Find

Evaluate the given expression ade 4 y.o estella sign a contract to not get a boyfriend until she is 30 M @XN N hang $30 sa XM. ade ng fore ong lang nakata na mawi- ang deposi an ang 5M X - OM XM

In (x2 +y2) W Integrate f(x,y) = over the region 1 5x2 + y2 S e 7. 7 The answer is 51m 2 -27: . (Type an exact answer. using 7: as needed. Do not factor.) 11 V121 -x2 Change the Cartesian integral _ _ dy dx into an equivalent polar integral. Then evaluate the polar integral. . . . Change the Cartesian integral into an equivalent polar integral. V

4. Write the equation of a circle with center (-5, -8) and radius 2. A ( x + 5) + ( y + 8) = 4 B ( x - 5) + ( y - 8) = 4 C ( x + 5) + ( y + 8) = 2 D ( x - 5) + ( y - 8) = 2 5. Determine what type of symmetry the graph of the equation has, if any. y = x - 3 A origin B x-axis C y-axis D none 6. ll]. Calculate the distance between the points (3, 4}

A spring hanging straight down from the ceiling with a weight attached to the end can be modeled by exactly the same ODE as a pendulum [which we looked at earlier in the class). If we attach a second spring to the weight of the rst spring, then we can model the whole thing as a system of two second-order CIDEs. For example, with some oonvenient

Solve the following initial value problem sin ( - 970), -46) The solution is r(0) = (Type an exact answer.)

5 GIVEN THAT f ( x ) = X- 5 AND 9 ( x ) = x2 - 5, FIND @ f(g (7) ) B f ( x ) @ g (g"(x) ) XI. LOGARITHMS 1 CONDENSE THE EXPRESSION INTO A SINGLE LOGARITHM 2 In ( x - 3) + In ( x+2 ) - 6 In x 2 EXPAND THE EXPRESSION In ( x 2 vy - 2 . .. . . 3w3 7EXPRESS y IN TERMS OF X : 3 In y = x + 2 1 In y = 2 Inx + In 10 5 In y = 4 linx + 3 X = In 4y SOLVE FOR

Question 4(Multiple Choice Worth 2 points) (01.08 MC) x2 + 4x Which of the following describes the domain of the piecewise function g (x) = x2 + 2x -8 for X

Solve each quadratic equation by any method. Find only real solutions in exact form, not rounded decimals. If necessary, write answers in simplified radical form. 1. 3x2 + 7x - 20= 0 2. 2x2 + 8x + 1=6 3. 6x2 + 14x - 3 = 3x + 7 4. - x2 + 2x + 9=4x +5 5. 2x2 - 9x + 6=7x2 + 17x - 18 6. A IW NIH - x2 + 0 7. 4x2 - 2x - 19 = 3x2 + 4x + 22

Problem 2 [Linear Model] A car rental company offers two plans for renting a car. Plan A: $25 per day and $0.10 per mile Plan B: $40 per day Twith free unlimited mileage How many miles would you need to drive for plan B to save you money? Problem 3 [The linear Function] Write an equation for a line pelpendicular to 10(3) = 3! + 4 and passing

(a) Show, using the properties of determinants under interchanges of rows and / or columns, that but dim din EijkElmn = K oj ojm 6kl okm okn and determine the constant K. By setting / = k and summing over k from 1 to 3 deduce that b) Eijkekmn = dimoin - dinojm, and hence that C) Eijkeljk = 20il, d) Eijkijk = 6. In these expressions the Einstein

8. This example is very similar to the one I did in lecture, but will have a couple of additional steps. Be sure you have finished this week's lesson before completing this problem. f(x) = x5-6x4+ 11x3- x2- 14x + 5; given factors (2 - i) and (2 + i) Steps: 1. Use synthetic division twice to factor (2 - i) and (2 + i) out of the 5th degree

Penod Number Classification Worksheet belongs. e-write each number in the Venn Diagram where REAL NUMBERS -19 RATIONAL IRRATIONAL 1.2 1. I INTEGERS 3:456 3.456 WHOLE -1.48298. II + 3 -44 NATURAL List all classifications of the number. al VIO b) -44 C) 3

Hello can o hve some help on 1-9 please , please can you write on a sheet of paper and not type with your computer EXERCISES 11.1 Finding Cartesian from Parametric Equations Exercises 1-18 give parametric equations and parameter intervals for the motion of a particle in the xy-plane. Identify the particle's path by finding a Cartesian equation for

Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a. p(v) = 4\\ 4v2 + 5, a=1 V - 1 lim p(v) = lim 4 \\ 4v2+ 5 V - 1 . . . ........ = 4 lim V 4v-+ 5 . . . ... . V -> by the ---Select--- = 4 lim V - 1 4v2 + 5 by the ---Select--- = 4 lim 4v2 V - 1 V - 1 + lim 5 by the

2. The length of a curve from x = 1 to x = 5 is given by f 15 V 1 + 9x4 dx. If the curve contains the point (1, 4), which of the following could be an equation for this curve. A. y=_+3 B. y=3x3+1 C. y=5-x3 D. y=6x+x3

please imagine the scenario " you went to a concert for your favorite music artist and you were standing near the state. the artist threw a souvenir into the crowd and you caught it! the souvenir was released at an angle of 30 degrees and was thrown with an initial speed of 20 ft per second. also the artist is standing on stage 15 feet above the

The bottom of a large theater screen is 9 ft above your eye level and the top of the screen is 30 ft above your eye level. Assume you walk away from the screen (perpendicular to the screen) at a rate of 6 ft/s while looking at the screen. What is the rate of change of the viewing angle \theta when you are 60 ft from the wall on which the screen

Calculus 3 : give me final answer only , no explanation needed. Section 12.5: Problem 4 (1 point) Evaluate the triple integral r dV where E is the solid bounded by the paraboloid = = 5y* + 52 and I = 5. 7.85Section 12.5: Problem 6 (1 point) Use a triple integral to find the volume of the solid bounded by the parabolic cylinder y = 4x and the

Evaluate the given line integral along the given curve. C is the triangle with vertices (0,1,2), (2,2,3), and (1,1,0) traversed in the order given

Consider the function f(x) = Vx - 6. (A) Find f (6) = 42 (B) Use Theorem 7, page 156 of the Stewart Essential Calculus textbook to find (f-1)' (6) (f-1)'(6) : 12 (C) Calculate f () and state domain and range of f-1. Use interval notation. If needed enter inf for co or -inf for -Do. f-1(ac) = x- + 6 Domain = (-00,00) Range = [6,00) Calculate

1) A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $(60)/(f)t and on the other three sides by a metal fence costing $(50)/(f)t. If the area of the garden is 168 square feet, find the dimensions of the garden that minimize the cost. 2) A poster is to have a total area of 125 square inches. The

The following box plot shows the scores of the student evaluations of the faculty at a large colleDescriptive Statistics: salaries of the employees of a certain company in US dollars Descriptive Statistics: salaries in US dollars Variable N Mean SE Mean StDev Minimum Q1 salaries in US dollars 21425 304301 2075 303764 16116 126034 Variable Median

5. Suppose fn : [0,7r] > R by fn(:c) 2 5mm\". TL (a) This sequence of functions converges pointwise to a limit as n > 00; what is the limit function f? (b) Does this sequence of functions converge uniformly? Please explain why or Why not. Hint: Find a uniform bound independent of a)

1. Exercise # 14 of Section 8.3. The table below shows the number of calories burned per minute, B : f (.3, w), for someone rollerbalding, as a function of the person's weight, w, and speed, 3. w\\s 8mph Qmph' 10mph 11mph 120 lbs 4.2 5.8 7.4 8.9 140 lbs 8.3 9.9 160 lbs 6.1 7 7 9 2 10.8 1801bs 7.0 8.6 1 10.2 11.7 2001bs 7.9 9.5 1 11.1 12.6 Estimate

only #4 please 3. Let f(x) = (sina)Inz. Find f'(x) using logarithmic differentiation. 4. Find the equation of the tangent to the curve x2 - ry - y? = 1 at the point (2, 1). 5. If V is the volume of a cube of edge length a and the cube expands over time, find dV/dt in

please explain A gasoline storage tank in the shape of a right circular cylinder with height 14 m and radius 5 m is completely filled with gasoline. How much work is required to pump all the gasoline out the top of the tank? The density of the gasoline is p = 125 kg/m' and g = 9.8 m/s2. (Use decimal notation. Give your answer to the nearest whole

The time it takes an average athlete to swim 100 meters freestyle at age x years can be modeled as t(x) = 0.18m2 8.463x + 147.376 seconds (a) Numerically estimate to the nearest tenth the rate of change of the time for a 15year-old swimmer to swim 100 meters freestyle. seconds per year (of age) (b) Determine the percentage rate of change of swim