Mathematics Questions and Answers December 02, 2020

Q1]. .. [10 points] Let In denote the left-endpoint sum using n subintervals. Compute Le for 2 f(x) = (I - 1) on [3,6]. Q2]. . . [10 points] Evaluate Jo + 1 dx by using Rieman sums. -COST Q3]. . . [10 points] Let F(x) = 13 - 4t + 3 dt. Find F(x). BinT I Q4]. . . [10 points] Evaluate dx V10 + 12 Q5]. .. [10 points] Find the area of the region

Read the instructions carefully and give exact answer. Rating will be given based on quality. The tables to the right give price-demand and price-supply data for the sale of soybeans at a grain market, where x is the number of bushels of soybeans (in thousands of bushels) and p is the price per bushel (in dollars). Use quadratic regression to

Suppose the flow rate (in cubic feet per second, cfs) of a river in the first 11 hours after the beginning of a severe thunderstorm can be modeled as f(h) = 0.855h3 12.05h2 9.95h 124.03 cfs where h is the number of hours after the storm began. (a) What were the flow rates for h = 0 and h = 11? f(0) = 124.03 Correct: Your answer is correct. cfs

Find a function f that satisfies the conditions. f(x) x 32, f(1) 5, f(4) f(x) 1

Calculus word Problem A particle moves along a straight line and its position at time + is given by s ( t ) = 13 - 7.5 + 2 + 12+ where s is measured in feet and + in seconds . Goto consider tijn the [0, co] Ing Andfood of lonoit a ) what is the position of the particle at time 3 ? pistolb ) what is the velocity ult) of the particle at time F? V (

5. FOR WHAT VALUES OF a &b DOES THE FUNCTION -(x) = axe 6 x 2 HAVE A MAXIMUM VALUE OF | OCCURING WHEN X=2 ($12) = 1 )

1. Practice similar A boat at anchor is bobbing up and down in the sea. The vertical distance, y, in feet, between the sea floor and the boat is given as a function of time, t, in minutes, by y = 25 + cos(2nt) ft. Find the vertical velocity, v, of the boat at time t. U = ft/min2 . Practice similar Find the derivative of g(q) = sin(cos q) g

Please show work on all steps taken to get to the answer. 1. Using the Maclaurin series for flix} = sin 2;, derive the Maclaurin series for gEx] = Isin 2x. Hint: It is not necessary to do any differentiation to do this problem. 2. By multiplying the appropriate Taylor series about c = (J, compute the first four terms of the Taylor series about c =

Mr. Castillo believes in you! Test Score: 1. Find the average rate of change of h(x) = -x2 + 2x + 2 over the interval |-2. - -. 2 + 21 -2) + 2 - 7 121 - 7) + 2

Please Help with question 6. Please try and keep solutions neat so they are easily followable Splitting [in Integral Firs? QJHS Please evaluate these integrals: final Answer a.) ll' ; ' . Final

Grace plotted a sinusoidal function, g(x), as well as its derivative function, g'(x). Which line is g(x) and which is g'(x)? Supply a possible equation for 905)

Please show all work 1.C. a. In rectangular coordinates the origin is (x, y) = (0,0) but in polar coordinates it is called the '3. Give three different representations of the pole {different from the lecture notes} 2.1. a. Because of the angle sign convention, when you prepare your polar graph paper you really have TWO sets of angles: positive

(1 point) The limit x2 - 4 lim x-2 x - 2 represents f' (a) for some function f and some some number a. State such an f and a. Enter your answer in the form " f (x), a", i.e. list the function f and the value a separated by a comma

1. Using https://www.desmos.com/calculator graph the derivative Function: (2/x2+1)+1. 2. Then graph Its antiderivative so that the Maximum value of the antiderivative Function is twice as great the Maximum value of the function (2x+1/x^2+x+1) 3. Using the graph of antiderivative Function estimate the y-intercept And the end value of the function

Let f be the function defined below on the given region R, and let P be the partition P = P, X P2. Find U, (P). f (x, y) = 3x - 3y R : 0

I'm not sure how to find the area of the given curves. Show ALL work for full credit. 1) Sketch the region enclosed by the given curves and find the area: a) y = cos(x), y = 2 - cos(x), OSx s 2n by = 3x - x, y = x, x=3

Please help me in 5 minutes Use the graph to guess possible linear factors of f(x). Then completely factor f(x) with the aid of synthetic division. 17) f(x) = 5x3 + 33x2+31x - 69 17) #+ 40- +

Define the following terms. derivative b. secant line tangent line d. tangent point Smoke is being emitted into the atmosphere from a smokestack. At any instant, the smoke filled regions form as an inverted right circular cone, the height is 2 times the diameter. If the rate of smoke emission is 200 m3fmin, how fast is the height increasing when

Compute the values of (y and A3; forthe function y = e53 + 4:3 given a: = 0 and A3 = (in: = 0.03. Round your answers to four decimal places, if required. You can use a calculator, spreadsheet, browser, etc. to calculate dy and y. fly = Number Ay = Number

Find the measure of angle x, if possible. Round to the nearest tenth. (If not possible, enter IMPOSSIBLE.) x x 11 32 8

Please show all work and steps thank you i don't get this aspect of integration Suppose J and g are continuous and all of the following conditions are true. f(x) dx =7, f(x) dx = 3, - g(x) dx =-12 , g(x) dx = -4 , J is an odd function and g is an - 3 even function. Evaluate the following integral. -2 a. [3f (x) - 58(x) ]dx = b . f ( x) dx = 0 -3 0

8. Could the functions described below be linear? Justify your answers. 12 -5 ) and f ( ( 1 ) , 2 a ) f( 3 3 2 4 6 5 3 b) f ( -5 = 2 F ( 1 and f( -4 A 3 3 O

What is the derivative of ex? What does it mean that the derivative is equal to the value of the function? If x} =3X2 2 , and gtx1=r'1(x) , find the slope of the curve g(x) = f '1(x) at the point (10,2)

_ - A price ceiling is given along with demand and supply functions, where D(X) is the price. in dollars per unit, that consumers will pay for x units, and S(x) is the price, in dollars per unit, at which producers will sell x units. Find (a) the equilibrium point, (b) the point (xc,pc), (c) the new consumer surplus, (d) the new producer surplus,

The velocity. v ms". of a particle. travelling in a straight line. at time t s after leaving a fixed point 0. is given by r = 31'2 l8: 4- 32. when: l a: 0. Find (i) the value of t for which the acceleration is zero. (ii) the distance of the particle from 0 when its velocity is a minimum. [5] A car moves on a straight road. As the driver passes a

Question 4 8 pts Use the integral test to determine the convergence or divergence of the series. Be sure to check all the conditions. Show your work clearly

hello tutor answer this handwritten thanks with solution subject calculus

1. Evaluate using spherical coordinates. 1 dzdyda 2

Find the length of the following three-dimensional curve. r(t)= (1+7t,4-3t,-8+3t),for15t54 Set-up the integral that gives the arc length. D L: {Jam 1 (Type exact answers.)

Consider the following function. _ 3 2 _ _ g(x)X +3X 90n[ 3,1] Find the derivative of the function. g '(X) = Find any critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) Find the absolute maximum value and the absolute minimum value, if any, of the function. (If an answer does

MATH 1171 2.5 Infinite limits D4x Definition 1. lim f(x) means that the values of f(x) can be made arbitrarily large by taking x sufficiently close to a (on either side of a) but not equal to a. a lim f(x) xa a lim f(x) 0 lim f(x) xa Definition 2. The line x a is a vertical asymptote of y f(x) if lim f(x) or lim f(x) 0. a We only need him

y=1 is an equilibrium solution of the differential equation dy/dx= y(y+1)(y+2) True or False and please expalin

The goal of this worksheet is to explore how we may use the line tangent to a function to tell 11s some information about function values. 1. Sketch a graph of f(.'L') = 3:2? as well as the line tangent to x) at 3: = 1' 2. Find the equation of your tangent line. 3. Find the y-coordinate of the point on your tangent line with arr-coordinate 1.1. 4.

Find a 7th degree polynomial approximation to Fix). at point a. Graph fix) and the polynomial on the interval given below . a ) fix = ex . a = 0 ; [ - 1, 1] b ) fix) = sin ( Ex); a = 0; [-TT, 1]

18. Which option is correct? Show work please

7. (04.03 HC) A constant volume of cookie dough is formed into a cylinder with a relatively small height and large radius. When the cookie dough is placed into the oven, the height of the dough decreases as the radius increases, but it retains its cylindrical shape. At time t, the height of the dough is 6 mm, the radius of the dough is 20 mm, and

Convert the complex number 0 - 2 into polar form. Express the angle using radians in terms of 7 over the interval 0

Please help DIRECTIONS: To receive full credit, make sure your work is neat and complete. 1. Let f(x) = V1+x. (a) Find Lo(x). (b) Use part (a) to help you approximate v1.06

I need help with this FRQ. Would you please solve this question and show the way how you solved it?

6. [0/12 Points] DETAILS PREVIOUS ANSWERS UWAPRECALC1 12.P.010. MY NOTES The populations of termites and spiders in a certain house are growing exponentially. The house contains 90 termites the day you move in. After four days, the house contains 175 termites. Three days after moving in, there are two times as many termites as spiders. Eight days

7 and 9 7. [0/1 Points] DETAILS PREVIOUS ANSWERS Convert the rectangular equation to polar form. ( x2 + 12) 2 - 6 ( x2 - y? ) ( x 2 + 12) . 2 - 6(2 -12) X Need Help? Read It Watch It 8. [1/1 Points] DETAILS PREVIOUS ANSWERS LA Convert the polar equation to rectangular form. r= -11 x2+12 -121 Need Help? Read It Watch It 9. [0/1 Points] DETAILS

28.Show work please D Question 28 4 pts The graph of f (x) = x - 1 is shown in the figure. Find o such that if 0

Refer to the pictures. How do you do 5.c, 6.c, and 6.d? 5 . Spread of a rumor. The rumor "People who study math all get scholarships" spreads across a college campus. Data in the following Time, t Number, N. Who table show the number of students N who have heard the rumor after (in days) Have Heard the Rumor time t, in days. The scatterplot of the

Please answer this question in full steps and have a good and clear handwriting please. 6. Use the technique of implicit differentiation to nd (:3) for the curve x4xy3 +3}? = 0. Use your answer to nd the slope of the tangent line to this curve at the point (1.1)

Based on the graph above, determine the amplitude, midline, and period of the function Amplitude: Period: Midline: y = Question Help: B Worked Example 1 Given the equation y = 4sin(3(x - 8)) + 7 The amplitude is: The period is: The horizontal shift is: units to the Select an answer v The midline is: y = Question Help: G Worked Example 1 Given the

Consider the parametric equations below' x:1+3t, yzzrz (a) Sketch the curve by using the parametric equations to piot points. Indicate with an arrow the direction in which the curve is traced as t increases. (b) Eliminate the parameter to find a Cartesian equation of the curve. Find a formula for the general term an of the sequence, assuming that

Find an equation of the plane passing through the three points given P = (4,2,9), Q = (6,7, 18), R = (11,8,12) (Use symbolic notation and fractions where needed. Give you answer in the form ax + by + cz = d.) equation of the plane: -39x + 57y 232 = 249 Incorrect

Find an equation of the sphere that pleases through the origin and wheeze center is (3, l, 3]. E

Find an equation of the sphere that passes through the origin and whose center is (3, 1, 3).

achieve.macmillanlearning.com + Monetary Policy Impact: AD Shift MATH 140 CALC ANLY GEOM I.. lectures_week14.pdf: MATH 14... 140_f23_inclass_w14-soln.pdf:. Assessment - Math 140 Fall 20.. Dashboard Assessment ? 6 of 9 Questions Attempt 2 2 of oo Attempts Correct Calculate the work W against gravity required to build a hemisphere with base of

solve all Find the integration ( 1 ) substitution of parts. Sin2x Cos 3x + (os 2x Sin 3 x ) dx ( 2 ) X ax J2x - 1 ( 3 ) X d x Cos ( x 2 ) (4 ) ( cos3x ) sin 3 xdx . (5 ) S ( secx ) dx . ( 6 ) sen dx

Find the critical point and the intervals on which the function is increasing or decreasing and apply the First Derivative Test to each critical point on the interval (-7 , 7] f (x) = 2e * cos(x) (Use symbolic notation and fractions where needed.) CE The critical point yields a local maximum. local minimum. Oneither maximum nor minimum (inflection

Find the accumulated present value of the following continuous income stream at rate R(t), for the given time T and interest rate k, compounded continuously. R(t) = 0.08t + 200, T = 10, k=8% . . . The accumulated present value is $. (Do not round until the final answer. Then round to the nearest cent as needed.)

Use the Theorum of Pappus to find the volume of revolu a ) 45 15 O W C) 2

Please answer this question thank you III '5? @' Question 8 The British scientist Sir Francis Gaiton studied inheritance by looking at distributions of the heights of parents and children. In 1886, he published data from a large sample of parents and their adult children showing the relation between their heights. The following graph is based on

For the cost function C(n), find the marginal cost at the given production level n = 100. n2 C(n) = - + 20n + 25000 1000 a. $19.62 per item b. $21.28 per item c. $9.61 per item d. $19.60 per item e. $19.50 per item f. $20.50 per item Evaluate the integral 3x2 dx 3 a. 38 b. 85.5 C. 10 d. 19 e. 43.6 f. 2Annual U.S. imports from China in the years

Find the volume of the region under the surface z = 7 / 1 + x 2 and above the triangle in the xy-plane with corners (0,0,0), (8,0,0) and (8,8,0).

Please answer the questions below fully and completely. Be sure to show your steps, use correct notation, and make your work clear. It is expected that you attempt each problem and if you get stuck, explain your uncertainty. Remember that fixes cannot be made on problems that have no attempt and/or explanation of the sticking point for you. 1. Use

Hi please answer the following and circle the answer. I have provided links that shows how to do the problem. Thank You!!! 1. https://www.youtube.com/watch?v=qUaavfKaWc8 1 Letf(:n) = for4m5. CC Part a) Use four approximating rectangles and right endpoints to estimate the area under f. (If necessary, round to four decimal places.) R4: Part b) Is

A child is flying a kite attached to a 20m long string. At first, the kite is directly above the child, but it blows east. The child notices that the angle between the string and the ground is decreasing by

8. Let x = sin (t) y = cos? (t) for 0

x sin (t) for O t E. Compute the area under the parametric curve 8. Let y cos2(t)

Find the series equal to the definite integral. \int _0^2\:sin\left(x^3 ight)dx

To convert from x degrees Celsius to y degrees Fahrenheit, we use the formula (x) = 2x + 32. Find the inverse function, If it exists. (If an answer does not exist, enter ONE.] Explain its meaning- O The inverse formula allows you to convert from x degrees Celsius to y degrees Fahrenheit. The Inverse formula allows you to convert from * degrees

Note: Give exact answers where possible (for example, is exact but 3.142 is approximate). 5. Hi? marks] Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the curves 1! = x2 and I = 3;: about the line I = 1. 6. [It] marks] The base of a solid is the region bounded by the parabolas y = x2 and y = 2

Find the equation of the function f whose graph passes through the given point. (Remember to use absolute values where appropriate.) f' (x) = x - 3x-+ 2. (3, -3) X - 2 f ( x ) =

If the work required to stretch a spring 3 ft beyond its natural length is 15 ft-lb, how much work (in ft-lb) is needed to stretch it 18 in. beyond its natural length? ft-lb

Find the center of the mass of a thin plate of constant density 5 covering the region bounded by 7|: 7|: the x-axis and the curve y= 2 cos x, - E 5x5 E

you have 1200 meters of barbed wire, electric fencing. you want to make a rectangular fence around your entire garden and then use more fencing to split the enclosed area into equally -sized rectangles to keep your minton one side and your other herbs on the other.What dimensions will maximize the volume of both enclosure

lhe Map As you walk through Gate 4, you realize that Gate 5 is nowhere to be found. In front of you lies an expansive desert as far as you can see. You look at your map and see that there is an alert for this area. The warning states that this desert is almost entirely guicksand, with only one path safely through the desert. That path is defined

calculs 3 Note: please write down the Answer by hand on paper and also write each answer with the number of the questions 18. [-/1 Points] DETAILS SCALCET9 16.1.028. Find the gradient vector field Vf of f. f ( x , y , z ) = x3 yev / z Vf ( x, y, z) = 19. [-/1 Points] DETAILS . SCALCET9 16.2.003.MI. Evaluate the line integral, where C is the given

Find the work done by a person weighing 121 lb walking exactly one and a half revolution(s) up a circular, spiral staircase of radius 5 ft if the person rises 17 ft after one revolution. Work = ft-lb Question Help: Message instructor Submit

7. (0303 HC) No calculator is allowed for this question. A function his dependent on x and is differentiable for all real numbers. Let g be the inverse of h. Part A: Use the derivative of inverse functions rule to write an expression for g' in terms of g, h, and x. (7 points) Part B: Use the table of values to nd gm. (3 points) x l 2 3 h(x) 4 3 1

Math& 15 1 Names: Derivative Practice 0. A tank of water has started leaking. The function f(t) gives us the volume (in cubic meters of water left in a tank t minutes after the leek formed. Explain what f(3) : 3000 and f '(3) : -60 tell us about the water in the tank. Find the derivative of the following functions 1. f(x)=x3 4x2 8x+20 2i foam/2H5

24.Each of the following equations represents a conic section. Identify the type of conic section: parabola, circle, ellipse of hyperbola. a. x22x+2y212y+3=0 .x210x+12y+1=0 x22x4y11 = O .x2+y2+5xy1=0 :2ch

A trail runner tries to run a hiking trail in record time. Consider a path through the mountains from x = A to x = B that is modelled by the function f(x). A B (a) (3 points) Assume first that the trail hiker runs a constant velocity U. Write down an expression for total time T that it takes the trail runner to run the path from x = A to x = B.

A bacteria culture starts with 320 bacteria and grows at a rate proportional to its size. After 2 hours there will be 54'] bacteria. {a} Express the population P after t hours as a function of 3. Be sure to keep at least 4 significant figures on the growth rate. PttH i| _[b] What will be the population after El hours? I I bacteria {c} How long

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Tracking I UPS ... Your Shopping... 0 Information V... Aurora Tweed L... webassign.net O Assignment 8 ... Consider the fol... Assignment 8 ... Start Page Course Hero Suppose these data show the number of gallons of gasoline sold by a gasoline distributor in Bennington, Vermont, over the past 12 weeks. Week 1 2 3 4 5 6 7 8 9 10 11 12 Sales (l,ooos

Aforce 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.) How much work does it take to stretch the rubber band this far? J

Assignment 21,22 -> provide answers in text form with little to no explanation Calculus Problems a ) suppose that a particular function f satisfies F " ( re ) = - ( 3 sin ( ne ) + 3 cos ( no ) ) , f (0 ) = - 2 , f ' ( 0 ) = 8 then we must have Flo ) = b) answer the same question but for F " ( 10 ) = 6 20 - 24 20 2 + 8 , FLO)= - 2 , F ' ( 0 ) = - 1

7 -6 -5 -4 -3- 2 -7 3 Find the slope of the line. Slope = m Enter your answer as an integer or as a reduced fraction in the form A/B. Question Help

AP Calculus BC Module 1 DBA Be sure to show and explain all work. Use concepts learned in this module to complete this problem set: determine limits algebraically, using graphs, and considering tables of data values; apply conditions of continuity; use of the Intermediate Value Theorem. . Determine each limit using the method indicated: a. Using a

a} Use a Riemann sum with 5 rectangles and lefthand endpoints to approximate the area between the :rraxis and f[a:) 2 111(1' | 2). where :13 E [l]. 15]. Round your answer to two decimal places. b) Is your answer in a) an overestimate or an underestimate for the actual area? Explain. {Your explanation should not involve integration or other

Use the graph of f (x) = below to find a number o such that If (x) - 0.5|

1 Use the graph of f (x) Enter the exact answer. Number below to find a number (5 such that If (c) 0.51 0.1 whenever 06 05 2

A cold metal bar at 30" C is submerged in a pool maintained at a temperature of 70C. After 10 seconds, the temperature of the bar is 200 How long will it take for the bar to attain a temperature of 30C? (Use decimal notation. Give your answer to one decimal place. Round any intermediate calculations, if needed, to no less than four decimal places.)

Algebraic For the following exercises, find the domain of the rational functions. 6. f (x) = x-1 x+2 7. f(x) = x+1 x2-1 8. f(x) = x2+4 x2-2x-8 9. f (x) = *+4x-3 x4-5x2+4 For the following exercises, find the domain, vertical asymptotes, and horizontal asymptotes of the functions. 10. f (x) = X- I 11. f (x) = 2 12. f (x) = X 2 - 9 13. f (x) =

Assume that the function f is one-to-one. If f-1(-4) = -8, find f(-8). Additional Materials eBook

Assurne that the function fis onetoone. If f1(4) 8, find Additional Materials eBook

QUESTION 9 Which graph represents a curve given by x = 4t + 5 and y = 2t over the interval -3 s ts 3

Sign In DiClicker Student -... MAA Logged in as MATHEMATICAL ASSOCIATION OF AMERICA g2023-90 / 11 / 11 Previous Problem Problem List Next Problem 11: Problem 11 (1 point) A force of 5 pounds is required to hold a spring stretched 0.5 feet beyond its natural length. How much work (in foot-pounds) is done in stretching the spring from its natural

Determine an expression for the instantaneous velocity of an object moving with rectlinear motion according to the function given, if s represents displacement in terms of time t. s=3t5-7t+5 Question 12 options: 3t4-7t 15t6-14t3 3t6-7t2 15t4-7

Asap and clear please and thank you. 4. Find the average value of the function f (r) = sin 3x on the interval [0, $]. ( A) 1 (B) 2 (C) 2 (D) 6 (E) 1 ( F) 2 (G) 0 (H) 5. Use Simpson's Rule with n = 4 to approximate the integral _, 20 dr. (A) X (B) (0) $ (D) ; (E) 2- (F) 45 (G) 18 (H) . Find the value of the limit lim cos x - 1 I-+0+ (A) B) -2 (C) 0

11.3 (1)1 x for 1

Please show work and explanation 7. (a) Find the .rvalues for which the functions f below change concavity or show that no such :1:Values exist. Figure 2: graph of y : Jetty) \=.' (u 10. * "A box has a square base of side :13 and height h. (a) * Find the dimensions 3:, h. for which the volume is 16 and the surface area is as small as possible. (b)

dy 16. Consider the differential equation E = I- 4." . Let y=f(x) be the particular solution to this differential equation with the initial condition f(2)=0. _' 0) Use Euler's method, starting at x:2 with two steps of equal size to approximate f(1.6). Show all work that leads to your answer. You may use a table to organize it

16. Communication a) Explain how to calculate the average speed for the first 2s in the walk illustrated by the following distance versus time graph. b) Calculate the instantaneous speed at I s. 10 Tarm)

Assignment questions The questions in this section contribute to your assignment grade. Stars indicate the difficulty of the questions, as described on Canvas. In 1952, A. Hodgkin and A. Huxley published a series of papers which culminated with a model for the electrical activity of a neuron. This model made a profound impact on subsequent

show all steps with drawn diagram pls! if possible could you follow the structure so it is easy to read. Math 251 c) Compute the fastest total time Nadia takes to the bus stop if Alania walks side walk rst then turn to grassy eld to get to the bus stop. BUS c) [3] Function used f(x): STOP d) draw your x on the left gure as what you indicate e) [3]

0 7 Decide if the improper integral f 2 do: converges or diverges. If it converges. find its value. 1 33 O converges to 7 O converges to 3.5 O diverges O converges to 14 00 Decide if the improper integral f 843: dx converges or diverges. If it converges, find its value. 0 O Diverges 1 Converges to 434 1 O Converges to E l Converges to 4e

X-8 a factor ? Use the factor theorem to determine if the given binomial is a factor of f (x). f(x) =x -4096 (a) x - 8 (b) x- 8

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a achieve.macmillanlearning.com Assessment Math 140 Fall 2023AO A... Calendar Assessment Achieve MATH 140 CALC ANIY GEOM I... Resources ChatGPT x Dashboard Try Again Attempt 10 0 2 of 9 Questions 4 of oo Attempts 2 Question 10 of oo Attempts 3 Question 0 of oo Attempts 4 Question 0 of oo Attempts 5 Question 0 of oo Attempts 6 Question 0 of oo

Read the instructions carefully and give exact answer. Rating will be given based on quality. The weekly marginal revenue from the sale of x pairs of tennis shoes is given by the equation below, where R(x) is revenue in dollars. 400 R'(x) = 40 0.02x + , x+ 1 R(0)= 0 Find the revenue function. Find the revenue from the sale of 2,000 pairs of shoes.

Observing a launch An observer stands 300 ft from the launch site of a hot-air balloon at an elevation equal to the elevation of the launch site. The balloon is launched vertically and maintains a constant upward velocity of 20 ft/s. What is the rate of change of the angle of elevation of the balloon when it is 400 ft from the ground? (Hint: The

Part D A lication APP 12 marks 1. The ratio of intensities of sound pollution measured at a major airport runway versus the local highway is 6420.4. lfthe sound level on the local highway is 51 dB1 determine the sound level on the airport runway. \/\/\/\/