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Mathematics Questions and Answers February 06, 2020

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thermometer reads 32.1 C. Calculate this temperature in Fahrenheit degr ahrenheit temperature F Submit Answer Retry Entire Group 9 more group attempts remaining
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15. Angle of Depression From a plane 3,000 feet in the air, the angle of depression to the beginning of the runway is 3 50. What is the horizontal distance between the plane and runway (That is, if the plane flew at the same altitude, how far would it be to the runway) Give your answer to the nearest tenth of a mile. (5,280 feet 1 mile)
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Find the first and second derivat y x8 1 y 2x8 y
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5. Even, or odd, or neither. Prove with algebra and a sketch of the graph (from calculator). A. f(x) 2xx 2x B. f(x) x
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For the realvalued functions f(x) x2 x3 and g(x)4x5, find the composition fg and specify its domain using interval notation.
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tan 15 4 () () (1,0) o () MING (0,1) (44) 81 05 4x MI4 (44) (1,0) 0 21 817 812 (0.1) (4) (4) (Type an exact answer, usin
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The mess in a restaurant can be measured by M(t). Assume that M(0) 0, the restaurant starts out each month completely clean Over time the rate of change in the mess is proportional to (100 M). After 50 hours the restaurant had a mess index of 20. A completely messy restaurant has a value of 100. How many hours does it take for the restaurant to
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a Calculate the definite integral f(x) dx by referring to the figure on the right with the indicated areas. Area A 1,204 Area B 2,308 Area C 3,079 G a B Area D 1,687
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Find the derivative of the function g(x) e(3x1) g(x) (43x)2 ex 4 3x
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Given x T 43 IM what is the exact value of sin(2 x)
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Of all numbers whose difference is 14, find the two that have the minimum product. What are the two numbers
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below owing questions about the function f, whose graph is show graph of the function f 2 (A) Find lim f(x). 2 (B) (C) 018 Find lim (0h)(0)1 does h 2 h10 h Find lim f(x) undele 0
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The graph of y f(x) (solid) and its tangent line at x 0 (dashed) is shown a second point on the tangent line is also marked. Assume f(x) is continuous. 10 9 8 109 8 7 6 5 Find f(x) lim x0 x lim f(x) 20 4e4 7 8 9 9 10
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A function f(x) is given below. Express the relationship between f(x) and f(x) in words, and write a differential equation that f(x satisfies. (x)6ex Express the relationship between f(x) and f(x) in words. Choose the correct answer below. OA. The derivative of f(x) is 6 times f(x). OB. The derivative of f(x) is 1 times e raised to the x1 power.
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Find the length and direction (when defined) of uxv and vxu. u 8i3j5k, v 4i 4j 2k luxv (Type an exact answer, using radicals as needed.)
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For the function f(x)(x1) (a) Find the critical numbers of (if any) (b) Find the open intervals where the function is increasing or decreasing and (c) Apply the First Derivative Test to identify all relative extrema. Use a graphing utility to confirm your results.
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Suppose a sphere of radius r is sliced by two horizontal planes h units apart as shown. Show that the surface area of the resulting zone on the sphere is 2xrh, independent of the location of the cutting planes. To show that the surface area of the resulting zone of the sphere is 2xrh, independent of the location of the cutting planes, find the
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Problem 29. 1 point Which of the below areas are equal to the following limit lim 818 n 3 2 3i n i (i) The area under the graph of 2x from x 0 to x 3 (ii) The area under the graph of x from x 2 to x 5 (iii) The area under the graph of 1x from x 0 to x 3 A) only (i) B) only (ii) C) only (i) and (ii) D) only (iii) E) only (ii) and (iii)
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Find the following integral. Note that you can check your answer by differentiatio 6e4v S dy
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Write a degree 3 Maclaurin Polynomial for f(x)4 sin(4x).
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(h) Investigate the continuity of the function f(x) x 0. x sin x, if x 0 at if x 0 0
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2. Let f(x)3cosx4sin x5 a) Determine the exact slope of f(x) at a 4 b) Determine the tangent line approximation to y f(x) at the point where a c) At the point where a , is f(x) increasing, decreasing, or neither Why
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Given the function f(x) xez, Determine the open interval(s) where the function is concave up Determine the open interval(s) where the function is concave down Determine any points of inflection.
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What is one concern with the use of geneticallyengineered, herbicidetolerant crops transfer of herbicide resistance to weeds O potential allergic reactions O Decreased Yield expense of using herbicides
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9. 5 points For the following functions, f(x, y) 4x 2y28xy. Find the minimum using steepest descent method starting from initial point (2,3). Calculate optimum step size at every step. I need details for several steps as clear as possible
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Find equations of the tangent plane and the normal line to the given surface at the specified point. xyz 8exyz, (0, 0, 8) (a) the tangent plane (b) the normal line (x(t), y(t), z(t))
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4. The top eyeglass retailers last year were XrayVision, YesSpecs and ZoomGlasses. Together, they accounted for 69 of total market sales. The combined share of XrayVision and YesSpecs was twice the share of ZoomGlasses, and the share of Xray Vision is less than the combined share of ZoomGlasses and YesSpecs by 55. What was the market share of each
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Solve the equation f(x) xxx1 given that one of its roots is a 1 A. x 1 B. z 1,1 c. 1 D. x0
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Find A, the area of the region under the curve y 2x3 9 and above the xaxis for 2 5.
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Fill in each blank with the appropriate number related to the exponential expression. 34 a. The base of the expression is Type your answer here b. The exponent of the expression is Type your answer here c. When simplified, 34 Type your answer here
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Evaluate the following integral. x41x2 TIT 000 sin xx sin y sin 4z dy dx dz x4 1 x2 TIT 000 sin xx sin y sin 4z dy dx dz
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For the polynomial below, 1 is a zero. 2 f(x)x 4x x 6 Express f(x) as a product of linear factors.
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Problem 5. 1 point If f(x) ln(ln x), find f(e). A) 22 B) 11 12 C) 2 20 D) In2 E)
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(1 point) Find the derivative of the function G(x) L 5 cos vt dt. G(x)
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At a computer store, a customer is considering 7 different computers, 8 different monitors, 9 different printers and 3 different scanners. Assuming that each of the components is compatible with one another and that one of each is to be selected, determine the number of different computer systems possible. There are different computer systems
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Use logarithmic differentiation to evaluate f(x). (x3) f(x) (4x8) 11 f(x)
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9. 5 points For the following functions, f(x, y) 4x 2y 8xy. Find the minimum using steepest descent method starting from initial point (2,3). Calculate optimum step size at every step.
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a) (3 points) Sketch the graph of f(x) 2 e by transforming the graph of y e. Include any relevant asymptote on your graph. (3,0) y0 OR x0
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Given the following linear system of ODE V 41 22 Y 10y14y2 what is the type of the critical point the critical point is spiral the critical point is saddle the critical point is proper node the critical point is center the critical point is improper node
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Use a graph of f to estimate lim f(x) or to show that the limit does not exist. Evaluate f(x) near xa to support you conjecture. f(x) 1cos (5x5) 5(x1)2 X8 a1 Each graph is displayed in a 1,3 by 0,5 window. Use the graphing utility to estimate lim f(x). Select the correct choice below and, if necessary, fill in the answer boz complete your choice.
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Write the following expression in terms of its cofunction. COS 3 The expression in terms of its cofunction is (Type an exact answer in terms of t. Simplify your answer.)
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Find y in two ways for the equation 2x 7y90. (A) Differentiate the given equation implicitly and then solve for y. (B) Solve the given equation for y and then differentiate directly. (A) What is the implicit differentiation of the given function OA. 2x7y 0 OB. 27y 0 OC. 27y 0 OD. 27y 0 (B) Solve the given equation for y. y Using either
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5. A model for the population growth of China is P(t) 0.000788t3 0.004312 7.24623t 1286.78 in year t, where t is measured in years with t 0 corresponding to the year 2000 and P(t) is measured in millions. (a) Show that the population of China is forecast to peak during 2057. (b) Find what the population of China will be when it peaks.
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B only please oz diod oals ous 12. Solve each of the following initial value problems (a) yy 2y2 y 2y1 y2 ends and B are fixed y(0) 3, y2(0) 1 babe three springs are (b) yy12y2position. A force is exerted aud 22y1 y2 placements of the masses y(0) 1, y2(0) 2 sume that there are
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A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 ft deep at its deepest point. A crosssection is shown in the figure. If the pool is being filled at a rate of 1 ftmin, how fast the water level rising when the depth at the deepest point is 5 ft (Round your answer to five decimal place) ftmin 6 12 16 6 3 T 9 Question
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Rewrite the following complex numbers in its polar form rcis (0), where 0 0 2. Give exact answers only. 1 a. 8 b. 3i A c. 99i r d. 2 3i r
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dy Use implicit differentiation to determine given the equation x y siny. dx dy dx 2x D By cos(y)
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Find the horizontal asymptote y 1x 2 Ny 2 x 3x 5
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Solve the following equation. 2 x 4x150 Larger x type your answer... Smaller x type your answer...
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lim ( Consider 2 sin(2t) to sin(2t) 2 t cos(2t) ). Using a table of values, the limiting value is (Enter DNE if the limit does not exist.) Submi
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15 PI For the following differential equation, determine (without solving) an interval on which the solution of the equation is certain to exist and be unique. Justify your answer. (int)yyccost, ()2
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2. Find the equivalent for the trig identity expression 1sinx cotx a. cosx b. sinx c. tanx d. cotx
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28. cos 314 40 A. .7030 B. .7112 C. .7030 OD. 7112
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Find the singular points and then classify each one as a regular or irregular point. (x22x3)y x(x 2)y (x 1)y 0
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Finance. A person wishes to have 22,600 cash for a new car 6 years from now. How much should be placed in an account now, if the account pays 5.4 annual interest rate, compounded weekly
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d f Let 6 sin(y) dy Find the particular solution to the above differential equation that satisfies the following initial conditions. 8 5 7 3 f(y)
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Use trigonometric identities to establish the identity tan(t) cot(t) 1 sin(t) cos(t) This question requires a file submission, so I am asking you to show at least 3 steps to get full credit.
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Find the sine and cosine of the angle 8. (Calculate r from the Pythagorean Theorem.) y sin(0) COS(A) 6 X (10, 24) i
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Question 6 4 Without graphing the function y 7 cos(9x), determine its amplitude and period. Leave answers in exact form type pi for . amplitude period Submit Question
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A particle moves along a line. At time t (in seconds), the particles velocity is v(t) t26t8 (in ms). Find the particles net displacement and total distance traveled over the time interval 0,5. Net displacement Total distance traveled (m) (m) To understand the terms net displacement and total distance travelled, imagine a particle that moves
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1. Find the general solution to the differential equation dy 2xy. dx
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Find the higherorder derivative. (6logy(x4)) Question 19, (6 log,(x4)) dx
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Suppose that f(600) 6000 and f(600) 10. Estimate each of the following. (a) f(601) (b) f(600.5) (d) f(598) (e) f(599.75) (c) f(599) (a) f(601) (Simplify your answer. Type an exact answer.)
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The assets and liabilities of a salesperson are listed below. Home Value 264,500 Retirement Portfolio 473,906 Credit Card Balances 58,236 Bank Loan 35,275 Mortgage 187,632 Car Value 22,750 Investments 139,664 Home Furnishings 23,100 What is the value of the liquid assets
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Let f(x) 4x 2 x 4x Determine the derivative of f. df dx Determine the slope of f at x 9. f(9)
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Question 15 (Multiple Choice Worth 5 points) (05.05 MC) Given x what is the exact value of cos(2x) 3 1011 12 O 132 3 2
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If sin x 52. Find the value of csc x. 15 25 53 35
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Given a solid bounded by the paraboloid z 162y in the first octant. Draw the projection of diagram using mathematical application (GeoGebra etc.) from a. xaxis (2 m) b. yaxis (2 m) C. zaxis (2 m) Hence, find the volume of the integral from each projection. a. xaxis (8 m) b. yaxis (8 m) C. zaxis (8 m)
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12) Write each expression in radical form. 7 12) (5b)4 A) (b) B) (106) C) (5b) D) (2b) Simplify. 13 13) (64x4) A) x4 B) 1024x15 C) 512x6 D) 6.x Write each expression in exponential form. 14) 14) 7m 15) 1 A) (3m) 2 B) m D) m C) (7m) Simplify. 3 15) (x10)5 A) x5 C) 10x3 B) 27x D) x 16 Write each expression in radical form. 1 16) (6b) A) 6b C) (7b)
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Part 1 Difference Quotient f(x) 1 x4 1 If h 0, then the difference quotient can be simplified into the form (x4)(ABh) That is f(xh) f(x) h 1 (x4)(ABh) where the coefficients A, and B can be functions of x or just constant terms. Find these coefficients A B 0 (Note Its possible for one or more of these coefficients to be 0.) Part 2 Derivative
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Save Jerome will be buying a used car for 10,000 in 3 years. How much money should he ask his parents for now so that, if he invests it at 10 compounded continuously, he will have enough to buy the car Jerome should ask for (Round to the nearest cent as needed.) mou
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on the given interval. (Ente Find the number c that satisfies the conclusion of the Mean Value Theorem your answers as a commaseparated list. If an answer does not exist, enter DNE.) f(x), 0,9 C Graph the function, the secant line through the endpoints, and the tangent line at (c, f(c)). 4 3 2 2 4 8
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Watch on YouTube SOH CAH TOA a B C b Note Triangle may not e drawn to scale. Suppose a 6 and b 11. Find an exact value or give least two decimal places sin(A) COS(A) tan(A) Submit Question esc F1 2. F4 F5 2 F2 80 F3 a olo 50 674 3 72 1 tab Q aps lock A W E R T S D LL F
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Suppose that lim f(x)9 and lim g(x)3. Compute the limits that exist. X4 X4 f(x) a. lim f(x)3g(x) b. lim f(x)g(x) c. lim 4f(x)g(x) X4 X4 x4 d. lim x4 f(x)g(x) a. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. lim f(x)3g(x) 0 x4 (Type an integer or a simplified fraction.) B. The limit lim f(x)
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Question 2 What is the area of the region in the first quadrant enclosed by ye A 0.516 sq units B 0.240 sq units 0.480 sq units D 1.032 sq units and the line y0.5.
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Given the Exponential Function, determine the Initial Value and Rate of Change as a Percent for each of the following. Initial Value Growth or Decay Rate as a Exponential Function 1850 400 Growth p(t) 1850(5) 3746 12 Growth f(x)3746(1.12) 4060 6 Decay d(t)4060(0.94) 3421 14 Decay f(x) 3421(0.86) 4375 25 Growth h(x)4375(1.055) 645 9 Growth 9(x)
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Part I Evaluate f(0) A. Identify the function that will be used when x 0. (1 point) B. Find the value of this function when x 0. (1 point) Part II Graph f(x). 5. 5 5 A. Graph the first function completely. (1 point) B. On the same graph you used to answer part (A), graph the second function completely. (1 point) C. Identify the value of x at
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Suppose that f(600) 6000 and f(600) 10. Estimate each of the following. (a) f(601) (b) f(600.5) (d) f(598) (e) f(599.75) (c) f(599) (a) f(601) 6010 (Simplify your answer. Type an exact answer.) (b) f(600.5)(Simplify your answer. Type an exact answer.)
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Find the solution to x y if x(0) 0 and y(0) 8. x(t) y(t) help (formulas) help (formulas) y 12x4y
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Sketch the region of integration and change the order of integration 22 f(x, y)dydx
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The (bounded) area between the curves f(x) 15x4 and g(x) 15a is . (Your answer should be a number.)
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4. Explain how to use the unit circle to evaluate a trig ratio for an angle with negative measure. 2T For example sin(45) or cos 3
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Given the autonomous system dx dy I, dt dt a. find the critical points. b. solve the phase plane equation and classify the critical points, analyzing trajectories of the syst c. find the general solution to the system and determine its stability, analyzing integral curves of system.
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Consider the function 1 f(x) (xx) 1x1 x2 subject to 2x1 x2 1 Find the range of values of constant y so that a) f(x) has a unique global minimum b) f(x) has a local minimum c) f(x) has a local maximum
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Make use of Laplace transform to solve the following differential equation that satisfy the y10y9y5t y(0)1 y(0) 2 given initial conditions
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Solve the linear differential equation y 3y sin 2x
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Evaluate. 2 x(x1)5 dx 1 2 Sx(x1)5 dx 1
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Find the extreme values of the function and where they occur. 17) y 1 x1 A) None B) Local maximum at (0, 1). C) Local maximum at (1, 0), local minimum at (1, 0). D) Local maximum at (1, 0), local minimum at (1.0)
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23. Find 2u v when u 4, 3 and v 1, 2 a. 7, 8 b. 3, 5 c. d. 1, 9
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Encuentras los interceptos y las asntotas, completa la tabla, y luego bosquejas la grfica de Expresar la expresin factorizada Intersecciones con x Intersecciones con y Asntota horizontal Asntota vertical Tabla de valores X Y f(x) 3x6 x2x8 x
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If investment A has an annual return of 4 with continuously compounded interest, and Jane has 500 after 4 years, how much money did she start out with A(t) is the amount of money at t years. O 426.07 420 O 410 350
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A cumulative percent of Americans in each credit score range as of April 2021 is summarized with the Ogive curve. If the minimum credit for mortgage the care is 620, which minimum percentile should the potential buyers fall in (Use the Ogive). 20th,30th, 50th, or 70th use numbers only 100.0 BOOK Cum Rel Frequency 600 400 200 6.0 0 200 400 600 800
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If a 20 and c 28, find the missing sides and angles in the right triangle, where a is the side opposite of angle A, b is the side opposite of angle B and c is opposite of the right angle, angle C.
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63.43 0.08852 177.24 0.823958 Submit Answer Retry Entire Group 8 more group attempts remaining more group
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Calculate the derivative of a function, A(r) r when r8
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PROBLEM 6. For a function f R R, f(x) xe5x 3p find the rightsided slant asymptote, 5p examine the monotonicity and find local extreme values, 2p verify if it is injective.
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Maintenance money for an athletic complex has been sought. Mr. Kendall, the Athletic Director, would like to solicit donation to cover all future expected maintenance costs for the building. These maintenance costs are expected to 1.5 million each year for the first five years, 1.8 million each year for years 6 through 10, and 2 million each yea
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Determine a region of the xy plane for which the given differential equation would have a unique solution whose graph passes through a point (xo, yo) in the region. C dy dx 33 xy
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Refer to the graph of y f(x) xx shown. a) Find the slope of the secant line joining (3, f(3)) and (1, f(1)). b) Find the slope of the secant line joining (3, f(3)) and (3h, f(3 h)). c) Find the slope of the graph at (3, f(3)). d) Find the equation of the tangent line to the graph at (3, f(3)). a) The slope is 3. (Type an integer or a simplified
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Textbook Videos An inverted pyramid is being filled with water at a constant rate of 55 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 5 cm, and the height is 13 cm. Find the rate at which the water level is rising when the water level is 7 cm. h b cmsec b
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