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february 2020
08

Mathematics Questions and Answers February 08, 2020

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O Points 0 of 1 The amount of carbon14 present in a paint after t years is given by y yo 0.00012 The paint contains 28 of its carbon14. How old are the paintings The age of the paintings is years (Round to the nearest year)

Find the linear approximation of f(x) ln x at x 1 and use it to estimate In(1.28). L(x) In(1.28)

Consider the set of all rectangles that lie in the first quadrant, have one edge along the posi tive xaxis, one corner at the origin, and the diagonally opposite corner on the curve y e. Find the dimensions of the rectangle in the set that has the largest area (remember to justify you have a max).

Let y tan(5x8). Find the differential dy when x 4 and dx 0.2 Find the differential dy when x 4 and dx 0.4

Consider Determine the derivative of y with respect to x. y 5x y x7 x 2y

Find , and T, N B for the given space curve. beginaligned r(t) (In (cos t)10 mathbfi1mathbfj(9t) mathbfk,pi 2

on the curve y x x x 1 where the tangent Determine the points on the curve y x is horizontal.

your answer. No x . Decimal answers MUST be correct to THRE decimal places. Question 8 log(3x 1) 2 1 pts

Which expression is equivalent to 16x11y8 81x76 Assume x 0 and y 0 O O 9 3 4xy g

two triangles, or no triangle at all. Solve the triangle that results. A99, a 14, b22 Select the correct choice below and, if necessary, fill in the answer boxes to complete yo (Round side lengths to the nearest tenth and angle measurements to the nearest degree OA. There is only one possible solution for the triangle. The measurements for the re

11. Given the polynomial function f(x)4xxx2, find a. Determine the maximum number of real zeros that the polynomial may have. b. Use Decartes Rule of Signs to determine how many positive and how many negative zeros each polynomial function may have. Positive Negative C. List all the potential rational zeros of the polynomial function.

Quiz Me Quiz Me 6.25 Solve applications involving partial derivatives. This quiz 5 point(s) possible Question 4 of 5 Resume later This question 1 point(s) possible Submit quiz A sports company has the following production function for a certain product, where p is the number of units produced with x units of labor and y units of capital. Complete

A room contains 8 people, each of a different age. The people leave the room in random order, one at a time. What is the probability that they leave the room in ascending order of their ages (youngest to oldest) The probability that they leave the room in ascending order of their ages is (Round to six decimal places as needed.)

f(x)3x2x g(x) 2x3 Find fg and fig. Then, give their domains using Interval notation. (f g) (x) Domain off 90 (fg)(x) Domain of fg

An office copier has an initial price of 2,300. A service contract costs 200 for the first year and increases 60 per year thereafter. It can be shown that the total cost of the copier after n years is given by C(n) 2,300170n30m. C(n) The average cost per year for n years is given by C(n) n (C) When is the average cost per year at a minimum, and

Using the information from the table below, draw the graph for a function f. Label all intercepts, horizontal and vertical asymptote(s), inflection point(s for full credit. Domain of f r and y coordinates of r intercepts of f x and y coordinates of yintercepts of f Equation(s) of vertical asymptote(s) Equation(s) of horizontal asymptote(s)

A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, 5.3 mi apart, to be 35 and 51, as shown in the figure. 35 51 A NOTE The picture is NOT drawn to scale. Find the distance of the plane from point A. distance from A Find the elevation of the plane. mi height mi 5.3 mi B a

If A2312 and B346k are the two vectors, find the resultant vector. 576 576 57 6 Osil76

Your Aunt Ruth has 540,000 invested at 6.5, and she plans to retire. She wants to withdraw 40,000 at the beginning of each year, starting immediately. How many years will it take to exhaust her funds, i.e., run the account down to zero O a. 24.55 Ob. 28.41 O c. 25.65 O d. 30.62 Oe. 27.58

Find the slope of the tangent to the curve y 1lnz at the point (1, 1). 1 1

Paul applies to sell souvenirs at a sporting event. He may be assigned to any of sections A through E, or he may be rejected. The table shows the probabilities of his being assigned to a particular section or being rejected. a) What is the probability that Paul is assigned to section B b) What is the probability that Paul is not assigned to

Q G www.awu.aleks.comalekscgixisl.exe1ouIgNsikr7j8P3JH1Bcn9FmfTjhEDJIOHE1xJTn4Drq13pMXuDJubk5exL9xBNgQlkoCE4DloeBTCd4V11EiUEKTsk5pblFxa8.. OGRAPHS AND FUNCTIONS Finding outputs of a onestep function that models a realworld... 16 Briana V Jina is driving on a highway. She uses one gallon of gas every 20 miles she drives. The distance, D (in

Let P (a) represent the population (in thousands) in a region a years since year 1950. Use function notation to represent that the population is 540,000 in the year 1978. O P(28) 540 O P(1978)540 O P(28) 540,000 OP(1978) 540,000

y log(log2x) The slope of the tangent line to the given curve at its xintercept is 1 2(In 2) 1 2x (log 2) 0

Assignment4 Problem 7 (1 point) Consider the function f(x) 12 30x4300x 2. f(x) has inflection points at (reading from left to right) D, E, and F where D is and E is and Fis For each of the following intervals, tell whether f(x) is concave up (type in CU) or concave down (type in CD). (, D D, E) E, F) F,00) Note You can earn partial credit on

Instructions Analyze each function by following the Curve Sketching Algorithm (p. 192). Identify all key intervals and features of the function concisely and clearly. Sketch each graph (by hand). Question 1 (domain range 1, intercepts 2 marks, asymptotes 1, intervals of increasedecrease 2, minmax 2, points of inflection 2, sketch 2) yx316x

Suppose y sin x. What is the xvalue between 2 and 4 corresponding to a yvalue of 1

17. Find the radius of convergence for (1) xk k1 k (a) R1 (b) R 0 (c) R 2 (d)

Determine the open intervals on which the graph of f(x)3x7x3 is concave downward or concave upward. concave downward on (0,0) concave upward on (00, 0) concave downward on (0,co) concave upward on (0,1) concave downward on (1,co) concave upward on (00,00) concave downward on (0,0) concave upward on (0,co)

For the given function, (a) find the slope of the tangent line to the graph at the given point (b) find the equation of the tangent line. 9 h(x)atx7 (a) The slope of the tangent line at x 7 is

Write the expression below as a single logarithm in simplest form. 3 log 4log 4

Let g(x) 173x cos(21). Use the 2nd derivative to determine whether the graph of g is concave up or concave down at the point where x 0.12. O Concave up O Concave down There is an inflection point at x0.12. O The graph has no concavity.

If 32x1 3x5, what is the value of x 2 3 O4 6

Let f(x) 3 cos x for 0 x

Determine the number of terms (n) in each arithematic series 0) a 11, a 44, S 330

173 Simplify. (8221 12) A) x (8x 1) O C) 2x x O E) 2x 18x4 O B) 8x x D) (2x4) (x 1)

Use Stokes Theorem to find the circulation of the following vector field around any simple closed smooth curve C. F (yz,2xyz, 3xyz2) The circulation is

All but one of the functions is differentiable for all real values of x. Which function is not differentiable for at least one real value of x Ax) x1 ) 8(x) 1 h(x) x (x) x3x

Let F(x) f(x) and G(x) (f(x)), You also know that a4 6, f(a) 3, f(a) 6, f (a) 3 Then F(a) and G(a)

f(x) 3x4 g(x)4x3 Find f g and fg. Then, give their domains using interval notation.

Let g(x, y) cos(x2y). (a) Evaluate g(2, 1). g(2,1) (b) Find the domain of g. 1 x 1, R 2 2 T 2 x 2y TC 2 2 x 2, 1 y 1 1 x 2y 1 (c) Find the range of g. (Enter your answer using interval notation.)

Solve for x where Tx 2 sinx cosx 0 cosx T T

Score on last try 0.5 of 1 pts. See Details for more. Next question Get a similar question You can retry this question below Consider the function (a) 50 11, 45 11. The absolute maximum of (a) (on the given interval) is at 0 and the absolute maximum of f(x) (on the given interval) is 11 The absolute minimum of f(a) (on the given interval) is at

Graph the polar equation. Identify the name of the shape. 40 r 4 sin (50) a) Identify the shape rose curve b) Identify the number of petals 20 x c) Identify the length of each petal 7 X d) For what values of 0 within 0, 2x) mark the maximum value of r e) Plot the tip of each petal below. (no need to connec them) 65

(10 points) A spherical balloon is inflated so that its volume is increasing at the rate of 20 cubic cm per second. What is the instantaneous change in surface ds area, of the balloon increasing when the radius is dt 4 40 cm Use V Tr and S4r. 3

Problem 5. (10 points) (Implicit Differentiation) Consider the curve ey 32 y 65. a. Find the equation of the tangent line at the point (0,8). b. There are two points on the curve with xcoordinate 0.1. Use part a. to estimate one possible ycoordinate of the point (0.1, y).

3. Sketch the graph of a function that satisfy the following conditions f(0) 0, f continuous and even. f(x) 2x if 0 3

Find the magnitude and the direction of the resultant vector. (6,2) 1M (10, 9) A. 8.06, 60.26 B. 19.42, 34.51 C. 8.06, 29.74 D. 19.42, 55.50

A game is played using a foursided wooden top, with one of four letters on each face, A, B, C, or D. Players compete for a pot of tokens. A player spins the top and takes one of the following actions, depending on which letter faces up. If A faces up, the player neither adds nor subtracts tokens from the pot. If B faces up, the player wins the

5. Find the rate of change of f(x) x on the interval 1 x 2. 6. Find the rate of change of f(x) x 4x 2 on the interval 0, a.

Consider the following function. f(x) x 32x 2 (a) Find the critical numbers of f. (Enter your answers as a commaseparated list.) x (b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) increasing decreasing (c) Apply the First

Find a b, 9a 7b, lal, and la bl. (Simplify your vectors completely.) ab a 91 8j7k, b 7i 9k 9a 7b 2 a a bl

Charlotte invested 33,000 in an account paying an interest rate of 72 compounded continuously. Alyssa invested 33,000 in an account paying an interest rate of 7 compounded daily. After 19 years, how much more money would Charlotte have in her account than Alyssa, to the nearest dollar

Find the real solutions of the following equation. 3 3 4 15 4 x10 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The solution set is (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate

Question 9 0.431 pt 3 94 Details Find the value within 0, 2) for function f(0) 9 sin(100) to reach its maximum value. 0 Question Help Message instructor Submit Question

Let f(x, y) 6x2 2233y6zy. This function has critical points at (0, 0) and (3, 3). Determine if these points are a local maximum, local minimum, or a saddle point. (0, 0) is a Select (3, 3) is a Select

Let s(t) 6t327t 180t be the equation of motion for a particle. Find a function for the velocity. v(t) Where does the velocity equal zero Hint factor out the GCF. t and t Find a function for the acceleration of the particle. a(t)

5. What type of conic section is the given equation 3x 4y4y6x120 a. circle b. parabola c. ellipse d. hyperbola

4. Jerry invests 6000 at 7.5a, compounded annually. a) Determine the equation of the amount, A, after t years. b) Estimate the instantaneous rate of change in the value at 10 years. c) Suppose that the interest rate was compounded semiannually instead of annually. What would the instantaneous rate of change be at 10 years

Use Pascals Triangle to find the binomial coefficient. 63

12. Determine the minimum of f(x)(10x 3x x 5) starting at x3 and using a step size A5.0. Using region elimination expanding pattern bounding plus six steps of golden section.

5. Let f(x)2r tanx I COS I Write an equation of the tangent line to the curve at the point P(0, 1).

Let h(x) 2x3 Determine the derivative of h at x 5. (h) (5)

3) Find eigenvalues and eigenfunctions of the boundary value problem xy Xy, y(1) 0, y(2) 0.

The radius of a sphere is increasing at a rate of 2 centimeters per hour. Determine the rate of change of the spheres surface area when the radius is 25 centimeters. square centimeters per hour

7. Z4 A. 2410i B. 2410i C. 24 10i OD. 24 10i

. Use the Cramers rule to solve the system of equations given below 4x y 23 4x 9y15

Assume that the rate of evaporation for water is proportional to the initial amount of water in a bowl. Jill places 1 cup and 8 ounces of water outside and notices that there is cup of water 6 hours later. After how many hours, t, will there be less than 1 oz left Let W(t) be the amount of water in the cup, and let t be measured in hours. Round

Solve each trig equation below. (All angles are in radians.) 17. cotxsin xsec x cscx for 0x2 (58) 18. 4sin2x4cosx50 for 0x27 (58) 19. sin x2 sin x cos x 0 for 0x 2 (58)

Find the indefinite integral by making a change of variables. (Use C for the constant of integration. xx6 dx

12. Find the roots of this function f(x)x 2x 2. A. 1 2 and 12 B. 1i and 1 i C. 122 and 12i2 OD. 12i and 1 2i

Using the MACRS rates from the following table, what is the book value of a 3,000 computer after 2 years Year MACRS Rate 12345 20.0 32.0 19.2 11.52 11.52 book value Round to the neare hundred

Which of the expressions ab 1. 4 a.b II. 2 III. ab are always even if a and b are distinct positive even natural numbers Only B) C) I ve Il D) I ve III E) Il ve III

2 Suppose the line y 5x 9 is tangent to the curve y f(x) when x 3. If Newtons method is used to locate a root of the equation f(x) 0 and the initial approximation is x 3, find the second approximation x2

Describe the surface in R represented by the equation x y 4. This is the set (x, 4x, z)x ER, ZER which is a horizontal plane that intersects the xyplane in the line y 4 x, z 0. This is the set (x, 4x, z)x ER, ZER) which is a vertical plane that intersects the xyplane in the line y 4x, z 0. This is the set (x, 4x, z)x ER, ZER) which is a

Suppose x and y are both differentiable functions of t and where c is a constant. x y c5 dy dx Determine given 3, x3, and y 1. dt dt dy dt

Find the slope and yintercept of the line. (If an answer does not exist, enter DNE.) 7x8y 16 slope 78 yintercept (x, y) 0,2 Draw its graph. O V No Solution 10 9 8 765 10 Graph Lay Clear All 9 8 Line 1 7 Delete 6 5 Point 1 Fill 4 3 Point 2 2 3 2 1 2 3 4 5 567 6 7 8 4 5 6 7 8 9 10

Expand the binomial by using Pascals Triangle to determine the coefficients. (2v 3)6

210 e8 , For the function f(x) find f1(x).

Apps (93) YouTube BITName Manag... MyUB Bullseye powered... Content Buffalo to New Yo... MTH 131, section... Ebook Economi... B 3. 1 Points DETAILS WANEAC7 7.4.013. Calculate the producers surplus for the supply equation at the indicated unit price p. HINT See Example 2. (Round your answer to the nearest cent.) p 102q p 36 Need Help Read It MY

Time Taken00242 Priscilla Puentes Attempt 1 Question 15 (3 points) What is the average value of f(x), between x 1 and x 5 for f(x) 4x 1 A 3.04 Unit Test Integral Applications Part 2 Pool 6 Question 16 (3 points)

Consider the function below. f(x)4x24x 2 (a) Find the critical numbers of f. (Enter your answers as a commaseparated list.) x (b) Find the open intervals on which the function is increasing or decreasing. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) increasing decreasing (c) Apply the First Derivative Test

Problem 5. Find the standard form of the equation of the circle x y 2x 12y 12 0. Then, state the center and radius of the circle.

The height y, in feet, of a football x seconds after it is thrown is modeled by the equation y16x2 24x 1. Wha information does the zero of the equation 616x2 24x 1 represent O the height of the ball after 6 seconds O when the ball is 6 ft above the ground the initial upward velocity of the ball Othe horizontal distance traveled by the ball

The U.S. Energy Information Administration projected that imports of petroleum products in 2005 would be 4.81 quadrillion Btu and would increase by 5.47 each year through 2020.

Consider the measurements shown. The most precise value is highlighted for each measurement. 9.3478 m 2.73 m What place value must the answer be reported to 1. ones place 2. tenths place 3. hundredths place 4. thousandths place

Basic Rule of Differentiation Score 047 027 answered Question 22 9 Let g(t) 2 x9 Determine the value(s) of t, if any, for which g has a horizontal tangent line. Og has a horizontal tangent line at t Og has no horizontal tangent lines. Submit Question esc F1 1 Q 3 02 80 F3 54 8 5 MacBook All W E R T A S D F Z X C 6

A tank of water in the shape of an inverted cone (i.e. circular base on top) is leaking water a constant rage of 1 ft3min. The base radius of the tank is 5 ft and the height of the tank is 14 ft. (a) At what rate is the depth of the water in the tank changing when the depth of the water is 6 ft (b) At what rate is the radius of the top of the

2 1. A 1000 L tank is draining such that the volume V of water remaining in the tank after t minutes is 1000 1 1000(11) t Find 60 the rate at which the water is flowing out of the tank after 10 min.

(1 pt.) Given the logistic function f(t) 3 find the value of t where the growth rate of the 12e 0.519 function is maximum. Leave your answer with 3 decimal places.

48. Find the solution set of this equation. x3xx1 A. 1 B. 2 C.3 D. 2, 1

dy Use implicit differentiation to find given the equation sin(xy) y. dx

Use reference angles to find an arbitrary angle for the tan 240 degrees. a. 120 b. 60 c.330 d. 18

Use the figure to find the exact value of the following trigonometric function. tan (28) tan (29)(Simplify your answer.) 15 17

5. Let C be the curve of intersection of the hyperbolic paraboloid z xy and the cylinder x y 1. (1) Find the curvature of C at the point P(1,0,1). (2) Find the osculating plane at the point P(1,0,1).

4. (3 points) Find the particular solution of the differential equation that satisfies the initial condition(s) f(x) sinx, f(0) 1, f(0) 6.

write the points that the graph on the dont exis

31. Write 3 loga 4 loga 7 as a single logarit A. loga 448 B. loga 84 12 I C.loga 7 D. logo 64 7

p 8 No, because p cannot be negative Yes, because each value of s corresponds to exactly one value of p Yes, because the relation defines p in terms of s No, because some values of p correspond to more than one value of s

Find the equation of the line tangent to the graph of x3 y 5xy 11 at (1, 3). The equation of the tangent line is

Showing 100 - 200 of 1506

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