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mathematics
february 2020
08

Mathematics Questions and Answers February 08, 2020

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(f) A rectangular flower garden with an area of 30 m is surrounded by a grass border 1 m wide on two sides and 2 m wide on the other two sides. What dimensions of the garden minimize the combined area of the garden and border by 15

Nevaeh invested 80,000 in an account paying an interest rate of 5 compounded continuously. Aaliyah invested 80,000 in an account paying an interest rate of 53 compounded monthly. After 13 years, how much more money would Aaliyah have in her account than Nevaeh, to the nearest dollar

Quilt squares are cut on the diagonal to form triangular quilt pieces. The hypotenuse of the resulting triangles is 36 cm long. What is the side length of each piece (Round your answer to he nearest hundredth).

Let h(x) x g(x). Given the following information, compute h (3). g(9)7, g(9) 3, 9(3) 5, g(3) 8, 9(2) 4, g(2) 9 Write your exact numerical answer in the box below.

Sketch the region enclosed by y 4x and y 9x2. Decide whether to integrate with respect to x or y. Then find the area of the region.

Use the Laws of Logarithms to expand the expression. log3(2x)

Graph the rational function. x10x2 f(x) 2x4 Start by drawing the asymptotes. Then plot two points on each piece of the graph. Finally, click on the graphafunction button 14 X Start over

55 4 4 3 2 3 2 1 2 3 2 In the above graph of y f(x), find the slope of the secant line through the points (4, f( 4)) and (3 ).

(x)x2 b) Find f(x) d) Graph f(x)

(The Cauchy Problem for the Diffusion Equation). We consider the initial value problem for a onedimensional diffusion equation with no sources or sinks U KU

What is the binomial expansion of (x2y) O 2x7 14xy 42x5y2 70x4y3 70x3y 42x2y5 14xy 2y O x7 14x6y42x5y2 70x4y3 70x3y 42x2y5 14xy6y7 Ox77xy21x5y2 35x4y3 35x3y4 21x2y5 7xy y7 Ox7 14x6y84x5y2 280x4y3 560x3y672x2y5 448xy6 128y7

(a) Most calculators can find logarithms with base following. (Round your answers to three decimal places.) logs(16) log log and base e. To find logarithms with different bases, we use the Change of Base Formula B.To find logs(16), we w (b) Do we get the same answer if we perform the calculation in part (a) using In in place of log Yes, the result

A circle is inside a square. The radius of the circle is increasing at a rate of 1 meter pe day and the sides of the square are decreasing at a rate of 1 meter per day. When the radius is 6 meters, and the sides are 16 meters, then how fast is the AREA outside the circle but inside the square changing The rate of chance of the area enclosed

ANSWERS This exercise involves the formula for the area of a circular sector. Find the area A of the sector shown in each figure. (a) A 5.37 (h) X 79 7 SALGT

Textbook Videos Find the critical numbers of the function f(z) 12x75x your answers to three decimal places. x is a Select an answer X is a Select an answer x is a Select an answer Question Help 1003 3 and classify them. Round

flaming stone over a castle wall. It is mounted on a Small hill and has a parabolic trajectory (neglecting air resistance.) Once it crashes into the ground on the other side of the castle Wall, it comes to rest. This motion is described by the function below, where X measured in meters, represents horizontal displacement from the launch position

1 59F Cloudy Score 400490 3649 answered Question 29 Find all solutions of the equation 2 sin x 3 0. The answer is A k and C Dk where k is any integer, 0 A C 2, A C B D Submit Question

(a) Sketch 0 in standard position. Then sketch an angle between 0 and 2x that is coterminal with 0. 4 G

6. Find the rate of change of f(x)x2x on the interval 1 x 9. (3 points, 2 points for the processsteps and 1 point for the final answer with correct units)

Find the composite function for the given functions. 2) f g for f(x)7x 12 and g(x) 4x1 A) 28x 5 B) 28x 47 C) 28x 11 D) 28x

In 2005, the world population was 6.4 billion. The exponential growth rate was 1.2 per year. Fin the exponential growth function.

40. Find the common difference in the arithmetic sequence 2, 7, 12, 17, 22,... A. 11 B. 5 C.5 D. 10

Find the Radon Transform (sinusoidal sine wave graph) for coordinate (3,5)

Find the directional derivative of f(x, y) sin(x 2y) at the point (2,2) in the direction 6. The gradient of fis Vf( V(2,2)( The directional derivative is

10. Given the function f(x) (x1)(x5) x3 a. Find the domain of fin interval notation b. Find the asymptotes of f(x), as well as any holes c. Find the intercepts of f d. Locate at least one point on each side near the vertical asymptote e. Sketch the graph of f. Label the intercepts, asymptotes, and any holes.

Let F(x) f(x) and G(x) (f(x)). You also know that a 11, f(a) 2, f(a) 3, f (a) 11 Then F (a) and G(a)

The graph of which function has a minimum located at (4,3) O f(x) x 4x 11 O f(x)2x16x35 Of(x) x4x5 O f(x)2x16x 35

Score on last try 0 of 10 pts. See Details for more. Next question Get a similar question You can 4z If f(x) find 6z2 f(x) Holpy Video

Find all solutions to the equation below log3(3x2)log3 x log3(x2) 1 x 6 is the only solution There is no solution x 1 or x6 Ox1 is only solution

6. A flying distance of 800 km is 10 cm on a map. What is the scale factor 1 km 100 000 cm So, 800 km cm diagram measurement scale actual measurement Leave scale factor as a fraction in lowest terms

A 6 foot tall woman walks at a rate of 6 feet per second toward a lamppost that is 15 feet tall. Determine the rate of change of the tip of the womans shadow when she is 9 feet away from the lamppost. feet per second Determine the rate of change of the length of the womans shadow when she is 9 feet away from the lamppost. feet per second

recursivel 48an and ai 0 an is bounded above by 17 using mathematical i an is an increasing sequence using

Textbook 2 5 4 32 1 1 2 Videos 3 4 5 The function graphed above is Increasing on the interval(s) Decreasing on the interval(s)

You want to estimate the mean cost for repairing microwave ovens. A random sample of 87 microwave ovens gave a mean repair cost was 54.70 and a standard deviation of 10.50. Find the margin of error for a 99.5 confidence interval for estimating the mean repair cost for all microwave ovens. Report your answer accurate to one decimal place. E Answer

5 If f(x) sin x, find f(x) 4 5(sin x) (cos x) Find f(2) 5(sin 42) ((cos) (21) 1.42) You gave an equation, not an expression. syntax incomplet

For questions 9 and 10, find the absolute maximum and minimum values of f if the domain is the indicated region R. 9. f(x, y) x 2xy 3y R (x, y) 2 x 4, 1 y 3. (Hint To determine boundary extrema, consider the following functions of one variable f(x, 1), f(x, 3), f(2, and f(4, y).) 0. f(x, y) x3xy y 2y 6x R the triangular region with

A rotating light is located 12 feet from a wall. The light completes one rotation every 3 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the lights angle is 25 degrees from perpendicular to the wall. light wall

Find the domain and range of the function graphed below. 5 3 2 1 27 54321 1 2 3 4 5 1 2 3 4 5 Domain Range

Consider the function whose graph is plotted below. 6 1.0 List the zvalues for which f(x) appears to not be differentiable. T (Enter the values as a commaseparated list. If there are no such values enter non

A company manufactures 2 models of MP3 players. Let x represent the number (in millions) of the first model made, and let y represent the number (in millions) of the second model made. The companys revenue can be modeled by the equation R(x, y) 140z 170y2z 4y zy Find the marginal revenue equations Rz(x, y) Ry(x, y) We can achieve maximum

Let A(x) p(u) du. The figure below illustrates the graph of p. 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 18 1 4 1 1 1 1 1 4 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 1 1 T 1 1 1 1 1 1 On the interval 0 x 6 A(x) has a local mimimum at x A(x) has a local maximum at x 1 1 1 8

Solve the given initial value problem. x(t) 68 86 x(t), x(0) 4 6 Question content area bottom Part 1

21 1 point Graph each function. f(x) x2x8 X2 p 27 3 ..p. ca 1 21 E 2 2 3

. Consider the function defined by f(x) x bx cxd. (a) Find f(x) using first principles. (b) The graph off has a local maximum and a local minimum point. Show that b2 3c

The population of rabbits (in thousands) in a forest at time t months is modeled by the equation R(t)50t2et8 where t 0 Determine the final number of rabbits in the forest by evaluating the limit at t approaches infinity 8 the population continues to increase as t increases 8000 50

23 3t 5t, y t 4 at t 1. 5. Find the equation of the tangent line to the curve at the specified value of the parameter x 3

You are considering investing in a bank account that pays a nominal annual rate of 7, compounded monthly. If you invest 3,000 at the end of each month, how many months will it take for your account to grow to 310,000 a. 72.18 Ob. 81.11 O c. 90.84 O d. 93.27 O e. 95.70

HM 13 Mean Value Theorem Score 3.339 39 answered Question 4 Score on last try 0.33 of 1 pts. See Details for more. Next question Get a similar question You can retry this question below If we apply Rolles Theorem to the function f(z) 2x2 821 on the interval 0, 4, how many values of c exist such that f(c) 0 What is the value of c If we try to

Solve the following Equations for 0 0 360 1.) sin(2x) (3) sinx 0 2.) cos sin 0 0

For the function f(z) 2x 2, write Newtons formula as Zn1 F(In) In f(in) f(Zn). for solving f(x)0. Type in xn for n In1

Find the exact value of cot W in simplest form. 20 Y X 29 W 21

Find the exact value of each expression. (a) tan(arctan(7)) (b) arcsin(sin(54))

core on last try 5 of 10 pts. See Details for more. Next question (x) 5 find 5 (x) Get a similar question You

Let g(x) (x8x3) Determine the equation of the tangent line to g at x 7. Report the solution using slopeintercept form.

Determine the slope of the tangent to the graph of y (x 3x 2)(73x) at (1, 8).

(b) Obtain the natural representation of the circular helix r(u)(a cos u, a sin u, bu), a0, b0,0 leq u

Watch help video Find the exact value of cos T in simplest form. 7 V10

3)5 he missing coordinates of the points that lie on the of yx and the corresponding points that lie on the of f(x) (x3)5. ts that lie on the raph of y x Corresponding points that lie on the graph of f(x) (x3)35 lify your answers.) (Type ordered pairs. Simplify your answer.) () (0) (1, ) main of f(x) is our answer in interval notation.)

wer in the space provided 5) Solve the triangle. Round your anwer to the nearest tenth. 110 3 4 B C 25

Find the equation of the tangent plane to the surface z7x3y 2xy at the point (3, 1, 1698). N

ate the given binomial coefficient. 33)(3) A) 10 33) B) 20 C) 120 D) 40

Vertical asymptotes at x3 and x6, x intercept s at (5,0) and (3,0), horizontal asymptote at y5

8. Find the cos 2x if cos x 47 2 17 a. 49 16 b. 49 32 C. 49

(1 point) Compute the curl of the vector field F 2y3 sin(x) cos(z) k curl

Textbook Consider the function f(z) 17z on the interval 3, 3. Find the average or mean slope of the function on this interval, i.e. f(3)(3) 3(3) By the Mean Value Theorem, we know there exists a c in the open interval (3, 3) such that f(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.

(1 point) For the surface with parametric equations r(s, t) (st, st, s t), find the equation of the tangent plane at (2, 3, 1 Find the surface area under the restriction s t 1

7. Rewrite with absolute value notation 3 3 B. x 3 C. 3 D. 3

A highway and a railway cross at and angle of 22 degrees. A passenger train is approaching the intersection at 74 miles per hour while a car is approaching the intersection at 80 miles per hour. Determine the rate of change of the distance between the passenger train and the car when the passenger train and the car are 5 and 1 miles away from the

Textbook If f(x) then (x) Videos 0 X (t 2t 6) dt

and work. When you are completed, take a picture and upload it to Schoology. 1. f(x) x5x2x8 Degree 3 (oddends go opposite) TL.C1 (Right side goes) yintercept (0)5012 260)8 0008 Potemiol zeros 12, 4, (2)(2) 5 (2)2(2) f(1) (1) 5 (1) 26)0 111528 68 1680 (OA) 4x6x8 (x4) (x2) 4X2 x40 x4 x20 x 2 2. f(x)2xx6x27x2 Degree 4

A 9digit phone number cannot start with 0 or 1. Assume that there are no restrictions on the remaining 8 numbers. How many telephone numbers are possible in which all 9 digits are different The possible number of 9digit telephone numbers where all the digits are different is

Compute the surface integral over the given oriented surface Fyi2jxk, F. ds portion of the plane x y z 1 in the octant x, y, z 0, downwardpointing normal

6. Convert the point from rectangular form to polar for (3,8) a. (73, 111) b. (5, 69) c. (73, 69) d. 13. 120)

5 Let g(1) 4, g(5) 3, and 1,9 g(2) dz 5. Evaluate the integral. 1 .5 zg (z) dz

An ant climbs up the trunk of a tree following the path modelled by the circular helix of mathbfr(t)langle 3 cos t, 3 sin t, t angle i) Find the length of the trunk helix that has the reference point r(0) 3i in terms of t . ii) If the ant starts at the point (3,0,0) and climbs up the trunk helix for a distance of 10 units, what is the ants final

Consider the function f(x) x 50x 11, 4 x 11. The absolute maximum of f(x) (on the given interval) is at x and the absolute maximum of f(x) (on the given interval) is The absolute minimum of f(x) (on the given interval) is at x and the absolute minimum of f(x) (on the given interval) is

1. What type of conic section is the given equation (x2) y y2 1 25 16 01 a. circle b. parabola c. ellipse d. hyperbola

25. Identify the conic by writing the equation x y 2x4y 4 0. a. Circle (x 1)(y 2) 9 b. Circle (x 1)(y2) 9 c. Ellipse 9(x 1)(y2) 9 d. Hyperbola (x 1) 9(y 2) 9

is the headquarters of Greedy The cable company is about to expand service to two nearby towns, Springfield and Shelbyville. There needs to be cable connecting Centerville to both towns. The idea is to save on the cost of cable by arranging the cable in a Yshaped configuation. Centerville is located at (7, 0) in the xyplane, Springfield is at (0,

Cegral 3xy 3xy ds, where C is the right half of the circle x2 y 25.

the given equations are x y 12 and xy0

Find the doonam and range of each fune the 56. y2log, x

Find the slope of the tangent line to the curve lz 2xy 3y 24 at the point (4,2).

(1 point) Use cylindrical coordinates to evaluate the triple integral z19 (x y) and the xyplane. x y V, where E is the solid bounded by the circular paraboloid

Region II First quadrant, bounded by yx and y1x and yx or each region A. Provide a sketch. C. Compute the volume of the solid when rotated... ...about the xaxis 1 x B. Compute the a ...about the yaxis ...about y2 ...about x1

The cost of controlling emissions at a firm rises rapidly as the amount of emissions reduced increases. Here is a possible model C(q)4,800 91q2 where q is the reduction in emissions (in pounds of pollutant per day) and C is the daily cost to the firm (in dollars) of this reduction. What level of reduction corresponds to the lowest average cost per

Textbook Videos If 2300 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box. Volume

Next question 321 Get a similar question You can retry this question below For the above rational function f(x) lowest 30. 30230 16z identify its three inflection points. 4x 2.5

Find the scalar and vector projections of b onto a. a (6, 7, 6) b (3, 1, 1) scalar projection of b onto a vector projection of b onto a

Simplify. sin x sec x sin x csc x x

, and the angle 0 is in the first quadrant 6. Given that sin 0 find the value for cos 0. 100 91 10 0100 O 91 10

(1 point) Let F(x, y) yixj and let C be the circle r (t) (cost) i (sin t) j, 0 12. A. Compute Note Your answer should be an expression of x and y e.g. 3xyy B. Compute Note Your answer should be an expression of x and y e.g. 3xy y C. Compute Fdr Note Your answer should be a number the whole xyplane

Question 1 (0.5 p Listen If g(x) 4 3x, determine the domain of g(x). (0,1 (0,) 3 O(, 0) U (0, ) (, 1) ,

6e Find the horizontal asymptotes of f (t) 2e1 (Use symbolic notation and fractions where needed. If there are more than one horizontal asymptote, give them as a comma separated list.) Equation(s)

A rectangle has a perimeter of 6x(3)9x(2)10x5 and a length of x. Find the width of the rectangle when the length is 21 inches.

Solve for x by factoring where O X T. tanx tan x 0 0, 1717, T Enter the next smallest value.

2n2 37. lim The limit n n2 A. 2. B. B. does not exist. O C. D. 0. 72

Let f(x)263x5. On which intervals is f decreasing Choose 1 answer A B 5 52 only 5 0 x only C x 0 only D x 0 only Google Classroom

Textbook Videos Use Newtons method to approximate a root of the equation 2x7 7 30 as follows. Let 11 be the initial approximation. The second approximation 2 is and the third approximation 3 is (Although these are approximations of the root, enter exact expressions for each approximation.) Question Help Video

sample of a radioactive substance decayed to 92 of its original amount after a year. (Round your answers to two decim. aces.) (a) What is the halflife of the substance yr (b) How long would it take the sample to decay to 65 of its original amount yr

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