S
  1. study help
  2. subject categories
  3. sciences
  4. mathematics
  5. june 2023
  6. 08

Mathematics Questions and Answers June 08, 2023

Expert-verified solutions to help you succeed

Let u (3, 1, 2), v (4,0,8), and w (6,1,4). Find the components of a. v W b. 6u 2v c. 3(v8w) cognize that d. (2u 7w) (8vu) held

Consider the matrix A below, where k is an arbitrary constant. For which values of k does A have wo distinct eigenvalues Where is there no real eigenvalue 5 points A()

Assume that when blood donors are randomly selected, 45% of them have blood that is Group O (based on data from the Greater New York Blood Program). If the number of blood donors is n = 8, find the probability that the number with Group O blood is x = 3. Round to 3 decimals.

A container has 11 red balls, 15 green balls, 10 white balls, and 8 yellow balls. A child picks up a ball from the container. Find the probability that the ball is red. Round to 4 decimals.

Estimate the instantaneous rate of change of h(t) 3t2 at the point t 2 In other words, choose xvalues that are getting closer and closer to 2 and compute the slope of the secant lines at each value. Then, use the trendpattern you see to estimate the slope of the tangent line. Your answer should be accurate to at least 2 decimal places. Question
image

The amount of carbon14 present in animal bones t years after the animals death is given by P(t)Poe 0 that has lost 30 of its carbon14 0.000120971 How old is an ivory tusk The ivory tusk is years old. (Round to the nearest integer as needed.)
image

What is the value of the following limit lim x16.5 x 16.5 1717 x 16.5

dy Find the derivative You do not need to simplify after finding the dx derivative. State which, of any, of the follow rules you used the product rule, quotient rule, and the chain rule. Show all steps. y x cotx
image

Evaluate the iterated integral. 14 1.1.0 12x (x y) dy dx 1 Points DETAILS SESSCALC Evaluate the iterated integral. ( (3 6y) dy dx

Assume that f(x) and g(x) are differentiable functions about which we know very little. In fact, assume that all we know about these functions is the following table of data The values of functions and its derivatives at some values of x x f(x) f(x) g(x) g(x) 23 5 8 1 1 19 7 0 9 3 25 3 5 3 1 4 9 28 2 3 6 This isnt a lot of information. For
image

Let f(x) x 8x 6x 7. Find the open intervals on which f is concave up (down). Then determine the xcoordinates of all inflection points of f. 1. f is concave up on the intervals 2. f is concave down on the intervals 3. The inflection points occur at x Notes In the first two, your answer should either be a single interval, such as (0,1), a comma
image

Let f(x) 8x 9. Find the open intervals on which f is increasing (decreasing). Then determine the xcoordinates of all relative maxima (minima). f is increasing on the intervals 2. f is decreasing on the intervals 3. The relative maxima of f occur at a none 4. The relative minima of f occur at x none 1. Notes In the first two, your answer should

Problem 4 Recall that the average value of a function on an interval a, b is given by 1 fave af f(x)dx. In the following exercise, find the average value fave of f(x) 4 x between a 0 and b2, and find a point c, where f(c) fave.
image

Suppose that f(x)dx 5, f f(x)dx g(x)dx 2. Then compute the value of the definite integral (3f(x) 4g(x)) dr Solution 3, f g(x)dx 1, and that

annual income is modeled by m(x) with x representing the number of years since 2018 and m(x) the gross income in hundreds of thousands of dollars. Explain what the equation below indicates with respect to gross annual income. You are being well paid for this consultation and need to give a concise yet detailed explanation. m(3)m(0) 30 1.39
image

A commodity has a demand function modeled by p 35 0.5x, and a total cost function modeled by C 8x 34. (a) What price yields a maximum profit X per unit (b) When the profit is maximized, what is the average cost per unit (Round your answer to two decimal places.) Need Help Read It
image

Consider the following series. 6 (4n) 246 ..... (2n2) Find a simplified expression for the ratio 1 an

Find the sum of the following series. (2) 3I 1978 (b) 00 3 n (n 3) n2,00 4n4 Suppose that the nth partial sum of the series a, is sn an is snn4 3n4 n1 (a) Find a4. (b) Find an. n1

Centerville is the headquarters of Greedy Cablevision Inc. 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 Y shaped configuation. Centerville is located at (10,0) in the

Consider an animal that forages in a field, which we will model as a flat 2dimensional space. The movement dynamics of the animal are given by the following linear system of ODES where dx dt A (a) Find the nullclines of this system. (b) Determine the direction field on the nullclines. Az (c) Sketch the phase plane, showing the direction field on

Solve the system of differential equations. dx 1) 4y 3 dt dy X x2 dt

M8 A1 20 3 32 (5) D M8 n2n 3 40 U .,Show if they converges ar diverges n 2) Show that the alternating series (1) . is convergent.. 201 1. n1 How many terms in the partial sum to Sn do we need in order to find approximate Sum with error less than 0,01 3) Find and classify the critical points of f(xiy). x y 4xy 1 4) Find the equation of the
Show if they converges ar diverges n 2) Show that the alternating series (-1) . is convergent.. 201 +1. n=1M8 A=1 20 +3 -3+2 (5) D * M8 n-27+3 -40 + U .

The annual sales S of a new product are given by 6000t 71 0sts 3 where t is time in years. S (a) Complete the table. (Round your answers to one decimal place.) t 0.5 1 1.5 2 S 2.5 Use it to estimate when the annual sales are increasing at the greatest rate. O 0.5 t 1 01
image

Determine the equation of the tangent line to the path r(t) (sin(3t), cos(3t), 8t58) at t 1. (Write your solution using the form (..). Use symbolic notation and fractions where needed. Use the equation of the tangent line such that the point of tangency occurs when t 1.)
image

1 1 Let f(x) and g(x) 29 x6 Then the domain of fog is equal to all reals except for two values, a and b with a b and a b Add Work Submit Question
image

1. Find the radius and interval of convergence of the following series. (2)(x3) Vn1 a) (2x 1) 711 (x 2)2n b) n1 c) n1 00 d) n(2x 1) n1 e) n1 Vn(x 2) 4n 1) (x5) f) n1 n n
image

The diagram below shows a squarebased pyramid. Determine each sum. (10 marks) d. N S a. ABCA R a. KNNR b. RSKR e. KNRS 1. KRNMSK 4. Copy each set of vectors and draw uV or UVw. (10 marks) c. MN MS 15 d. KMNK 5. Use a diagram to explain how each vector sum can be expressed as a single vector. (5 marks) b. STUSV

0.2t C(t) 120(e A study shows that the concentration C(t) (in micrograms per milliliter) of antibiotic in a patients blood serum after t hours is ebt), where b 1 is a constant that depends on the particular combination of antibiotic agents used. Solve numerically for the value of b for which maximum concentration occurs at t 1 h. Assume that the
image

Consider the following. Demand Function 128 2 p Find the price elasticity of demand for the demand function at the indicated xvalue. elastic Quantity Demanded X 5 Is the demand elastic, inelastic, or of unit elasticity at the indicated xvalue The demand is elastic at this xvalue. The demand is inelastic at this xvalue. The demand is of unit
image

Explain why the Integral Test does not apply to the series. (Select all that apply.) 9 sin(n) Let f(x) n1 9 sin(x) X

Please explain what a and what b 8 7 b S f(x)dx f f(x)dx f f(x)dx 5 5 a
image

Suppose that (1)2,4)7, f (1)7, (4) 5, and f is continuous. Find the value of Ixtr x xf (x) dx.

Find the derivative of the function. 1 3 5x 8 f(x) f(x) X

5. Polar Slope. The polar function below defines a circle. Find a parametric formula for the derivative and use it to find the approximate rectangular coordinates of one point on the circle where the tangent is horizontal. rsin(0)cos (0) DERIVATIVE POINT WORK dy dx
image

3. Intersections. Find the six intersections of the following two parametric curves. Give exact values for the coordinates. Determine which of the intersections is a collision. Curve 1 Curve 2 xsin(2t) x cos(t) 0t2 ysin(t) ysin(t) INTERSECTIONS (ALL) COLLISIONS On the graph, circle the points that are collisions. WORK
image

2. An IVP. Give the explicit particular solution of the IVP. Also, state the domain of the solution, which is the largest interval containing the initial point where the function is defined. Hint To find the explicit solution, complete the square in y. dy3x2x1 2y2 dx EXPLICIT SOLUTION DOMAIN WORK y(0)0
image

Find equations of the spheres with center (3, 3, 6) that just touch (at only one point) the following planes. (a) xyplane (b) yzplane (c) xzplane
image

You stand 20 ft from a bottle rocket on the ground and watch it as it takes off vertically into the air at a rate of 17 fusec. Find the rate at which the angle of elevation from the point on the ground at your feet and the rocket changes when the rocket is 45 ft in the air. At the moment the rocket is 45 ft in the air, the angle of elevation is

You and a friend are riding your bikes to a restaurant that you think is east your friend thinks the restaurant is north. You both leave from the same point, with you riding 12 mph east and your friend riding 10 mph north. After you have travelled 3 mi, at what rate is the distance between you and your friend changing After you have travelled 3

Find parametric equations for the line that is tangent to the given curve at the given parameter value. r(t) (3 sin t) i (t 5 cost)j (2 e) k, What is the standard parameterization for the tangent line X y Z t0 (Type expressions using t as the variable.)
image

An airplane is flying overhead at a constant elevation of 4035 ft. A person is viewing the plane from a position 3010 ft from the base of a radio tower. The airplane is flying horizontally away from the person. If the plane is flying at the rate of 650 ftus, at what rate is the distance between the person and the plane increasing when the plane

Complete the parametric equations for the line where the planes 4y z 12 and 2x 9y 7z 27 intersect. x(t) y(t) 37t z(t)
image

Given u 7 (2, 0, 1), find ( 5v) ( 3v). Submit Question
image

Suppose that and y are differentiable functions of t and that 2 y, then dz dt Use either prime or operator notation in your answer. If your answer contains, for example, the derivative of y with respect to t, then type or y(t). If 10 and d 2 when z 6 and y 4, then dz dt (6,4)
image

Analyze and sketch the graph of the function f(x) 4x7 x3 Label any intercepts, relative extrema, points of inflection and asymptotes. You work must be neat, readable and mathematically correct. If your work in not neat, you will not get full credit. You must use appropriate standard notations as needed. Graph without supporting analysis will earn
image

The great pyramid has base length 6 231 meters and height h 152 meters. Assume one side of this pyramid can be represented by a triangle formed by points depicted in the following diagram. Find the area (in square meters) of one side (shaded green in the diagram). h Area b (0, 0, h) You may enter your answer as an expression or as a number
image

A rectangular box with a volume of 76 ft is to be constructed with a square base and top. The cost per square foot for the bottom is 20, for the top is 15, and for the sides is 1.5. What dimensions will minimize the cost What are the dimensions of the box The length of one side of the base is The height of the box is (Round to one decimal place as

Final all local and absolute extrema for the following functions on the given intervals a. f(x) 2x 9x24x 1 on 0, 2. b. g(x) 2x 4 cos x on 0, 2 c. h(x) on 2,1 x4 x9
image

2. Let R be the region bounded by the rays 0 a, 0 3 and the curve r f(0), as shown in Figure 1. Use the Greens Theorem area formula fxdyydx, where C is the boundary curve of R to show that the area of R is A (0) do.,y B R Figure 1 r f(0)
imageimage

A company produces two types of solar panels per year x thousand of type A and y thousand of type B. The revenue and cost equations, in millions of dollars, for the year are given as follows. R(x,y) 6x 4y C(x,y)x3xy6y 14x53y2 Determine how many of each type of solar panel should be produced per year to maximize profit. The company will achieve
image

For the function f(x)3x4, do the following. (A) Find the average value of f(x) on the interval 0, 2. (B) Use a graphing calculator to graph the function and its average value over the interval 0, 2 in the same viewing window. (A) Find the average value of f(x) on the interval 0, 21. The average value is (Type an integer or a simplified fraction.)
image

Let r OP ijk. A force F (0,24,0) is applied at P. Find the torque Tabout O that is produced.

Given f(x)9x a. Find the linearization L(x) off at x 1. b. Use the linearization to approximate 9. Give your answer as a reduced fraction.
image

The springflex exercise system consists of a spring with one end fixed and a handle on the other end. The idea is that you exercise your muscles by stretching the spring from its natural length, which is 34 cm. If a 120 Newton force is required to keep the spring stretched to a length of 54 cm, how much work is required to stretch it from 49 cm to
image

For f(x)2x416x9 find the following. (A) f(x) (B) The slope of the graph of f at x 2 (C) The equation of the tangent line at x 2 (D) The value(s) of x where the tangent line is horizontal (A) f(x) (B) At x 2, the slope of the graph of f is (C) At x 2, the equation of the tangent line is y (D) The tangent line is horizontal at x (Use a comma to
image

3) Given the recurrence relationship (n 2)(n1)an2an0 for n 0, 1, 2,.... find ag and ay in terms of ao and a.

Find dw dt dw dt E where w(x, y, z) xyz xy, with x(t)et, y(t) e 2 and z(t) et
image

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 2x 4y xy R(x, y) 150x 50y 2x Find the marginal revenue equations R(x, y) Ry(x, y) We can acheive maximum
image

Solve the initial value problem. dx 3) 6x 5y dt dv dt 5x 4y x(0) y(0) 13 0

10 8 6543 2 1 6 4 2 N 4 6 8 10 1 2 3 4 5 The function graphed above is Concave up on the interval(s) Write your answer using interval notation Concave down on the interval(s) Write your answer using interval notation a There is an inflection point at Write your answer as an ordered pair. Question Help Video Message instructor Submit Question
image

Find the equation of the line normal to the graph of yx2 at (2, 2).

Given 2 x xy, x uv w, yuve Find when u 2, v 1, w0
image

Find and classify the critical points of f(z,y) 2ry4x 4y 24y36. Local maximums Local minimums Saddle points For each classification, enter a list of ordered pairs (x, y) where the maxminsaddle occurs. Enter DNE if there are no points for a classification.
Find and classify the critical points of f(z,y) = -2ry-4x + 4y +24y+36. Local maximums: Local minimums:

Suppose that f(x,y)2ayylaly with 1 a, y 1. 1. The critical point of f(x, y) is at (a, b). Then a and ba 2. Absolute minimum of f(x, y) is and absolute maximum is
Suppose that f(x,y)=2-ay+y-la+ly with -1 a, y 1. 1. The critical point of f(x, y) is at (a, b). Then a and

Find the critical numbers of the function f(x) 3x5 15x4 5x3 and classify them using a graph. X X is a is a is a Select an answer Select an answer Select an answer,Find the critical numbers of the function f(x) 3x5 15x 10x 9 and classify them. At x At x At x the function has a the function has a the function has a Neither a max or min

Consider the given functions on the interval 0, 1, where m and n are positive integers and n m. f(x)x and g(x) xm Find the centroid of the region bounded by f and g. (x, y) Need Help Submit Answer Read It
image

A lifeguard needs to rope off a rectangular swimming area in front of Long Lake Beach, using 600 yd of rope and floats. What dimensions of the rectangle will maximize the area What is the maximum area (Note that the shoreline is one side of the rectangle.) Let x be the length of a side of the rectangle perpendicular to the shoreline. Write the
image

Use the integration capabilities of a graphing utility to approximate the volume of the solid generated by revolving the region bounded by the graphs of the equations about the xaxis. (Round you answer to four decimal places.) y 6x y x Submit Answer 1 Points DETAILS LARCALC12 7.2.063. MY NOTES ASK YOUR TEACHER PRACTICE ANOT A cone of height H

For y f(x) 2x 7, x 4, and Ax 2 find a) Ay for the given x and Ax values, b) dy f(x)dx, c) dy for the given x and Ax values. a) Ay (Round to four decimal places as needed.) b) dy f(x)dxdx c) dy (Round to two decimal places as needed.)
image

Assume that C(x) is in dollars and x is the number of units produced and sold. For the totalcost function C(x) 0.01x 0.5x 50, find AC and C(x) when x 80 and Ax 1. AC (Simplify your answer. Type an integer or decimal rounded to two decimal places as needed.) C(x) when x 80 is (Type an integer or a decimal.) per unit.
image

The average cost for a company to produce x units of a product is given by the function A(x) to estimate the change in average cost as production goes from 250 units to 251 units. The change in average cost is approximately dollars. 20x 1250 X . Use A(x)
image

The integral represents the volume of a solid of revolution. 27 (y 5) 7y dy (a) Identify the plane region that is revolved. (b) Identify the axis of revolution.
The integral represents the volume of a solid of revolution. 27 / (y + 5) 7-y dy (a) Identify the plane

4 The volume of a cantaloupe is approximated by V 1 r. 3 when the radius is 6.4 cm. How fast is the volume changing at that moment The volume is changing at a rate of about (Round to one decimal place as needed.) . The radius is growing at the rate of 0.7 cmweek, at a time weeks. cmweek. cm. cmweek. cmweek.
image

Evaluate the following limit or explain why it does not exist. lim (13x cos x) x0

z x xy, z uvw5, y u ve dz dv Find when u 2, v3, w 0

6 x Find the total cost of the first 64 units (from x0 to x64) A companys marginal cost function is C(x) Total cost where x is the number of units. Question Help Video Post to forum Submit Question,If f(x) 12x x 6 and f(1) 8, find f(x). f(x) Question Help Post to forum Submit Question
imageimage

10x 50 The average cost for a company to produce x units of a product is given by the function A(x) production goes from 50 units to 51 units. The change in average cost is approximately dollars. Use A(x) to estimate the change in average cost as
image

Find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit. Assume that revenue, R(x), and cost, C(x), of producing x units are in dollars. R(x)2x, C(x)0.05x 0.6x3 What is the production level for the maximum profit units What is the profit (ITM)
image

1. Find the derivative of each function. a. f(x) 13x4 7x 5x 11x 75 2 marks b. f(x) (x 2x 4) (x 3) 3 marks . 3 marks 7x) 2 marks c. f(x) 3x6x7 4x1 d. f(x) (4x7x e. 12 y x 4 marks f. f(x) 156 1 marks g. (x) (1 3x) (x 2) 3 marks 2 ) i. (x) (2x 3)(5 x) (x 2x 1) 4 marks n. f(x) ( 2x1 3x 1 3 marks
image

Set up and compute the triple integral 2x y zdV over the hemisphere with equation x y 2 64, that lies above the xyplane. (a) Set up the integral. Type rho for p, theta for 0 and phi for .

Consider the following numerical example of the ISLM model C 248 0.55YD 150 0.14Y887 G 304 T 243 i 0.04 Derive the IS relation. (Hint You want an equation with Y on the left side of the equation and everything else on the right.) Y i. (Round your calculations of the intercept and slope terms to two decimal places.) The central bank sets an

A Ferrari is heading south at a constant speed on Broadway (a north/south street) at the same time a Mercedes is heading west on Aloha Avenue (an east/west street). The Ferrari is 624 feet north of the intersection of Broadway and Aloha, at the same time that the Mercedes is 400 feet east of the intersection. Assume the Mercedes is traveling at

Random guesses are made for the 60 multiple choice questions on a English test, so n=60 p=1/4 ( because each question has possible answers of a, b, c, d and only one of them is correct). Round to 1 decimal.

A forced vibrating system is represented by d y (t) 6 dt2 This question accepts formulas in Maple syntax. Plot Help Preview ( y(t)). 5 y(t) 52 sin (t) The solution of the corresponding homogeneous equation is given by y(t) Ae5t Bet. Find the steadystate oscilation (that is, the response of the system after a sufficiently long time). Enter
image

We can rewrite some differential equations by substitution to ones which we can solve. (a) Use the substitution v 5 x 4y 6 to rewrite the following differential equation 5 (5x4y6). tan (3x) dy dx dv in the form of f(x, v). dx Enter the expression in and which defines the function f in the box below. For example, if the DE can be rewritten as
image

For the compound below please determine which of the three protons (a), (b), or (c) is more acidic using the ARIO rule and explain your reasoning. Note To answer the question correctly, please draw both Conjugate Base 1 and Conjugate Base 2 and 3. Determine which of the two protons is more acidic using the ARIO rule and explain your reasoning if

David would like to make a single payment of $2000 at the end of year 7 so that it will be equivalent to payments of $100, $1000, and $900 made at the ends of years 1, 12, and X years, respectively. Assuming an effective rate of interest of 5% per annum and the method of equated time, solve for X.

Jane takes classes at both Westside Community College and Pinewood Community College. At Westside, class fees are $98 per credit hour, and at Pinewood, class fees are $115 per credit hour. Jane is taking a combined total of 16 credit hours at the two schools. Suppose that he is taking w credit hours at Westside. Write an expression for the

The number of self -employed people in a country increased 3.6% from 2007 to 2008 . It then decreased 6.3% from 2008 to 2009 and another 3.9% from 2009 to 2011 . If there were 14.7 million self -employed people in 2011 , how many were there in 2007 ?

Test whether the following matrices are nonsingular 1 (0) 7 1 1 (a) 19 13 7 1 0 1 40 42 1 (b) 5 60 7 03 (c) (d) 133 495 301 1086 0 4

Suppose that the stock price S, follows lognormal distribution St Soe(a80.50) toiz Prove that the conditional expectation of lognormal prices, when terminal stock price ST falls below Kis where d d E(ST ST K) Soe(as)r N(d) N(d) In(SoK) (a6 0.50)T OVT In(SoK) (a80.50)T d oT,Hints E(ST ST K) is defined as E(ST STK) E ST1ST
Suppose that the stock price S, follows lognormal distribution St= Soe(a-8-0.50) t+oiz Prove that theHints: E(ST ST < K) is defined as E(ST STK) = = E [ST1{ST

Solve for x and y x+2y=5 3x+8y=9

Prove that if P is monotone and subtractive that is if A,B belongs to the sample space S and A subset of B, then, P(A) less than or equal to P(B) and P(B-A) = P(B)-P(A)

Find the integration. (1) DJ das 136833 11 Ja a x tanto da dz

Question 3 which of the following n 2 muova n1 E n2 2 n on 2 n1 n1 egn 1 nlogn 1 n log (1) 2. cocond 166 E palugsg are convergent 9

Consider the function f(x) = 3x^3 - 5x^2 + 2x + 7. Find the x-coordinate(s) of the point(s) on the graph of f(x) where the tangent line is parallel to the line y = 2x + 3.

Solve the following system of equations: 2x + 3y + z = 10,x + 2y - 3z = -4,3x - y + 2z = 6

Consider the sequence of numbers: 2, 5, 10, 17, 26, 37, ... Find a formula to determine the nth term of this sequence, and then calculate the value of the 20th term.

In Chapter 4 of your textbook, Brimley uses Table 4.4 to highlight significant funding differences between states that use a form of pupil weighting for funding special education and special needs students. Review Table 4.4 in Chapter 4 and evaluate the equity or fairness of such large variances in the amount of money allocated to educate special

uantitative research is when a researcher sets up experiments that have results which can be seen as numbers and hard data. In these types of experiments a measurable result should be assessed for. Ghanad (2023) goes on to explain that the researcher in a quantitative experiment selects a problem to answer why patterns are present and why they

Showing 1 - 100 of 1505
  • 1 / 16