If demand is p = , supply is p = x + 1, and the market equilibrium is (9, 10), create the integral used to find the (a) consumer’s surplus. (b) producer’s surplus.

Q: Computer algebra systems sometimes need a helping handfrom human beings. Try to evaluate integral  (...

A: To evaluate∫1+lnx1+xlnx2dx  ........1

Q: Find the critical numbers of f, if any, (a) find the open intervals on which the function is increas...

A: fx=x2x2-9 Differentiating with respect to x, we get f'x=dx2dx·x2-9-dx2-9dx·x2x2-92=2x·x2-9-2x·x2x2-9...

Q: Consider the function f(x) = x' – 15x2 + 73x - 115 defined on the interval [4, 6]. Verify the Mean V...

A:

Q: Consider a triangle with vertices X, Y, and Z.

A:   Definition used -              Triangle law of vector addition -                  According to tri...

Q: Solve the following equation. tan x = 1

A: Given: tanx=1

Q: describe the given set with a single equation orwith a pair of equations. The plane through the poin...

A: Plane passing through the point 3, -1, 2 and perpendicular to the z-axis. Since the plane is perpend...

Q: Q1. Sketch the curves in polar coordinates. (a) r = 4 – 4cos0, (b) r² = 9cos20

A: (a) The given equation of the curve is r=4-4cosθ. Sketch the graph of the given curve using a graphi...

Q: Find the second derivative of the function.        f(x) = x/(x − 1)

A:

Q: Find the center C and the radius a for the spheres x2 + y2 + z2 - 6y + 8z = 0

A: To Determine: Find the center C and the radius a for the spheres  Given: we have an equation x2+y2+z...

Q: Determine whether the following series converge or diverge using the properties.

A: If the series is geometric, one have to check the common ratio If absolute value of common ratio is ...

Q: Solve the equation : 10x - 1 = (2x + 1)2

A: 10x-1=(2x+1)2

Q: Find the point on the line –5x +4y – 1 = 0 which is closest to the point (-3,4). : Write y as a line...

A: From -5x+4y-1=0 we get:4y=5x+1y=5x+14So any point on the line -5x+4y-1=0 is of the form x, 5x+14

Q: Find the general solution of the differential equation

A: We have given differential equation drds=49r We have to find general solution of differenial equatio...

Q: 23.

A: Given that ∑k=48 k7. Compute the sum as follows.  

Q: Find the indefinite integral. (Use c for the constant of integration.) (2ti + j + 3k) dt

A: Given, ∫2ti +j+3k dt We have to find the above integral.

Q: Dot Product and Projections in Exercises 1–8, find

A: 1. Given v=2i-4j+5k, u=-2i+4j-5k (a) To find v·u. v·u=2i-4j+5k·-2i+4j-5k=2·-2+-4·4+5·-5=-4-16-5=-25 ...

Q: Use a system of linear equations with two variables and two equations to solve. 185 students enrolle...

A: Let the number of passing students be x and the number of failing students be y. The total number of...

Q: An experimental drug lowers a patient's blood serum cholesterol at the rate of t(square root of)100 ...

A: Given  An experimental drug lowers a patient's blood serum cholesterol at the rate of t100−t2 units ...

Q: Use the matrices below to perform matrix multiplication. -4 11 4 7 B = 6. 4 9 0 12 8 -10 3

A:

Q: Evaluate the limit, if it exists.

A: We have to evaluate the limit: limx→164-x16x-x2 It is 00 form, since there is square root function i...

Q: simplify ( variables represent nonzero real numbers) ? (2x-3yz-6)(2x)-5

A: amn=amna-m=1am

Q: A differential equation is said to be exact when ôM/əx = ƏN/əy where M and N are its corresponding c...

A: -M=2lnx+xy-3 & N=3x2y-lnx+3y⇒M=-2lnx-xy+3 & N=3x2y-lnx+3y Now partially differentiating M=-2...

Q: Consider the function defined on the indicated interval. f(x) = 2x² – 4x – 6, [–1,5] %3D - Find the ...

A:

Q: Please solve it fast

A:

Q: let u = [-3, 4] and v = [2, -5]. Find (a) thecomponent form of the vector and (b) its magnitude. 3u ...

A: u=-3, 4 & v=2, -5 a). 3u-4v=3-3, 4-42, -5=-9, 12-8, -20=-9-8, 12--20=-17, 32

Q: plot the function and use the graph to estimate the value of the limit.

A: Given: y=limx→02x-cosxx we know that graph of given function can be drawn as below

Q: Use the matrices below to perform the indicated operation if possible. B = 10 6 C -5 If the operatio...

A: Given: The matrices are B=-106-52 and C=0971.

Q: Change the order of integration and hence evaluate J J² dy dx.

A: Explanation and Solution is given below....

Q: Use mathematical induction to prove that 12 + 22 + 32 + ...... + n2 = n(n + 1)(2n + 1)/6 for all pos...

A: 12+22+32+.......+n2=nn+12n+16 Step 1: For n=1, Left hand side=12=1 & Right hand side=11+12·1+16=...

Q: The rate of change of the number of coyotes N(t) in a population is directly proportional to 650 − N...

A: Consider N(t) as the population of the coyotes after t years. Consider the given statement as the ra...

Q: Verify that the following pairs of curves meet orthogonally. a. x? +y? = 4, x? = 3y? b. x = 1- y, x=...

A:

Q: sketch the region bounded by the given lines andcurves. Then express the region’s area as an iterate...

A: Given, x+y=2 We can defined the shaded region as follows: D=x,y/0<y<2-x,   0<x<2

Q: The graphs show the percentage of jobs in the U.S. labor force held by men and by women from 1970 th...

A: Given that the mathematical model show the percentage of jobs in the U.S. labor force held by men an...

Q: (a) Show that the absolute value function F(x) = |x| iscontinuous everywhere.(b) Prove that if f is ...

A:

Q: Determine whether the graph of x = y2 - 1 is symmetric with respect to the y-axis, the x-axis, or th...

A: The given equation is: The graph of this equation is:

Q: Use properties of logarithms to expand the logarithmic expression  log2  5√(xy4/16) as much as possi...

A:

Q: A farmer has 20 feet of fencing, and he wishes to make from it a rectangular pen for his pig Wilbur,...

A:

Q: Hello, I only need the solution for e and f, as you can see I already have the solutions from a to d...

A: e) Given that A=number of coffees=2k=-0.5So, c(t)=2e-0.5tc'(t)=2e-0.5t(-0.5)c'(t)=-e-0.5tAt t=2, c'(...

Q: Solve the following first order DE. 3. y' + 2y = y?

A: We have to solve the first order differential equation: y'+2y=y2 Rewriting the above equation, y'+2y...

Q: The diagram shows part of the curve with parametric equations x = 2 In(r+ 2), y =+21 + 3. (1) Find t...

A: The gradient of any curve y is given by its derivative dydx. The given parametric equations of the c...

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.