A certain toll road averages 238,000 cars per day when charging $1 per car. A survey concluded that increasing the toll will result in 700 fewer cars for each cent of toll increase. What toll should be charged in order to maximize the revenue?

Q: 1. Find solutions for the divergence and curl of the vector field vat (1, 0, -1). v (x,y,z) = x²z²i…

A:

Q: 7. tions Compute the general solution of the system of differential equa- 3 x-(-8-29), 0-20 y. -6 27…

A:

Q: Elimination of Arbitrary Constants: In the following problems, eliminate the arbitrary constants…

A:

Q: Sketch the solid whose volume is given by the iterated integral and rewrite the integral using the…

A: Given : A volume is given by the iterated integral  ∫y=-1y=1∫x=y2x=1∫z=0z=1-xdzdxdy To Find :Plot…

Q: Let p (> 0) be the first of the n arithmetic means betw numbers and q (>0) the first of n harmonic…

A:

Q: When the students in the class lined up four to a row, there was one left over; when they lined up…

A: The hint clearly says to use the Chinese Remainder Theorem and we shall use it. First we shall…

Q: Solve the following differential equations: 1. y(lnx - In y) dx = (x ln x - x ln y - y) dy

A:

Q: . A spring with a 3-kg mass is held stretched 0.6 m beyond its natural length by a force of 20 N. If…

A:

Q: Prof. Einstein walked 13.6 m in a direction 55.0° north of east as shown. a) How far did he travel…

A: Kindly refer to Step 2 for the solution.

Q: Questions: 1. Let A = {1,2,3,4,5). Let F be the set of all functions from A to A. Let R be the…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.3 cm/min.…

A:

Q: The tangent plane at a point Po (f (uo.Vo) 9 (4o.vo),h (uo.vo)) on a parametrized surface r(u,v) =…

A: Answer of the first question is given, plz repost the second question.   The equation of a circular…

Q: if sisa group of order p", then its center 2 pleing a prime s

A:

Q: Let f(x) = x² - x. (a) Express (x²-x)dx as limits of Riemann sums, do not evaluate the limit. (b)…

A:

Q: 1) Deduce the special case ( for the special) case si z = g(x,y) SS SSF Cry + y ) dudv . D (x,y) ED…

A: As per the question we are given the general form of the surface integral of an vector field F over…

Q: dm dx Prove that: — m „¸a- '2F₁(a,b;c;x)]=(a)_xª−¹ ₂F₁(a+m,b;c;x)

A:

Q: for Convert the inequalities below to equalities by adding sack variables. Use 81 and 82 variables.…

A:

Q: A. Verify if the given equation is a solution of the given differential equation: (Show your…

A:

Q: Find a potential function f for the field F=e4y+52 (3 i+ 12xj+ 15x k). A potential function is…

A: Since both questions are different. So as per our guideline, we are supposed to solve only one…

Q: dt -We can get the roots m² +Gm +8 -0 corresponcting by using it's ^ auxiliary equation

A: Here we find characteristics roots. Complementary Solution  Particular solution.

Q: 1) J²₁+ 2y² + 103 = 3x² 2

A:

Q: A dead body was found within a closed room of a house where the temperature was a constant 65° F. At…

A: A dead body was found in a closed room. Temperature of room  65°F. Temperature of the body at time…

Q: G is a finite group and Z is its centre, then class equation of G is expressibi o(G) o(G) = o(Z) + E…

A:

Q: The tangent plane at a point Po(f (uovo)g (uovo),h (uo.vo)) on a parametrized surface r(u,v) =…

A:

Q: Find a positive integer n such that is a square, 3 is a fifth power. is a cube, and i

A: Given: n2, n3, n5To find: A positive integer n such that n2, n3, n5 is a square, cube, and fifth…

Q: Form the matrix associated with the given minimization problem and find its transpose. Use "f" for…

A:

Q: Consider the vector field F = The vector field is not conservative (4x + 3y, 3x + 7y). The vector…

A:

Q: -3 2 Let M = 1 -1 -3. Find C₁, C₂, and c3 such that M³+C₁M² + c₂M + C3I3 = 0, where Is is the…

A:

Q: A singular value decomposition of a matrix A is as follows: -0.5 0.5 -0.5] [15 0 0.5 -0.5 0.5 0.5…

A:

Q: en prove that there exists a rational numb =k. Hence, prove that the numbers √2,

A:

Q: Let H = Span{V₁, V₂) and K= Span{v3.V4), where V₁, V2, V3, and v4 are given below. 5 0 HO- V₂ V3 -…

A:

Q: Determine whether the information results in one triangle, two triangles, or no triangle at all. 5.…

A:

Q: Graph each function using degrees. 3) y sin 0-2 90° 180° 2709 360° 450° 540 4) y = cos 0 +2 90° 180°…

A:

Q: Use the simplex method to maximize the following: Maximize f 4x1 + 7x2 + 8x3 subject to 3x1 + x₂ +…

A:

Q: Evaluate the following summations. (9) Σ% (3 + 5k). 100 (n) Σ% 3· (1.1)*. *Show All Your Work.

A: The given problem is to find the sum of the given following summations.

Q: 2. Find the area of one petal of the graph r = 2 cos 20. Sketch the graph.

A:

Q: 2. Determine the general value of the following. tan(2 - 5j)

A: According to the guideline, only one question can be answered. Please repost other question…

Q: The population of bacteria in a culture grows at a rate proportional to the number of bacteria…

A:

Q: 4. 5. (x²+4) dy = (2x8xy) dx (2x + y + 1)y' = 1 Hint: Let u = 2x+y+1

A:

Q: use the following theorem to find £ ( 2 (1= (ost) Theorem: If £(f(t)) = F (s), then £ ( f(+)) = (*…

A:

Q: Find Cartesian equation for the curve represented by the parametric equation x=et-6, y = e²+

A: To find the Cartesian equation we have to write a equation in terms of the variable x and y only. I,…

Q: Consider the power series (-1)^x^ n=1 9m (n²+4) M8 interval of convergence gues From x = to x =…

A: Ratio test -: If a series ∑n=1∞anxn is given and  limn→∞an+1an=L if L<1,then series converges…

Q: Find the critical points, domain endpoints, and local extreme values for the function. y=…

A: Let,  y=f(x)=-x2-4x+5,  x≤1-x2+5x-4,   x>1. Clearly, f(x) is defined for all x∈ℝ.  Hence, domain…

Q: Use the series solution method to solve the Volterra integral equations: 호 - - f (x - 1)u(t)dt *12.…

A:

Q: Does the function 5 3-x f(x)= have a vertical asymptote at x = 3? Why or why not? (Completing a…

A:

Q: ||projn (x) || = x. n |n||2 || n x. n |n||²

A: Given:  projnx=x·nn2n=x·nn2n. To do: We have to explain how the expression factored out.

Q: -0.625x + y y' = -x -0.625y X =

A:

Q: 2. Let x = 3 cost, y = -3 sin t a. Eliminate the parameter and write an equation in rectangular…

A:

Q: Be V a vector space over IR, {e, S < V, dim S < dim V (m < n). em} and show Σ(ve)e, =Σ(ve)e wer j=1…

A:

Q: Solve the differential equation y' = Ay where 1 1 1 2 1 2 1 0 1 A = y 3 y (0) = H +

A: The given problem is to solve the given matrix differential equation with given initial condition.