The rate of change of the time it takes to mow a lawn is inversely proportional to the square of the number of people, p, who are mowing the lawn. What is the differential equation which describes the rate of change of mow time, M(p)? O O O dM dp dM dM dp о М || || || KA || kp k P KR kp

Q: Find all relative extrema. Use the Second Derivative Test where applicable. (If an answer does not…

A:

Q: A hemispherical dome has a diameter of 700 m. A search light was placed at a point A located at the…

A: The solution is given below

Q: find a set of parametrix equations of the line through the point (5,6,2) parallel to vector v=

A: find a set of parametrix equations of the line through the point (5,6,2) parallel to vector…

Q: find an equation in spherical coordinates for the equation given in rectangular coordinates x^2 +…

A: We have to find spherical coordinates form

Q: Let f(x, y) be a function with continuous second partial derivatives. Suppose we know that (-1, 2)…

A:

Q: Consider the function on the interval (0, 2x). f(x) = 2x + 4 sin(x) (a) Find the open intervals on…

A: The given function,   fx=2x+4 sinx

Q: Find the second partial derivative for the function z = x7-7xy + 6y2 with respect to x.

A: Solution of given question is written in below steps.

Q: Prove the identity. 2 sin 20 cos 20+ cos 40=1-sin 40 To verify the identity, work each side…

A: sin2θ+cos2θ = 1.

Q: Find the exact value of the expression in radians and degrees. tan 1¹ (1) Find the exact value of…

A: This question can be solved using the concept of inverse trigonometric inverse.

Q: Find the radius of convergence, R, and the interval of convergence, I, of the following series. (1)…

A: (1) The given series is ∑n=1∞n(x-1)n

Q: Solve the initial value problem y(x)= dy da + y cos = 4 cos x, y(0) = 6

A:

Q: Find the limit as x approaches -1 for O-1/2 O 1/2 O-1 01 x+2 -1 x+1

A: Concept: L'Hospital's Rule: A general technique for assessing indeterminate forms like 0/0 or ∞/∞ is…

Q: A rate of change of H is given by Solve for k where H > -25. O 0.458 O 0.346 0.255 O 0.144 dH = k…

A: topic- differential equation

Q: Question 12 a)! Let C be a curve defined by the vector equation r(t)=. P(32, 52, e³2) Show that the…

A:

Q: use triple scalar product to find the volume of the parallelpiped u= v= w=

A:

Q: L) Prove that (3-2)(x+2) = 3 +21 iFitwas

A:

Q: 2) × 2+4i 3+1 and 2=3-1 2+i 2 prove that x² + 3xy + y² = 6 if it was

A:

Q: If n(A) = 106, n(A ∪ B) = 141, and n(A ∩ B) = 46, find n(B).

A:

Q: Σ(−1)n n² + 2n + 3 5η3 + n + 1 n=1 11.

A:

Q: Evaluate the double integral. Sxy² da, D is enclosed by x = 0 and x =

A:

Q: Find the radius of convergence, R, of the series. R = 00 Σ n = 1 7 || xn 4n - 1 Find the interval,…

A: We have to find out the interval

Q: Express the following as a linear combination of u =(3, 1, 6), v = (1, -1, 5) and w = (4, 2, 4).…

A: To write down the vectors into the linear combination of the given vector.

Q: (a) lim x² - x + 6 X2 x 2 x² + 2x - 3 x² (b) lim x - 6 x 3 x² - 2x - 3 x - 4 (c) lim x+4√√√x-2

A: a.limx→2x2-x+6x2+2x-3=4-2+64+4-3=85b.limx→3x2-x-6x2-2x-3limx→3x-3x+2x-3x+1limx→3x+2x+1=54

Q: 2x + 2 6x³ +5x² - 4x y = 3

A:

Q: Rewrite the following equation with the variables separated. 3xy' + 2y = sin(y). dy (sin(y)+2y) O O…

A:

Q: Apply Descartes' Rule of Signs. Determine the number of possible positive and negative real zeros…

A:

Q: A manufacturer estimates that its product can be produced at a total cost of C(x) = 45,000+ 100x +…

A:

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A:

Q: 1 n (Inn)3/2 Σ(-1)". n=3

A: Given: Here, an=1n(ln n)3/2≤1n(n)3/2=1n5/2. So, the given series is absolutely convergent by the…

Q: b. Stan ³0 sec²0 do

A:

Q: (b) If G(x) = CV: 1 cos (t¹) dt, compute G'(x).

A:

Q: • 5x²+1 (t²-t) dx F(x) =

A:

Q: dp dt Suppose that the current population is 100,000. (a) What is the predicted rate of growth 3…

A:

Q: 5 +1 Tsimplify denomina 7) (1+i) (1-1) = 4 the Following without using the de noctor Prove that

A:

Q: find the standard equation of the sphere with center (4,3,3) and radius 7

A:

Q: a) 2+ + = 1. H

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: a. Find an equation for the secant line through the points where x has the given values. b. Find an…

A:

Q: -π/3 sinx-cosx sinx+cosx Evaluate f dx

A: To evaluate the following integral.∫0π3 sin x-cos xsin x+cos x dx

Q: 1 2-4 를 -5 금 dr

A: Since the third question is incomplete, solve first and second integral

Q: 7x (x+3)³ a. Find lim F(x). X-3 Let F(x)= b. Find the vertical asymptote of the graph of F(x). c.…

A: F(x)= 7x/(x+3)3  a) find the limit of F(x) when x tends to -3 .  b) find the vertical asymptote of…

Q: V. Provide up to the 5th degree Taylor Polynomial of the given function: f(x)= xex by about x=-1

A: Given :fx=xe-xx=-1

Q: find the area of the triangel with verticies A=(0,0,0) B=(2,1,1) C=(3,1,2) round to 2…

A: This question can be solved using the concept of area of triangle using vectors.

Q: Solve the given differential equation by undetermined coefficients. y" - 8y' + 20y = 100x² - 91xex…

A:

Q: Find the volume when the following region is rotated about the y-axis: y = √4x², y = 0, x = 0.

A:

Q: = Find the area of the region bounded by the curves y on the interval [0, 1] as seen in the shaded…

A: This question can be solved using the concept of area bounded by curves.

Q: For the IVP, y'=f(x,y), y=yo, x=xo, iff and df/dy are continuous discontinous defined undefined then…

A: Here we have to choose the correct option.

Q: onsider the following. w=x^2/y ,  x=t^2 ,  y=t+1 ,  t=3 (a) Find d2w/dt2 using the appropriate…

A: Given :w=x2yx=t2  y=t+1t=3

Q: Suppose that over a certain region of space the electrical potential V is given by the following…

A:

Q: · F(x) = 5* (S₁²¹6 (√₁+ u²) du) dt

A:

Q: [4x 4x csc (4x) cot (4x) dx =

A: