A population is modeled by the differential equation dp dt P 4200 (a) For what values of P is the population increasing? (Enter your answer in interval notation.) PE (c) (b) For what values of P is the population decreasing? (Enter your answer in interval notation.) PE = 1.5P 1 What are the equilibrium solutions? (Enter your answers as a comma-separated list.) P =

Q: Describe and sketch the surface in R³ represented by the equation: x²+z² = 25.

A: If we consider the graph of x^2+z^2=25 we must notice that however it seems a circle in xz plane…

Q: Where on the path r(t) = (t² −5t)i + (2t+1) j + 3t² k vectors orthogonal? are the velocity and…

A: The given path

Q: Find the volume of the solid generated by revolving the region in the first quadrant bounded on the…

A: The region bounded on the left by the circle , on the right by the line , andabove by the line  is…

Q: A force of 10 lb is required to hold a spring stretched 4 inches beyond its natural length. How much…

A: The solution is shown in step-2

Q: Q35. If the value of the determinant |1 1 64- 1 ω 11 w² ω value of k.< -1 - w | = k(w³² - w) where a…

A: W

Q: Find the exact value for the expression under the given conditions. Write your answer in simplest…

A:

Q: A beekeeper has a colony of 1,000 bees, increasing at a rate of n'(t) bees per week. What does the…

A:

Q: Find the Maclaurin series for cos(x) using the Maclaurin series for sin(x). x³ x5 x7 3! 5! 7! Sin(x)…

A:

Q: Evaluate the integral. T 8 (₁³3 [138 - 1/√3 arctan(y) 1 + y² - e T 4 dy

A:

Q: 1. Evaluate the definite integrals. • Le 0 (a) (b) e-x/2 dx 1 L₁₁42 dr dx 1 + x²

A: The given integrals are;a) e-x/2, limit from 0 to 4b) 4/(1+x2), limit from 0 to 1.

Q: Initially 10 grams of salt are dissolved into 40 liters of water. Brine with concentration of salt 4…

A: Initially 10gm of salt are dissolved to 40lt of water. Brine with concentration of salt 4 gm per…

Q: Find the values of a and b that make the following piecewise function differentiable everywhere.…

A: To find the values of  and  that make the following piecewise function differentiable everywhere.

Q: Let f(x) (fg)(x) = 3x + 4 and g(x) 4x² + 3x. After simplifying, 4

A:

Q: Consider the following. (If an answer does not exist, enter DNE.) f(x) = In(2 + sin(x)), 0≤x≤ 2π…

A: Given: To Find: To Find: To find the interval(s) on which  is concave up and concave down.To find…

Q: Her the following vector function. r(t) = (4 sin(t), t, 4 cos(t)) Find the unit tangent and unit…

A:

Q: Find the product and simplify if possible. ((n+k)^(2))/(n-k)*(n)/(n^(2)+nk)

A:

Q: r(t) = e' i + e' sint j + e' costk with respect to arc length Reparametrize the curve measured from…

A:

Q: By inspecting a graph of y = sinx, determine whether the function y = sin x is increasing or…

A:

Q: 2 1.5 10.5 0051 B 0.5 1 1.5 2 8 6 ind the surface area of the portion of the bowl z = 5 + x² + y²…

A:

Q: Q30. R = {(i, i), (i, n), (g, g), (n,n), (n, i), (o, i), (o, o), (o, n)} is a relation on set B =…

A: The given relation isAnd set

Q: Use the theorem given below to find the curvature of r(t) = √√√6t² i + 2tj + 2t³k. k(t) Theorem: The…

A:

Q: For the function y = f(x) = 1x³ +4: df dx ƒ'(−7) = 147 a. Find at x = -7. b. Find a formula for x =…

A: The given function .To find,(a)  at .(b) .(c)  at .

Q: Suppose f is a differentiable function of x and y, and the following applies. p(t) = f(g(t), h(t))…

A:

Q: Find the directional derivative of the function at the point P in the direction of the point Q. X…

A: The function is The points are  and

Q: (5x + 3) dx = (Simplify your answer.) 0

A:

Q: 6. Trace the curve: r² = a² (1 + 2 cos ) (degrees) r Ⓒ (degrees) r e (degrees) r e (degrees) r 0 90…

A: Here, we have given a curve:We have to sketch the graph of the given equation.This equation is in…

Q: Find a power series for the function, centered at c. 4x g(x) = x²+2x-3 g(x) = Σ n = 0 C = 0…

A:

Q: Find the first partial derivatives of the function. f(x, y, z) = xz - 6x³y²z4 fx(x, y, z) fy(x, y,…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) [√ 7 + x 7-X dx

A:

Q: S Consider the vector field F = Evaluate r(t) = t²i+t³j, 0≤t≤1 F-dr along the curve C:

A:

Q: 4. Use the Fundamental Theorem of Calculus to find the derivative. G(x)= = [² (1+1²) dt

A:

Q: Evaluate I= f (secx) dx and say what substitution you use to evaluate the integral. OI-2 and we use…

A:

Q: y method to find the relative extrema 16x²(x + 1)³. e is no relative maximum or minimun ho ahoak hor

A:

Q: Suppose the clean water of a stream flows into Lake Alpha, then into Lake Beta, and then further…

A:

Q: Convert the point (x,y,z)=(3,1,-3) to spherical coordinates. Give answers as positive values, either…

A:

Q: Suppose that a thin metal wire in the shape of a semicircle occupies the curve C, where C' is the…

A:

Q: 6. A closed rectangular container with a square base is to have a volume of 3456 in³. The material…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: The point (x,y,z)=(5,-3,1) expressed in cylindrical coordinates.

A: The point (x,y,z)=(5,-3,1)

Q: A particle is moving with the given data. Find the position of the particle. v(t)= sin(t) cos(t),…

A:

Q: Use Lagrange multipliers to find the points on the cone z2 = x2 + y2 that are closest to the point…

A:

Q: iven the vector function r(t) = (4 cost, 4sint, t) for t = = . Find the: 2 mit tangent vector for t…

A:

Q: Assume B is an n × n matrix, n > 1, and det(B) = 4. (a) Find n such that det(−5B) = 100

A: Given:We are required to find:

Q: Show diagram, define variables, state formula, theorem, equation or function used, Show…

A:

Q: -0.02832t grams, The amount of a radioactive isotope present in a certain sample at time t is given…

A:

Q: Find the length of the curve. r(t) = 9i + 4t²j + 5t³k, 0≤ t ≤ 1

A:

Q: Use logarithmic differentiation to compute the derivative of y = y' = (x³ + 3)7(x8 – 5)5 (+⁹+8)⁹

A:

Q: 8. A cylindrical can, open at the top, is to hold 700 cm³ of liquid. Find the height, h, and the…

A: Since you have asked multiple questions in a single request we would be answering only the  eighth…

Q: HERE KEPINTE 0, 0. 0 PANE JOUL PRE INFERRENTE SAULEI CAN 2000.00 MADELELEZI ELIOTOTDIENT INTENAN…

A: we have given integration

Q: Solve. 1 X-6 1 X 11 6 2 x - 6x O A. ± 6i OB. +√√6i C. {x|x is a real number and x #0 and x #6} O D.…

A:

Q: 6. Suppose a population grows at the rate dP/dt = 2e³t, with initial population size P (0) = 1.…

A: A population grows at a rate  with initial population size P(0) = 1