.Fishing story An angler hooks a trout and reels in his line at 4 in/s. Assume the tip of the fishing rod is 12 ft above the water and directly above the angler, and the fish is pulled horizontally directly towards the angler (see figure). Find the horizontal speed of the fish when it is 20 ft from the angler. 12 ft Decreasing at 4 in/s

Q: Use a triple integral to find the volume of the solid bounded by the parabolic cylinder y = 8x² and…

A: Find the volume bound by the Planes and cylinder ,using triple integrals in general coordinates

Q: Let T: VW be a linear transformation. Then T is injective (also known as 1-1, or one-to-one) if, and…

A:

Q: (b) Find a simplified formula for n. Σ(14) i (c) Use induction to prove your formula from (b).…

A: ∑i=1n1i-1i+1=1-12+12-13+.....+1n-1n+1=1-12+12-13+....-1n+1n-1n+1=1-1n+1=nn+1 Therefore…

Q: . Let f(x) be the function with McLaurin series xn n². n=0 (1) Find the McLaurin Series of f'(x).…

A:

Q: MATH 140 - Lecture 8 Worksheet 1. (a) How many lists of length 3 are there, if the first two entries…

A: keeping a note ?as per our company guidelines we are supposed to answer ?️only first 3 sub-parts.…

Q: 3. Suppose f: X→ Y, and A, BCY. Prove that (a) f¹(AUB) = f¯¹(A) u ƒ-¹(B). (b) f-¹(An B) = ƒ-¹(A)…

A:

Q: Just

A: We use definition of linear operator to find matrix matrix representation with respect to basis.

Q: 6) Find the exact area of the surface generated by rotating about the y-axis the curve defined by…

A: If a curve y=f(x), a≤x≤b is rotated about y-axis is obtained as  The surface area is given by…

Q: Belle Inc. makes bags and sells them for $36 each. The total revenue at the break-even point is…

A:

Q: Given 0, 0≤t<5 5, 5 ≤ t < 20 0, 20 ≤t Use Laplace transform to solve the initial value problem f(t)…

A:

Q: 16. Construct (draw) a circuit to represent the corresponding symbolic statement. (pVg)^~p

A:

Q: Suppose that u and v are two unit vectors in 3D and the angle between them is π 3 . i. What is |u ×…

A: We know that the vectors i, j and k denotes the unit vectors in the direction of x-axis, y-axis and…

Q: We can define a one-to-one correspondence between the elements of Pn and Rn by p(x) = a1 + a2x +…

A: It is given that, there is one-to-one correspondence between the elements of Pn and ℝn defined by ;…

Q: i) Let A be the Let T: RM → Rn be defined Is it true or ii) Find a basis for iii) Nullity (T) = 2x4…

A: Given: A matrix A=24681046 and the linear transformation T:ℝm→ℝndefined by T(v)=Av. To find: i) n=4…

Q: (2)(-_ A) f(x, y) = 2²-y. Sketch 4 level curves of f(x, y). B) Evaluate the following limit or show…

A: The level curves of a function f of two variables are the curves with equations f(x,y) = k, where k…

Q: Suppose the solid W in the figure is a cone centered about the positive z-axis with its vertex at…

A:

Q: Find a bound on the error in approximating the definite integral using the following methods. (Round…

A: We need to use error bound for trapezoidal and Simpson rule  For trapezoidal  rule ET≤K(b-a)312n2…

Q: 2. (4 points) Verify that 223 is a prime number. Show your work and explain your reasoning.

A:

Q: e 1 v2 ar () 2).J 12 av ar

A:

Q: Example 19.5 The dimensions of a rectangle are given in base 2. The width is 10₂ cm and the length…

A:

Q: Use the Fourie expansion to explain why the note pro ne note produced by a violin string rises…

A:

Q: Find the integrating factor and the general solution of the following differential equations. 7. dl…

A:

Q: 5. Prove each of the following statements:. (a) If m, n are odd integers, then mn is an odd integer.…

A:

Q: The table time (z.) 1 2 3 4 5 6 infections (y = f(x)) 32 37 34 48 53 69 depicts the number of newly…

A: We will be solving first three question as mentioned. The given table is: Time xi 1 2 3 4 5 6…

Q: Given the three simple statements: pp: The cow is brown. qq: The horse is orange. rr: The monkey is…

A: In conditional statements, "If P then Q is denoted symbolically by P→Q The symbolic form of P and Q…

Q: For males born in a certain country in the year 1991, their life expectancy was 66.4 years. For…

A: We have to solve the given problem by given data.

Q: 7 Use the Intermediate Value Theorem to show that there exists a number CE [4,6] such that hcc) =…

A: Introduction: The theorem's conclusion is as follows. There is at least one number x in the closed…

Q: Graph the solution set of the following nonlinear system of inequalities. x² + y² ≥ 36 x² + y² ≤81…

A: We have to draw

Q: Consider the curve given by the polar equation An sketch of the curve looks as follows: r = cos(30).…

A: The given equation is r= cos3θ

Q: Find the volume of the solid V in the first octant bounded by x + y + z = 5 and x + y + 4z = 5. (Use…

A:

Q: (a) an=4+3an-1, 40 = 6 (b) an=2an-1 +3an-2, 40 = 4, a₁ = 9

A:

Q: The cost C, in dollars, of renting a moving truck for a day is given by the function C(x) = 0.45x +…

A:

Q: Find the least common multiple of 2^2,3^3 ,5 and 2^3 ,3^2,7. (You do not need to fully simplify your…

A:

Q: Determine whether the matrix is elementary. If it is, state the elementary row operation used to…

A:

Q: Πο Ω(q+1)t-q + 1 ΠoΩ_q+1)t-q/Ω(6q+5) ΠoΩ (q+1)t-q + 1 ΠoΩ(q+1)t-q/Ω(5q+4) o Th+1 1 = -ΣΠ h=o k=1 Πο…

A: Given: The Information that leads to the required proof.We need to prove the equations marked in…

Q: Let A = {1, 3, 5, 7, 9), B = {3, 6, 9), and C = (2, 4, 6, 8). Find each of the following. (Express…

A:

Q: 13(b) Define real numbers an for all n E N by a recurrence relation as follows: ao = 1 and √4an-1+5…

A:

Q: Find a bound for the number of iterations needed in bisection method to achieve an approximation…

A: The given equation is,                           x-cosx=0 over the interval 0,1.

Q: The given Riccati equation is y'- y²-yeatr + sin²x = 0 Also it is given that, the particular…

A: Solving Riccati equation when one particular solution is given. y=y1+1/u

Q: Use Newton's method to approximate a root of the equation Let £₁ = 1 be the initial approximation.…

A: Given : f(x)=e0.5x2+x-4 ,  x1=1 To Find :Second approximation x2             : Third approximation…

Q: 13(c) Construct a graph G that has all of the following properties: (i) G has exactly 6 vertices,…

A:

Q: 2. Suppose you buy a house for $320,000. You have $40,000 for a down payment, and finance the rest…

A: The house costs $320000. The down payment is $40000. So, the rest amount is $(320000 - 40000)…

Q: 9. Determine whether S is a basis for R³. 10. Determine whether S is a basis for P₂. S = {(0,3,0),…

A: Let V be a vector space and S be a subset of V then S is basis of V if and only if  i) S is L.I ii)…

Q: 4. For each of the following conditions, construct a 3 x 3 matrix the given properties. (a) dim…

A: Nullity of the matrix

Q: 9. For each of the following, construct a truth table to determine whether the wffs in the pair are…

A:

Q: the point 225. Consider the pyramid with the base in the xy-plane of [-2, 2] × [-2, 2] and the…

A:

Q: 3. Determine whether each statement is true or false and justify your answer. (a) If A is a 271 ×…

A:

Q: Find the integrating factor and the general solution of the following differential equations. 5. y(x…

A: The given differential equation, yx-1dx-x2-2x-2ydy=0 We have to find the integrating factor and…

Q: Consider the alphabet justify your answers, and not simply state numerical values. {a,3,7,8). Answer…

A:

Q: Find the critical point of the function f(x, y) = 5x − 5y² — ln(|x + y|). C = Use the Second…

A: