4.6 Question 7 For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is proportional to v³. It is believed that migrating fish try to minimize the total energy required to swim a fixed distance. If the fish are swimming against a current u (u < v), thenthe time required to swim a distance L is L/(v - u) and the total energy E required to swim the distance is given by the formula below, where a is the proportionality constant.E (v) = av³.v uDetermine the value of v that minimizes E. (Note: This result has been verified experimentally.)

Given that the problem is : Differentiating the E(V) :

Answered: Determine the value of v that minimizes…

Math

Advanced Math

Determine the value of v that minimizes E.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.CR: Chapter 11 Review

Problem 61CR

See similar textbooks

Related questions

Q: 2 -2 EXB Solve X²³ Y-3x² y +6xý - 6 y = 30 X By using inverse operator

Q: Use the Limit Comparison Test to determine the convergence or divergence of the series. lim n18 n =…

A: Note: As per our guidelines, we can solve first question. Please repost the remaining one.

Q: Consider the vector v = 1 + 4t in terms of the standard basis for P2, {1, t, t²} and new basis B =…

Q: Find the inverse of the matrix below. Show your work. A = [14 460 1 0-4 1 0 2 0 -3 0004

Q: Find the determinant of 3 -1 0 20 05 01 1 8 -4 0 1 0 -4 2 NO using properties of the determinant.

Q: Find the following limits. You may use any theorem we have proved, such as Arithmetic of Limits.…

Q: equations: +3y 2y 3x+10y X -X 2z + 4z = - - Z = = -1 10 18

A: (A) Express the given system in matrix form as AX=B where , and…

Q: Use Jacobi's method and Gauss-Seidel to solve 2 0 2-4 0 0 0 0 0 ܟ݁ 20 2 -4 0 0 0 0 0 x: 0 2-4 2 0…

A: As per the question we are given a sus of linear equation \(Ax = b\) where is a tridiagonal matrix…

Q: Haggis Supermarkets (HS) have purchased 6 liters of irn bru from a local producer. Each liter of irn…

Q: 1.UA Hamburger Hamlet (UAHH) places a daily order for its high-volume items (hamburger patties,…

A: To solve these problems, we will use the Economic Order Quantity (EOQ) model for inventory…

Q: Use Fubini's Theorem to evaluate 14x²x 00 ¡¡₁. 00 4xexy dx dy. 4xexy dx dy = (Type an exact answer.)

Q: Suppose you have two alloys: (A), with 7 ounces of silver per pound, (B), with 14 ounces of silver…

A: To solve this problem using Leonardo’s method of double false position, we need to make two false…

Q: Let G = GL(2, R), the invertible 2 x 2 matrices with multiplication as operation. Let K = {M € GL(2,…

A: Let , the invertible matrices with multiplication as operation.Let .Prove that is a normal…

Q: Calculate the average required room rate using the above information. If the differential between…

A: The Nanaimo Inn, equipped with 60 rooms, anticipates a 70% occupancy rate. The proprietor aims for a…

Q: 1 2 + xn (a) Prove by induction that în > 0 for all n € N. (b) Prove that (n) is a contractive…

A: (a) We have to prove by induction that xn > 0 for all nЄ N.(b) We have to prove that (xn) is a…

Q: Which function is always positive? 3 O a) ♬(x) = 2x²+4 Ob) f(x)- 1 O c) x)- (x-4)² +4 d) B and C

A: We have to check which Function is always positive

Q: t YA Find t and the terminal point determined by t for each point in the figure, where t is…

A: The general point on a unit circle is

Q: Determine whether the limit lim xsin exist, 72 I

Q: Show directly from definitions that if sn and tn are sequences so that limn→∞ sn = -8 and limn→∞ tn…

Q: For f(x)=3x^(2)-7x, find A. f(a) B. f(a+h) C. Find and simplify (f(a+h)- f(a))/(h), for h!=0 Note:…

Q: Consider the function z = F(x,y) = x¹/4.8 4.4, where x = 2ln(y) + 4.4. What is the value of the…

Q: Solve the reccurence relation a_n = sqrt (a(n-2) / a(n-1)) with initial conditions a_0 = 8, a_1 = 1…

A: We have to solve the recurrence relation a_n = sqrt (a(n-2) / a(n-1)) with initial conditions a_0 =…

Q: Could you explain to me how to find the inverse Fourier transform of the function __ (w+4)² 32 a.…

Q: me if a sequence is arithmetic, geometric or neither? G sequence.

Q: A chemical engineering design project requires that you accurately estimate the molal volume (v) of…

Q: so sorry the matrces are meant to be together so it's [ 1 0 ] and the numbers below of that matrix…

A: Given set of matrices is{M1=[1101], M2=[1−10−2], M3=[−1−1−11], M4=[04−18]}A set of vectors…

Q: Let G be a group and H a subgroup of G. Let H = <R2> in the group D6 of symmetries of a…

A: The objective of the question is to find the elements in the set rHr^-1, where H is a subgroup of…

Q: How to find p2sin2θ from x2+y2? How do you know it is p2sin2θ?

Q: Let A = 2 147 2 13 and b -9 -6 Z = -887 -83 Define the linear transformation T: R² R³ by T() = Az.…

Q: 1. Show that k1601 = k (mod 17) for any k.

Q: 6. The force of interest 8 (t) at time t (measured in years) is given by 0.08 = 0.06 (0.04 for 0<t<5…

A: (a) Derive expressions for V(t) , the present value of 1 due at time (t):The present value V(t) is…

Q: Using the residue at infinity, evaluate the following integral. (z + 1)² dz |2|=3 2² (z − 1)

Q: (5) Let ƒ : (a, ∞) → R be such that lim xf(x) = L, L € R. Prove that lim f(x) = 0. X48 x→∞

Q: Question 2: a. Let G be a group and a E G. Show that if |a| = n, then |a¹| = n. b. Without computing…

Q: Question: Z - Z is a group under componentwise addition and Z is a group under addition. ZXZ Prove…

Q: Find the volume of the solid formed by rotating the region Inside the first quadrant enclosed by…

Q: 7.5. It's a rough approximation, but let's treat a spinning ice skater as a solid cylinder with a…

A: It's a rough approximation, but let's treat a spinning ice skater as a solid cylinder with a radius…

Q: Let B= = (1, +2, (x - 1)², 42³) be an ordered basis for P3. Find the coordinate vector of f(x) = 1x³…

Q: Determine the dimensions of Nul A. Col A, and Row A for the given matrix. A= 00 00 0 0 5 5 4 6 0 0 1…

Q: Let a₁ = b , a₂ = and b = (a) Write b as a linear combination of a₁ and a2. T(b) = 32 a₁+ a2. (b) If…

A: (a) We have to write b as a linear combination of a1 and a2.(b) We have to find T(b).

Q: Determine whether the geometric series converges or diverges. If it converges, find its sum. Ž…

Q: Identify the function that matches the graph except at x = 2. -54-3-2 T a) f(x)= O 29 1 -2 ↑ TY 1 2…

Q: 9. If : G→ H is a group homomorphism and G is abelian, prove that (G) is also abelian.

Q: Solve the given differential equation by undetermined coefficients. y"" - y" - 25y' + 25y = 3 - ex +…

Q: 6. Let S denote the toroidal surface whose equation in cylindrical coor- dinates is (r - 3)2 +22= 1.…

A: The equation of the toroidal surface in cylindrical coordinates is .The region is the space…

Q: A. Find the Laplace transform of each given expression (5 (2) i++ t sin(3t) + y, where x = z(t), a…

Q: Hercules Films is deciding on the price of the video release of its film Bride of the Son of…

Q: (a) Calculate Let n ≥ 1 be an integer and let F(y, z) = y¹−¹ √√y² + z². G(y, z) = 2 Ə əz -F(y, z) —…

A: Given functionF(y,z)=yn−1y2+z2Partial derivatives with respect to z∂F∂z=yn−1zy2+z2…

Q: a. Sketch the graph of the function on the given interval. b. Calculate Ax and the grid points x0,…

Q: Find the right match for the following ODEs in the dropdown menu y' + y" = 2x²y 10y' y e = - 2…

Question

4.6 Question 7

For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is proportional to v³. It is believed that migrating fish try to minimize the total energy required to swim a fixed distance. If the fish are swimming against a current u (u < v), then
the time required to swim a distance L is L/(v - u) and the total energy E required to swim the distance is given by the formula below, where a is the proportionality constant.
E (v) = av³.
v u
Determine the value of v that minimizes E. (Note: This result has been verified experimentally.)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Using the given data in this problem.

VIEW

Step 2: Second differentiation to the E(v)

VIEW

Solution

VIEW

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here