Consider the system of differential equations dx dt x(t) y(t) -2y Convert this system to a second order differential equation in y by differentiating the second equation with respect to t and substituting for a from the first equation. = dy dt Solve the equation you obtained for y as a function of t; hence find x as a function of t. If we also require x(0) = 4 and y(0) = 1, what are x and y? = -2x.

Q: Let y = (x + sin(x))5. Find g(x) and f(x) so that y = (fog)(x), and compute the derivative using the…

A:

Q: Confirm that the below limit meets the conditions to apply l'Hôpital's Rule and then solve the…

A:

Q: Evaluate th

A: The given integral is 2 , limit from 3 to 7.

Q: Solve the initial value problem. dr-csc² 50 cot 50, 42) de 43) dy dx 3 (7) - y(0) = 6 (6 + x)2'. = 3

A:

Q: d. Let t= H hours be the time during the workday (0 ≤1≤8) when G(t) = 100. N(t) = 20(1-H)sin(). Find…

A: Given data:- Let, t = H 0≤t≤8 Gt=100Nt=20t-Hsint27

Q: Confirm that the below limit meets the conditions to apply l'Hôpital's Rule and then solve the…

A:

Q: (sin² y + x coty)y' = 1

A: I have appended the formula used in the solution part of the question.

Q: Find the derivative of the function by the limit process. g(t)= t3+5t St g'(t) = Submit Answer

A:

Q: A baseball team plays in a stadium that holds 50000 spectators. With the ticket price at $8 the…

A: Topic- Application of Derivatives

Q: An airplane has an airspeed of 410 kilometers per hour bearing N45°E. The wind velocity is 70…

A: Given 1. Air speed of airplane Vap=410 KMPH in N45°E 2. Wind speed  Vw=70 KMPH in N30°W

Q: The function f(x) = 2x³ – 36x² + 192x - 3 has two critical numbers. The smaller one is x = and the…

A:

Q: A rancher wants to fence in an area of 500,000 square feet in a rectangular field and then divide it…

A:

Q: The formula for the volume of a cone is given below. Find the rate of change of the volume for each…

A: Given; dr/dt =4 inches per minute and h=6r.

Q: 12) Use Newton's Method to find the closest root to xo =1 for f(x)=x-In(x+4)

A: Given: Function f(x)=x-ln(x+4) and x0=1To find: use newton method to find the root near to x0=1

Q: Determine the interval M n n2

A:

Q: ver (++)

A:

Q: Evaluate the integral. (41) ² (1 + 1)² dx

A:

Q: Solve (5x2y2 O a. b. 2 ln 3 In a In xy² + 17y²) dx (x+2)³(x²+9) y³ |(x+2)³(x²+9) Y - -1 3 tan-¹() =…

A: Given 5x2y2-xy2+17y2dx-x3y+2x2y+9xy+18ydy=0

Q: Use the shell method to find the volume of the solid generated by revolving the shaded region about…

A:

Q: Given f''(x) = = Find 76 10 - - 36 sin(6x) and f'(0) = 2 and ƒ(0) = − 6.

A:

Q: Two sides and an angle are given below. Determine whether the given information results in one…

A: Two sides and an angle are given below. To determine whether the given information results in one…

Q: = solve (y² + 2y² + ay +18) dx. (5x³y²-x²y + 17x²) dy

A:

Q: 13. Show that there are no tangents to the curve y = can be concluded about the graph? 2x+1 4x +3…

A: We have to prove that negative slope is not possible for graph.

Q: Let (a) (b) (c) f(x) = log (2 x² + 3) -log(5) - 6 f(1) = The slope of the tangent line to the curve…

A:

Q: 7. Сучу+9 93)dx хоч до з 3 - и х 'dyto

A: Let's solve given differential equations.

Q: Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall…

A:

Q: Answer both the question11) Find the payment necessary to amortize the loan. Round to the nearest…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as a…

Q: II. Write as an English sentence and determine if it is true or false. 8. VXER, 3YER. x+y=10 9.…

A: 8)  Given, ∀ x ∈ℝ, ∃ y∈ℝ, x+y=10 Solution: For every x in ℝ(Real Numbers) there exist y in ℝ such…

Q: Consider the following function. f(x)=√x-4, What is the domain of f? (Enter your answer using…

A:

Q: At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west at 16 knots and ship…

A:

Q: Note: If you need to input a number such as √2 you can do this by inputting sqrt (2). Let f(x)=…

A:

Q: Find the limit of the following sequence or determine that the sequence diverges. {(₁-²2)"} Select…

A:

Q: 12 The function f is defined by (a) Write down the value of x that must be excluded from any domain…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: Use a graphing utility to graph the curve defined by the parametric equations x(t)=3t sint, y(t) =…

A:

Q: 10. A tank originally contains 380 litres of brine holding 450 N of dissolved salt. Eight litres/min…

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

Q: If we apply Rolle's Theorem to the function f(x) = 2x² - 8x - 1 on the interval [0, 4], how many…

A:

Q: Evaluate the following integral or state that it diverges. 00 6 3 cos O A. F2 2 T Select the correct…

A:

Q: e interval [-20, 16]. such as inflection points in ascending order, i.e. smallest x values first. Is…

A: We will find the required.

Q: Find the area enclosed by the given curves. TU TU 26) y = sin x, y = csc 2 x, ≤x≤ 3 2 27) Find the…

A:

Q: Find the second-order partial derivatives of the function. Show that the mixed partial derivatives…

A:

Q: Find the derivative of the function by the limit process. g(t) = ³ + St g'(t)=3t+5 Submit Answer

A: given       g(t) = t3+5t Derivative of the given function follow this formula   d/dx (xn) = nxn-1…

Q: 4. Use the Integral Test to determine if the following series converges or diverges. You may assume…

A:

Q: with side length a from each corner and folding up the sides. Find a formula for the volume of the…

A:

Q: Evaluate the integral. esin−1 3x √1-9x² 32) dx

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

Q: WHAT WOULD SPECFICALLY GO IN EACH BOX. Please circle the two answers that go in each box.

A: Given Problem:- limx→∞7xtan2x

Q: Evaluate the triple integral: 元 SS1² S² π/2 O 0 12p sin p cos 0 dp do do

A: The answer is given below:

Q: Given f''(x) = - 16 sin(4x) and f'(0) Find f ¹ƒ(3/3) = = 6 and f(0) = - 5.

A: SOLUTION-

Q: Find the critical number for y = f(x) = x (x + 2)²

A: NOTE: Refresh your page if you can't see any equations. . the given function is take derivative…

Q: A baseball team plays in a stadium that holds 54000 spectators. With the ticket price at $9 the…

A:

Q: A population of 450 bacteria is introduced into a culture and grows in number according to the…

A: Given, p(t)=4505+4t73+t2