Let y(t) represent your bank account balance, in dollars, after t years. Suppose you start with $70000 in the account. Each year the account earns 4% interest, and you deposit $4000 into the account. This can be modeled with the differential equation: dy 0.04y + 4000 dt y(0) = 70000 Solve this differential equation for y(t) y(t)

Q: Find the derivative w = sin* y cos*y a. sin³ 2y cos 2y b. sin² 2y cos 2y c.sin 2y cos 2y d. sin 2y…

A:

Q: Determine whether f(t) is continuous, piecewise continuous or neither on [0, 10] and sketch the…

A: Here, the given function is: f(t)=tt2-1 The function is not defined at x=1.

Q: DeltaMath Monday, May 9, 2022 Assignme X + → C A b…

A: Triangle

Q: a) Find the solution of the following differential equation: y'' − 2y' = x − e3x

A: As per the company's guidelines, we are supposed to solve the first question for you, kindly repost…

Q: Q2\Find the point at which the tangent to the curve y = v4x2 + 1-2 has its slop 2

A: Given: y=4x2+1-2 Slope = 2 We know that slope of tangent to a curve y is defined as dydx

Q: 9. f(x) = (x² + 3x + 1)100 %3D

A:

Q: 4. Use synthetic division to show that c is a zero of the given polynomial function. a. P(x) =x'-4x²…

A: a. P(x)=x^3-4x^2+5x-2 At c =2 Hence by synthetic devision 2| 1  -4    5    -2    => coefficient…

Q: 6. f(x) = 2x2-7x-11 Sx2 es

A:

Q: The buyer for a retail store located in a shopping mall has convinced himself that if he prices…

A:

Q: 7. Find the derivative of In y + exy? ey sin 2x. %3D -

A: Here, the given implicit function is: ln y+exy2-ey=sin 2x...(1)

Q: A particle is moving in space with position function R(t) = (cos(4t), sin(4t),5 – 3t) а. Find the…

A:

Q: 3. Use the Intermediate Value Theorem to show that the following equation has a solution. sec(x) =…

A:

Q: Estimate the area under the graph of f(x) 1 over the interval [3, 7] using five I+ 2 approximating…

A: The given function is f(x)=1x+2 over the interval [3, 7] We have to use five approximating…

Q: Find the domain of y = log(2 – lx). The domain is:

A:

Q: V9, 0< y< 4 Find the area of the surface generated by revolving the curve x = about the у-ахis.

A: We have to find the surface area.

Q: B2. dx Let g(?) = " 4t

A:

Q: Given that (x + 2) is a factor of the polynomial 2a – 5x2 + ax + a, the - value of the constant a is

A: If (x+2)  is factor of the polynomial 2x3-5x2+ax+a then remainder will be zero when we divide (x+2)…

Q: Choose any 5 of the following problems to complete. Solve the problem by following the procedure for…

A:

Q: Find the equation of the tangent line to the curve g(x) = 4x² – 3x + 2 at the point (1, 3).

A: As we know that; The expression for the equation of the tangent line is: y-y1=mx-x1 Where; m is the…

Q: A farmer finds that if she plants 50 trees per acre, each tree will yield 55 bushels of fruit. She…

A: It is given that, If a farmer plants 50 trees per acre, each tree will yield 55 bushels of fruits.…

Q: Find the solution of the following differential equation: y'' − 2y'= x − e3x

A:

Q: Find fractional notation for the infinite sum. (These are geometric series.) 0.1313131313...

A:

Q: 12. Solve the second-Order differential equation: d²y - y = e* (use method of variation of…

A:

Q: Find f '(x). f0) = (+4)5 f(x) f '(x)=|

A:

Q: (6) In the interval 0 <x< 2n, the solutions of the equation tan? (x) = tan(x) are? (A) "/4 (B) "/4,…

A:

Q: 8. Find the dimensions of the largest-volume cylinder that can be inscribed in a sphere of radius 10…

A:

Q: Find the radian measure of the central angle of a circle of radius 3 meters that intercepts an arc…

A:

Q: farmer finds that if she plants 90 trees per acre, each tree will yield 30 bushels of fruit. She…

A:

Q: .3 29. dr 18 31. 1/2 sin (x/2 + 1) d

A:

Q: Question 5 > Find the value V of the Riemann sum V = > f(ck)A¤k k=1 for the function f(x) = x² – 2…

A:

Q: For problems 3 & 4 find the arc length function for the given vector function. 3. F (t) = (f', 2r°,…

A:

Q: Consider the integral / 3x* (25 + 1) dz. In the following, we will evaluate the integral using two…

A: ∫ 3x4x5+1dx=3·∫ x4x5+1dx=3·∫ x9+x4dx=3∫ x9dx+∫ x4dx=3x1010+x55Add a constant to the…

Q: 4. For each series determine if it is convergent or divergent. Give reasons for your answers. (-3)*…

A:

Q: In calm waters, the oil spilling from the ruptured hull of a grounded tanker forms an oil slick that…

A:

Q: (7x-6x+8) dx |(7x - 6x + 8) dx =| /Simplifu vour anci Mor /Cimpli6 5. 5.

A: We can solve this as follows:

Q: POS jma- 3 d 1 sin t dt %3| dx 1 1 (A) – x sin(x²) (B) sin(x²) (C) x sin(x²) (D) –sin(x²) ов O O O O

A:

Q: 11. The position of a particle as it moves horizontally is described by the given equation S=sint -…

A: Here, the displacement function is given by: s=sin t-cos t, 0≤t≤2π Now, to find the maximum and…

Q: length of the curve r = 4 sin 20 for ÷sos 6 2

A: To find the length of the curve r=4 sin 2θ for π6≤θ≤π2.

Q: Determine whether converges or diverges. If it converges, find the sum. Paragraph U - Ay + v ...…

A: We have to find out sum

Q: (9) If f(x) = 2x +k and g(x) = (x – 5)/2, for what value of k is f(g(x)) = g(f(x))? %3D (A) 15 (B) 5…

A:

Q: Find the MacLaurin series for the function f(x) = x cos (2x) at a = 0.

A: Using the definition of maclaurin series ee can find series or by given function's series we can…

Q: Given that lim f(x) = 0 x-a lim g(x) = 0 lim h(x) = 1 xa lim p(x) = 0 lim q(x) = 00, xa evaluate if…

A:

Q: x3 Evaluate f using substitution (3-2x)5

A:

Q: Find the area of the region between the following curves by integrating with respect to y. If…

A:

Q: (10) Which of the following is(are) true for the function f(x) = 2 - log3(x + 1) ? I. The x and y…

A:

Q: Find y subject to the given conditions. y"= 12x, y"(0) = 14, y'(0) = 4, and y(0) = 4

A: To find y subject to given conditions.

Q: (cost -1/2 <x< 0 The funaction f(t) = is %3D sint 0<x<n/2 а) even b) odd c) neither

A:

Q: 14. A rocket is being launched straight up from ground level, and the launch is being monitored by a…

A:

Q: 7. (2x-y)dx+x dy = 0 Ans x+=c

A: Given problem:- solve (2x2-y) dx+xdy=0

Q: Differentiate the three possible types of boundary conditions that can be used for second-order…

A: