Differential equations Questions and Answers

Solve the following equation. x^-2 - 4x^-1 - 5 = 0 Larger x = Smaller x =

Find the relative maximum and minimum values. f(x,y) = e^(8x² + 5y² + 6) Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The function has a relative maximum value of f(x,y) = at (x,y) = B. The function has no relative maximum value. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The function has a relative minimum value of f(x,y) = at (x,y) = B. The function has no relative minimum value.

A rental car company charges $35 plus 35 cents for each mile driven. Part1. Which of the following equations could be used to model the total cost, C, of the rental where m represents the miles driven. C= 3.5m + 35 C= 35m + 3.5 C= 0.35m + 35 Part 2. The total cost of driving 150 miles is;

Let f(x,y)=x² - 4xy-y. Compute f(3,0) and f(3,-3). f(3,0)= (Simplify your answer.) f(3,-3)= (Simplify your answer.)

Enter the solution set of the equation. If the equation has no solution, enter no solution in the box. x x +2 + 4 x - 3 = 20 x2 - x - 6 Type your answer and submit

find the characteristic equations of dx/1=dy/-(2+x)=dq/-xe^x+q What is the general solution

On which interval is the IVP (z cos x)y' + 2y = x+1, y(-5) = 2 guaranteed to have a unique solution? (-∞,∞) (-∞,∞) (-5,∞) (-5,0) (-π,π) (0,π 2) (-π 2,π 2) (0, π 2) (-π 2,0) (-2π,-3π 2) (-5π 2,-3π 2) (-5π 2,5π 2)

Solve the equation f(x) = x³ = x²-x+1 given that one of its roots is a = 1 A. x = {1} B. z={-1,1} c.z={-1} D. z = {0}

Mark dropped a phone from his apartment balcony. In an apartment below, Madelyn noticed the phone pass by her 2.4-meter tall window in 0.026 seconds. From how high above the top of Madelyn's window did Mark drop the phone? Round the solution to the nearest tenth, if necessary. motors

Let d²f dy² = 6 sin (y) Find the particular solution to the above differential equation that satisfies the following initial conditions. f'(π 2) = 8 f(5π 3) = 7

Let f''(x) = 1 2x3 2 Find the particular solution to the above differential equation that satisfies the following initial condition. f has a horizontal tangent line at (1, 2).

Let h''(t) = -3 sin(t) Find the particular solution to the above differential equation that satisfies the following initial conditions. h'(π/2)=8 h(4π/3)=3 h(t)=

Let d² f/dv²=4 Find the particular solution to the above differential equation that satisfies the following initial conditions. • f'(3) = -8 f(1) = 6 f(v) =

Let d² f/dz²=e^- 4z Find the particular solution to the above differential equation that satisfies the following initial conditions. f'(0) = 8 f(0) = 7 f(z) =

Let dg/dy=3e^y Find the particular solution to the above differential equation that satisfies the following initial condition. • g(-3) = 2 g(y)=

Let h''(x) = 36x + 16 Find the particular solution to the above differential equation that satisfies the following initial conditions. • h'(0) = 2 • h(- 6) = -1 h(x)=

Let d^2h/dt²=30t Find the particular solution to the above differential equation that satisfies the following initial conditions. h'(0) = 7 h(9) = -5 h(t)=

Let dh/dx=-6/1+x^2 Find the particular solution to the above differential equation that satisfies the following initial condition. • h(1) = -3 h(x)

Find the area of the region under the graph of the following function. f(x) = 2xe-x from x = 4 to x = 7

Use long division to find the quotient and remainder. (4x² + 30x+14) / (x + 7) What is the quotient? What is the remainder?

If a = 20 and c = = 28, find the missing sides and angles in the right triangle, where a is the side opposite of angle A, b is the side opposite of angle B and c is opposite of the right angle, angle C.

If A = 31° and c = 19, find the missing sides and angles in the right triangle, where a is the side opposite of angle A, b is the side opposite of angle B and c is opposite of the right angle, angle C.

A line that passes through the points (-4, 10) and (-1, 5) can be represented by the equation y=-5 3(x-2). Which equations also represent this line? Select three options. y=-5 3x-2 y=-5 3x+10 3 3y = -5x + 10 3x + 15y = 30 5x + 3y = 10

Solve the equation and write the solution set. 2x² 13x +2=0

Find (gof)(x) for the given functions. Simplify the expression. Do not enter any spaces in the answer. f(x) = 6x - 1, g(x) = 5x + 2

Given the following function, determine the interval for the principal cycle. Then for the principal cycle, determine the equations of the vertical asymptotes, the coordinates of the center point, and the coordinates of the halfway points. Sketch the graph y = tan (x - π 3)

Give the order of the differential equation below, where y represents a function of the variable x. y-2y'-x²y" = 5 Choose the correct answer below. A. The given equation is a second-order differential equation because it involves a second derivative but no higher derivative. B. The given equation is a first-order differential equation because it only involves a first derivative. C. The given equation is a third-order differential equation because it involves a third derivative but no higher derivative. D. The given equation is a first-order differential equation because it involves a first derivative but no higher derivative.

Define first order Linear differential equation and find the solution of given differential equation. dy/dx + y/x = x² If y=1 when x=1.

Use ordinary division of polynomials to find the quotient and remainder. (b2-3b-28)÷(b + 2) Choose the correct quotient. A. b-28, R 11 B. b-7 C. b-4 D. b-5, R (-18)

Fill in each blank with the appropriate number related to the exponential expression. -34 a. The base of the expression is Type your answer here b. The exponent of the expression is Type your answer here c. When simplified, -34 = Type your answer here

Use a substitution v=y' to reduce the order and solve the differential equation. Then apply the initial values to find the solution to the initial value problem. d²y /dt²+ 1/y (dy/dx)^2= 0; y(-1)= 1, y'(-1)=1

Of all numbers whose difference is 14, find the two that have the minimum product. What are the two numbers?

Find the relative maximum and minimum values. f(x,y) = x³ +y³ - 24xy Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The function has a relative maximum value of f(x,y) = at (x,y) = (Simplify your answers. Type exact answers. Type an ordered pair in the second answer box.) B. The function has no relative maximum value. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The function has a relative minimum value of f(x,y) = at (x,y) = (Simplify your answers. Type exact answers. Type an ordered pair in the second answer box.) B. The function has no relative minimum value.

The population density of a city is given by P(x,y)= -25x²-20y² + 200x+600y + 180, where x and y are miles from the southwest corner of the city limits and P is the number of people per square mile. Find the maximum population density, and specify where it occurs. The maximum density is people per square mile at (x,y)=

If it is possible to solve for y in terms of x, do so. 2x - 9y = 18 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. y= B. It is impossible to solve the equation for y in terms of x.

Find y' in two ways for the equation 2x + 7y + 9 = 0. (A) Differentiate the given equation implicitly and then solve for y'. (B) Solve the given equation for y and then differentiate directly. (A) What is the implicit differentiation of the given function? A. -2x-7y' = 0 B. 2+7y' = 0 C. -2+7y' = 0 D. 2-7y' = 0 (B) Solve the given equation for y. y= Using either method, y' =

Use the price-demand equation to find the values of p for which demand is elastic and the values for which demand is inelastic. Assume that price and demand are both positive. x = f(p) = 1936-4p² The values of p for which demand is elastic are (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) The values of p for which demand is inelastic are (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)

1. Find the general solution to the differential equation dy/ dx = 2xy².

*2. Find the solution to the following initial value problem: dy/ dx = e^y+x given that y(0) = 0

For the function f(x)=(x-1) 4/5 (a) Find the critical numbers off (if any); (b) Find the open intervals where the function is increasing or decreasing; and (c) Apply the First Derivative Test to identify all relative extrema. Use a graphing utility to confirm your results.

Use the chain rule to find dz/dt z = sin(x) cos (y), x = √t, y = 6/t

Solve the system of the simultaneous differential equations dx/dt + y = e^t, x(0) = 1 x - dy/dt = t, y(0) = 1

Next question A motorcyclist being monitored by radar accelerates at a constant rate from 0 mph (v(0)=0) to 55 mph in 18 sec. How far has the motorcycle traveled after 18 sec? (Hint: Convert seconds to hours.)

Given x = π/3 what is the exact value of sin(2π - x)?

Consider the following. x = sin(6t), y = cos(6t), z = 12t, (0, 1, 2π) Find the equation of the normal plane of the curve at the given point. Find the equation of the osculating plane of the curve at the given point.

Consider f(x) = 38x² -112 / x²-8 Determine the intervals on which f is decreasing. f is decreasing on: f is decreasing nowhere. Determine the intervals on which f is increasing. f is increasing on: f is increasing nowhere. Determine the value and location of any local minimum of f. Enter the solution in (x, f(x)) form. If multiple solutions exist, use a comma-separated list to enter the solutions. f has a local minimum at: f has no local minimum. Determine the value and location of any local maximum of f. Enter the solution in (x, f(x)) form. If multiple solutions exist, use a comma-separated list to enter the solutions. f has a local maximum at: f has no local maximum.

Consider g(w) 11 ln(10 - 9 ln w) = Determine the intervals on which g is decreasing. Og is decreasing on: Og is decreasing nowhere. Determine the intervals on which g is increasing. Og is increasing on: Og is increasing nowhere. Determine the value and location of any local minimum of f. Enter the solution in (w, g(w)) form. If multiple solutions exist, use a comma-separated list to enter the solutions. Og has a local minimum at: g has no local minimum. Determine the value and location of any local maximum of f. Enter the solution in (w, g(w)) form. If multiple solutions exist, use a comma-separated list to enter the solutions. Og has a local maximum at: g has no local maximum.

An oceanographer claims that the mean dive duration of a North Atlantic right whale is 11.4 minutes. A random sample of 33 dive durations has a mean of 12.4 minutes and a standard deviation of 2.3 minutes. At x = 0.05 is there enough evidence to reject the oceanographer's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. Ho: Ha: (Type integers or decimals. Do not round.) The claim is the hypothesis. (b) Use technology to find the P-value. Find the standardized test statistic, t. t = (Round to two decimal places as needed.) Obtain the P-value. P = (Round to three decimal places as needed.) (c) Decide whether to reject or fail to reject the null hypothesis. Ho because the P-value (d) Interpret the decision in the context of the original claim. There enough evidence at the % level of significance to (Type integers or decimals. Do not round.) greater than α. support reject the claim that the mean dive duration of a North Atlantic right whale is minutes.

Find the partial derivatives of the function f(x, y) = xye^3y fx(x, y) = fy(x, y) = fxy(x, y) = fyx(x, y) =

Given the following linear system of ODE: V₁' = 4y₁+2y₂ V₂' = 10y₁-4y₂ what is the type of the critical point? the critical point is spiral the critical point is saddle the critical point is proper node the critical point is center the critical point is improper node