Given f''(x)= 4x-6

and f'(-2)=5 and f(-2)=1

FIND: Find f'(x)=

and find f(2)=

A rancher has 600 feet of fencing to enclose two adjacent rectangular corrals (see figure).

(a) Write the area A of the corrals as a function of x.

(b) Construct a table showing possible values of and the corresponding areas of the corral. (Round your answers to two decimal places.)

Use the table to estimate the dimensions that will produce the maximum enclosed area. (Round your answers to two decimal places.)

(c) Use a graphing utility to graph the area function.

Use the graph to approximate the dimensions that will produce the maximum area. (Round your answers to two decimal places.)

(d) Write the area A as a function of x in standard form to find analytically the dimensions that will produce the maximum area.

(e) Compare your results from parts (b), (c), and (d).

They are very similar.

They are significantly different.

a)

Let y be the solution of the equation

y ′ = sqrt(1 − y^2) satisfying the condition  y ( 0 ) = 0.

Find the value of the function  f ( x ) = sqrt(2)*y ( x ) at x = π/4.

(The square root in the right hand side

of the equation takes positive values and − 1 ≤ y ≤ 1)

b)

Let y be the solution of the equation

y ′ = 5 x^4 sin ⁡(x^5) satisfying the condition y ( 0 ) = − 1.

Find y ( (π)^1/5 ).

c)

Find the largest value of the parameter r

for which the function y = e^(rx) is a solution of the

equation y ″ − 12 y ′ + 27 y = 0.

d)

Let y ′ = − 3x^2*e^(-x^3) and let y ( 0 ) = 1.

Find  ln ⁡ ( y ( 2 ) ).

e)

Find the smallest value of the parameter r

for which the function y = e^(rx) is a solution of the

equation y ″ − 12 y ′ + 27 y = 0.

A bulldozer’s velocity (in m/s) at a time t is given by v(t)=t^2-t+3.

(a)Estimate the displacement of the bulldozer on the time interval using 0≤t≤5 Midpoint Riemann Sum with 10 subintervals. Specify the value of,n ,Δx, and the chosen sample points.

(b)Find the exact displacement of the object on the time interval 0≤t≤5 using the limit definition of the definite integral.

Thank you,

   (b) Find the equation of the tangent line to the curve

       8x^2y^3-5x^2+7y^3=10(x-3y) , at the point (2,-2).   

   (c) Given T''=6x^2y^3-cosx+5y^2-siny+10x^2-e^-3x ; determine:

1. T'=∫(T'')∂x                                      
2. T'=∫(T'')∂y                          

              (d) Solve the equation cosecxcosydy-10xdx=0 , separably.

Solve the following system. If the​ system's equations are dependent or if there is no​ solution, state this.

3x - 4y -z = 9

2x + 2y + z = 0

5x - 2y + 2z = -1

The solution is....

PLEASE MAKE SURE THIS IS CORRECT. I KEEP PAYING FOR THE WRONG ANSWER!

Find f(x) if f is a linear function that has given properties.

f(-1)=1, f(3)=9

f(x)=

Not all operators are commutative, namely, a*b = b*a.

Consider functions under the operators addition, subtraction, multiplication, division, and composition.

Pick two of the functions and use a grapher (like Desmos) to graph the functions under the operators. If the functions are commutative under the operator, the graphs should be identical (overlap everywhere) when you change the order in which the functions are entered with the operator. Determine which operators seem to the commutative and which operators seem not to be commutative using graphs as evidence. Explain what you learn.

Some functions you might use are below.

F(x)  = 2x + 1

G(x) = x^2 +2x +1

H(x) = sin(x)

I(x) = e^x

J(x) = log(x)

K(x) = 1/x

Use Laplace transform to solve the initial value problem y''+y'= π with y(0) = π, y'(0) = 0.

A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 8 inches below the equilibrium position.

(a) Find the position x of the mass at the times

t = π/12, π/8, π/6, π/4, and 9π/32 s.

(Use

g = 32 ft/s²

for the acceleration due to gravity.)

(b) What is the velocity of the mass when

t = 3π/16 s?

4

   ft/s

In which direction is the mass heading at this instant?

upward

downward

    
(c) At what times does the mass pass through the equilibrium position?

0

   ,  n = 0, 1, 2,  

A mass of 1 slug is placed on a vertical spring with constant k = 16 lb/ft. Starting at t = 0 a force equal to f(t)= 8sin(4t) is applied to the system. Find the equation of motion if the surrounding system offers a damping force equal to 8 times the instantaneous speed. Consider x(0)=0 x'(0)=0.   differential equations

Use Newton's Method to approximate the zero(s) of the function. Continue the iterations until two successive approximations differ by less than 0.001. Then find the zero(s) to three decimal places using a graphing utility and compare the results.

f(x) = x³ − 6.9x² + 10.79x − 4.851

A. Find the region bounded by the curves y = (x−3)^2 and y = 12−4x. Show all of your work.

B. Find the equation of the tangent line to the curve 5x^2 −6xy + 5y^2 = 4 at the point (1,1) Show all of your work. Thanks

You run a small furniture business. You sign a deal with a customer to deliver up to 600 chairs, the exact number to be determined by the customer later. The price will be $ 130 per chair up to 500 chairs, and above 500 , the price will be reduced by $ 0.25 per chair (on the whole order) for every additional chair over 500 ordered.

An investment offers an onetime bonus of 2% of the principal after being invested for 5 years. If $50 000 is invested at 4.75% compounded annually for 10 years, describe how the graph of the investment with the bonus differs from the graph of the investment without the bonus. Include any calculations.