4. At age 35 you start saving for retirement. Your investment plan pays 6% APR compounded monthly and you want to have $2,000,000 when you retire at age 65.
        a) How much do you need to save each month?
        b) Suppose you had started saving when you were 30 years old. How much would you need to save each month?
        c) Suppose you had started saving when you were 25 years old. How much would you need to save each month?
        d) Were you surprised by the answers in parts a - c? Discuss the effect of time on the growth of money.

Personnel in a luxury hotel readily offer advice and recommendations about services and area activities. Complete each sentence with the correct verb form, either the infinitive, present indicative, or present subjunctive, according to the context.

Evaluate the surface integral

F · dS

for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.

F(x, y, z) = x i + y j + z⁴ k

S is the part of the cone z =

beneath the plane

z = 1

with downward orientation

y"´-9y"+26y´-24y=1 y(0)=y´(0)=y"(0)=1

1. Determine if the following deduction rule is valid:

p∨q
¬p

_______

∴ q

2. Determine if the following is a valid deduction rule:

(p∧q)→r
¬ p ∨ ¬ q

________

∴     ¬r

3. Suppose p and q are (possibly molecular) propositional statements. Prove that p and q are logically equivalent if any only if p↔q is a tautology.

You are standing at a base of a Ferris Wheel which is 4 m above ground while your friend is riding. The Ferris Wheel is 8m in diameter. Describe how the shape of the sine curve models the distance your friend is to the platform you are on. Identify the function that will model this situation as well as a function that will model the if we measure his distance to the ground. In your explanation use the following terms:

• Sine
• Function
• Radius
• Repeat
• Rotate
• Amplitude
• Period
• Intercept
• Maximum
• Minimum
• Axis of the curve

Assume the reader understands derivatives, and knows the definition of instantaneous velocity (dx/dt), and knows how to calculate integrals but is struggling to understand them. Use students’ prior knowledge to provide an explanation that includes the concept and physical meaning of the integral of velocity with respect to time.

Reminder: The user is comfortable with the calculations, but is struggling with the concept. To fully address the prompt, emphasize the written explanation in English over the calculation.

Do Not Copy Paste Any Answer

2. Describe the image of the circle |z − 3| = 1 under the M ̈obius transformation w = f(z) = (z − i)/(z − 4). Be sure to explain why your description is correct

Order reduction

Generate the general solution for each of the given equations if y_1 is known to be a solution.

1. y``-4y'+4y=0, y1=e^2x

2. y''+2y'+y=0, y1=xe^-x

3.x^2y''-xy'+2y=0, y1=xsin(lnx)

Use a triple integral to determine the volume of the solid bounded by paraboloid x2+y2=z and the plane z=4y. Round your answer to two decimal places.

Suppose A is an n × n matrix with the property that the equation Ax = b has at least one solution for each b in R n . Explain why each equation Ax = b has in fact exactly one solution

please explain step by step. see if the given matrix A is diagonalizable, if so, give a diagonal matrix similar to A as well as a matrix P so that P⁻¹AP is the diagonal matrix below.

3 1 -1

0 0 -2

0 1 2

maclaurin series for x=.5, 1.5 radians f(x)= (tanx - sinx -2.75) to the third derivative

The numerical aspect of statistics can be described as "numbers with social context." What does this mean to you?

Solve the initial value problem using systems of Linear Differential Equations. Please try to use computer typing

x’ – 4y = 3

x + y’ = 2

IVP: x(0) = 0, y(0) = 1