An investment pays 8% interest compounded continuously. If money is invested steadily at the rate of

​$16,000​, how much time is required until the value of the investment reaches $160000?

2) Given f'(t)=-0.5t-e^-2t, compute f(5)-f(3)

3) Find the area under the given curve over the indicated interval.

y= 6x^2+x+3e^x/3; x=1 to x=5

Next, let’s suppose a rancher wants to fence off a rectangular shaped enclosure that has two identical sections. You can think of this as a rectangle with an additional fence dividing the rectangle in half. For the sake of this question, he wants that additional fence running North-South (up-down). He still has 2400 feet of fencing that he can use. What are the dimensions that gives the enclosure the most area?

(a) Use the sketch of the pen below for this question. Appropriately label the relevant information in the sketch. Remember, East-West is right-left, North-South is up-down.

(b) Based on the sketch above, what equation is being maximized?

(c) Based on the sketch above, what equation represents the given constraint?

(d) Find the dimensions of the enclosure that gives the largest area.

(e) How much fence is used on the East-West sides? How much fence is used on the North-South sides? What is the ration of the amount of fence used on the East-West sides to the amount of fence used on the North-South sides?

Problem 7. Consider the line integral Z C y sin x dx − cos x dy. (Please show all work)

a. Evaluate the line integral, assuming C is the line segment from (0, 1) to (π, −1).

b. Show that the vector field F = is conservative, and find a potential function V (x, y).

c. Evaluate the line integral where C is any path from (π, −1) to (0, 1).

Under ideal conditions a certain bacteria population is known to double every three hours. Suppose that there are initially 100 bacteria.

(a) What is the population after 15 hours?
(b) What is the population after t hours?
(c) Find the population after 20 hours.
(d) Find the time at which the population reaches 50,000.

Given that f "= - 12 (x-2) ^ 2 + 4, estimate the error obtained by approximating the integral of f (x) on the interval [1.5,2.5] with n = 4, using trapezoids.

Find the domain of the vector function r(t)= <sent,lnt,1/(x-2).

find the equation of the plane that passes through the point (-1,3, -8) and is parallel to the plane 3x-4y-6y = 9

find the equation of the line parallel to the plane 2x + y + z = 8 that passes through the point (1,2,3)

Please answer this 4 i need them quickly

Find the absolute maximum and minimum values of the function, if they exist, over the indicated interval.

Where no interval is specified, use the real line.

a)?(?)=−8x^3 + 9x^2 + 6x - 5; [−2,0]

b) ?(?)= x^2 + 2/x ; (0 ,∞)

A tank has the shape of a sphere with a radius of 5 m. It is filled with water up to 9 m.


(i) Let x be the height in meters measured from the bottom of the tank. The weight in Newtons of a thin layer of water between x and x + Δx is approximately P (x) Δx. What is P (x)?
P (x) =
Express the answer by a formula. Recall that the density of water is ρ = 1000Kg / m3 and that the gravitational acceleration on the surface of the earth is g = 9.8m / s2.


(ii) The work in Joules required to pump this thin layer of water 2 meters above the tank is approximately w (x) Δx. What is w (x)?
w (x) =
Express the answer by a formula.


(iii) Using the previous results, determine, in Joules, the work required to pump all the water 2 m above the tank. Give its numerical value to 3 significant figures.
Answer: 

Find the Taylor series for f(x) centered at the given value of

a=1

fx=6x^-2

Danica and Darrelle have developed a lucrative business selling handmade silver bracelets. Darrelle makes the more complex bracelets and Danica makes the simpler ones. It takes Darrelle 4 hours to make 3 bracelets and Danica can make 5 bracelets every 2 hours.

a. Convert this scenario into linear equation(s); show both the standard form and the slope-intercept form of your equation(s).
c. Each bracelet Darrelle sells makes $10.50 in profit. Each bracelet Danica sells makes $3.50 in profit. If Darrelle and Danica work the same amount of time, explain each of the steps you will use and then calculate how many hours will it take for the whole business to make at least $500 profit?

There are three boxes in front of you. They are as follows: – BOX A, which has the following statement written on it: “Box C is empty.” – BOX B, which has the following statement written on it: “This box contains $100.” – BOX C, which has the following statement written on it: “Box B is empty.” One of the three contains $100 and the other two are empty. The box with the money has a true statement on it, while the empty boxes have false statements on them. Which box has the money?

Consider the following function. (If an answer does not exist, enter DNE.) f(x) = x2 + 5 − x

(a) Find the vertical asymptote(s). (Enter your answers as a comma-separated list.)
x =

Find the horizontal asymptote(s). (Enter your answers as a comma-separated list.)
y =
(b) Find the interval where the function is increasing. (Enter your answer using interval notation.

Find the interval where the function is decreasing. (Enter your answer using interval notation.)

(c) Find the local maximum and minimum values.

(d) Find the interval where the function is concave up. (Enter your answer using interval notation.)

Find the interval where the function is concave down. (Enter your answer using interval notation.)

Find the inflection point.

(x, y) =

(e) Use the information from parts (a)-(d) to sketch the graph of f.

Let C be the boundary of the quarter circle with radius 1, oriented counterclockwise (Figure 1). Evaluate H C(ex + y2) dx + (ey + x2) dy

1) Find the following indefinite integrals.

    a) (4-3xsec^2 x)/x dx

    b) (5 sin^ 3 x ) / (1+cosx)(1-cosx) dx

2) A particle starts from rest and moves along the x-axis from the origin at t = 0 with acceleration

       a(t) =   6 - 2t (ms^-2) at time t. When and where will it come to rest.

       Remember dvdt = acceleration and dsdt = velocity

3) Use substitution to find the following integrals.

    a) (9x)/ sqrt of (3+x2) dx                         Let U = 3+x^2

    b) (dx) / (25- x^2 ) Let x = 5 sin U

4) Consider the integral 1∞ 1 / (2x+1)^3 dx.

    a) Explain why the integral is improper.

    b) Determine whether the integral is convergent or divergent and if convergent, evaluate he integral. (Show all working)

For the following pair of functions, ?(?) = ? 2 − 2, ?(?) = √? − 3 Find each of the following, and State its Domain: a) Find (f + g)(x)

b) Find (f – g)(x)

c) Find (f*g)(x)

d) Find (f*f)(x)

e) Find (f/g)(x)

Net income for the company for the year was $300,000, and 100,000 shares of common stock were outstanding during the year. The income tax rate is 30%. For each of the following potentially dilutive securities, perform the shortcut antidilution test to determine whether the security is dilutive. Assume that each of the securities was issued on or before January 1. Treat each security independently; in other words, when testing one security, assume that the others do not exist.      (10)
1. 10,000 convertible preferred shares (cumulative, 5%, $100 par). Each preferred share is convertible into three shares of common stock.
2. 500 convertible bonds ($1,000 face value, 10%). Each bond is convertible into 25 shares of common stock.
3. 20,000 convertible preferred shares (cumulative, 10%, $50 par). Each preferred share is convertible into two shares of common stock.
4. 2,000 convertible bonds ($1,000 face value, 8%). Each bond is convertible into 15 shares of common stock.
(b) Is It Possible For A Company To Have Positive Cash Flow But Still Be In Serious Financial Trouble?