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Equation describing the motion of a buoy

Please explain how to solve to the following problem: A buoy oscillates in simple harmonic motion y = A cos omega(t) The buoy moves a total of 3.5 feet (vertically) from its low point to its high point. It returns to its high point every 10 seconds. (a) Write an equation describing the motion of the buoy if it is at its

Related Rates : Application of Derivatives Word Problems

2 (a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in terms of dr/dt (b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1m/s how fast is the area of the spill increasing when the radius


Differentiate: 1) y=(cos(x)^cot^2(x) 2) find the second derivative of sin(x^2*y)=-cos(x^2*y) note: *=multiply


The curve y = ax2(ax sqaured) + bx passes through the point (2, 4) with gradient 8. Find a and b I have the answer but do not understand how to get to it. Therefore, could you please show full workings. Many thanks.

Derivatives and Graphing : Local Maxima and Minima and Sketching Graphs

The function has a derivative everywhere and has just one critical point, . In parts (a)-(d), you are given additional conditions. In each case decide whether is a local maximum, a local minimum, or neither. Explain your reasoning. Sketch possible graphs for all four cases. a) b) c) d) Please see th

Application of Derivatives Word Problem : Future Value of Investment

Assume that you collect P dollars from a transaction and being a mathematics wiz, you have developed formula to calculate the future value of your investment: where, r is the rate of interest and t is the time horizon. Suppose you invest your profit, P dollars, from above transaction, and invest it in a bank at 5% rate of

Linear Isometry, Radon-Nikodym Derivative and Isomorphisms

Let be a measurable space and let be two -finite measures defined on . Suppose and is the Radon-Nikodym derivative of with respect to . Define by Show that is a well-defined linear isometry and is an isomorphism if and only if (i.e are mutually absolutely continuous). ---


I am not sure how to set up this problem, I think that I have to use the exponential rule, but after that I am lost. (See attached file for full problem description with complete equations) --- The quantity q, of a certain skateboard sold depends on the selling price, p, in dollars, so, we write q = f(p). You are give


For this equation E= (-C/r) + D(-r/P) (Where c, D, and P are constants) Do the following procedure: 1. Differentiate E with respect to r and set the resulting expression equal to zero. 2. Solve for r0 in terms of C, D and P. Here is where I am at in the problem: I have obtained a derivative (and I'm look


Find the first derivative of problem in attached file. It is only one problem. Find the 1st derivative of f(x) = (e^x + e^-x)/x

Derivative problems

Prob. 2. The area of a rectangle (x,y) is the product xy. The perimeter of a rectangle P is 2x+2y. For a given P, find x and y that gives the largest area of a rectangle (x,y) for given perimeter P. Hint: Maximize A(x) = xy, where y = (P-2x)/2. Prob. 3. Find the 1st derivative of f(x) = [(3 - x^(2/3))][(x^(2/3) + 2)^(1/2

Differentiating ln x

Question 1 says to differentiate using the quotient rule f(x) = 1 + 2x/1-2x where x < 1/2. My answer is -8xsquared/1 - 2x squared.(at x = 1/4) Question 2 says rewrite the expression of f(x) = ln (1 + 2x/1 - 2x) (-1/2 <x<1/2) by applying a rule of logarithm and then differentiate. So rewriting f (x) = ln (1 + 2x) - (1 - 2x) =

Non linear PDE.

I cannot use mathematical symbols. Thus, I will let * denote a partial derivative. For example, u*x means the partial derivative of u with respect to x. Moreover, I will further simplify things by letting p=u*x and q=u*y. Also, ^ denotes a power (for example, x^2 means x squared) and / denotes division. This is the problem: T

Applications of Derivatives : Velocity of a Particle

Let: v(t) = { 2t 0< t < 5 {10 5< t < 10 be the velocity of a particle given in meters per second. Find the distance traveled by the particle from t = 0 to t = 10 seconds. --- Please see the attached file for the fully formatted problems.

First and Second Derivatives : Using Implicit Differentiation

X^2y^2-2x=3 I'm trying to verify my answer for the first derivative, and see if I got the second one right as well. For the first derivative I got (1-xy^2)/(x^2y) I think I'm having a problem with the 2nd derivative because I got x^2-2x^3y^2+x^3y^4 It doesn't look right to me,