# Posts by Tezuka

Total # Posts: 11

**Calculus**

You have a conical tank, vertex down, which is 12 feet across the top and 18 feet deep. If water flows in at a rate of 9 cubic feet per minute, find the exact rate of change when the water is 6 feet deep. You know the rate of dV/dt (inflow), and you can get the volume of a ...

*April 4, 2007*

**Calc**

Problems, once again. 1. Compute the average value of: f(x} = x/(x+3) over the interval [-a,a] 2. Find the area of the region bounded by the graph of: y = 2√(x^2 + 1) X axis Y axis Line x = 1 On the first, integrate, then divide the integral by 2a. On the second, ...

*March 17, 2007*

**Calc**

Calculate the area bounded by the x-axis and the function f(x)= -(x-a)(x-b), where a<b and a and b are constants. Please do it out in steps so I can understand it, and try to simplify the final answer and leave it in factored form. Frankly, I would multiply out the ...

*November 27, 2006*

**Calc**

Is f(x)=|x+2| integrable? Please give a reason behind your answer. Yes, it is piecewise integrable. http://www.mathwords.com/p/piecewise_continuous_function.htm Could you explain that a bit more? I understand that is is continuous, but how does that relate to integration?

*November 27, 2006*

**More Calc**

There is a ditch that is 18 feet deep at its deepest point. A rock is dropped from the rim above the deepest point. a. Write the height of the rock as a function of t in seconds. b. How long will it take for the rock to hit the ditch floor. We want a position function, or y(t...

*October 7, 2006*

**Calculus**

A rectangle is bounded by the x-axis and the semicircle y=ã(25-x^2). Question is, what length and width should the rectangle have so that its area is a maximum, and what is the maxuimum area? Area= length*width = 2x*y= 2x*sqrt(25-x^2) Now, take that, differentiate...

*October 6, 2006*

**Calculus**

A rectangle is bounded by the x-axis and the semicircle y= ã(25-x^2). What length and width should the rectangle have so that the area is maximum? Place the semi-circle so it's center coincides with the origin. If you go a distance x to the right the max ...

*October 1, 2006*

**Calculus...again**

I'm gonna have abunch of questions, cause I have a test. >_< If you planened to fence a rectangular pasture that must contain 4000 sq meters, what dimensions would require the least amount of fencing? Perimeter= 2l + 2w area= lw=4000 or l=4000/w P= 2(4000/w + w) Now ...

*September 30, 2006*

**Calculus**

Find two numbers such that the sum of the first plus three times the second is 600 and their product is a maximum. x + 3y=600 xy is a max. This is the problem statement. let U be the function equal to xy. U=xy = y(600-3y) Now, maximize U (take derivative, set to zero), and ...

*September 30, 2006*

**Live Help**

This may not be homework...but how do I go about using the live help for this site? At this point, live help is not available. Computer glitches, you know. So keep posting your questions on the message boards. Especially in the afternoons and evenings, there are usually ...

*September 19, 2006*

**Math**

A norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. Find the dimensions of a Norman window with maximum area if the total perimeter is 16 feet. X = the width of the rectangle. Y = the length of the rectangle. X/2 = the radius ...

*September 17, 2006*

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