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Q: X varies directly with y and inversely with z x equals 0.12 when y equals 12 and z equals 2 Find x when y equals 1200 and z equals 1?
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How much should I expect to pay to rent an average house in Calgary?

You should expect to pay about $1200 a month to rent an average house in Calgary. Read more at www.calgarypedia.com/index.php/Housing_(Rental)


A rectangular piece of sheet metal with an area of 1200 in2 is to be bent into a cylindrical length of stovepipe having a volume of 600 in3 What are the dimensions of the sheet metal?

The dimensions are approximately 191 inches by 6.28 inches.This produces a cylinder with about a 2 inch interior diameter, 1 inch radius, and a cross section of 3.14 square inches, 191 inches long.---Area of the rectangle, A = LW =1200 in^2where A is also the lateral area of the cylinder L.A.L.A. = 2(pi)rhVolume of the cylinder, V = (pi)(r^2)(h) = 600 in^3Now, let's find the height and the radius of the cylinder.Let denote W with x, and let W be the height, so h = x. So, L = 1200/x. Let L to be the circumference of the base, so C = L. So we need to find the radius.C = 2(pi)r1200/x = 2(pi)r600/x = (pi)rr = 600/[(pi)x]Let's substitute what we know into the volume formula:V = (pi)(r^2)(h)600 = (pi)[600/((pi)x)]^2](x)600 = (pi)[(3600/[(pi)^2)(x^2)](x)600 = (pi)[3600/(pi)^2)(x^2)](x)1 = 600/[x(pi)]x(pi) = 600x = 600/pi So,W = x = 191 in (approximately). Then,L = 1200/191L = 6.28 inOr you can work like this: Since,L.A. = 2(pi)rh = 1200h = 600/[(pi)r] Substitute h into the volume formula and find r;V = (pi)(r^2)(h)600 = (pi)(r^2)[600/((pi)r)]1 = r substitute r into the height formula;h = 600/[(pi)r]h = 600/[(pi)(1)]h = 600/(pi)h = 191 So,h = L = 191 in, andW = 1200/h = 1200/191W = 6.28 in


How can clculate return duct size?

There are going to be allot of varying opinions on this one but it's fairly simple to get in a good ball park. You want between 600 to 800 feet per minute of air flow so you need to know the CFM of your air handler and then you can calculate it this way. Ftcube /min divide by Ft / Min = Ft square. At 1200 CFM for a flow rate of 800 Ft/min you get a result of 1.5 square feet which is 216 square inches. If you divide by 8 for the prefab 8 inch duct you need a 27 inch wide dimension or 16 X 13.5. Good luck on your project.


A rectangular swimming pool is to be build with an area of 150 square meters The owner wants 2-meter wide decks along either side 3m wide decks at the two ends Whats the smallest property?

Supposing that the actual pool is (a)m long and (b)m wide, then the total property will be (a+6)m long and (b+4)m wide.The next step is to find a relationship between a and b.ab = 150Therefore a = 150/bTherefore, total property area will be:(150/b + 6)(b+4)= 150 + 600/b + 6b + 24= 6b + 600/b + 174= 6b + 600b-1 + 174Taking the derivative and setting it to zero:0 = (6b + 600b-1 + 174)'= 6 + -1*600*b-2= 6 - 600/b2Therefore:6 = 600/b21 = 100/b2b2 = 100b = 10a = 150/10= 15To check whether we have the minimum for area, take the second derivative:(6 - 600/b2)' = (6 - 600b-2)'= 0 - -2*600b-3= 1200b-3= 1200/b3If b is positive, the second derivative will also be positive, so we do have a minimum.Therefore total area of the property:(a+6)m * (b+4)m = (15+6)m * (10+4)m= 21m * 14m= 294m2