2013年3月9日 · For a minimal surface area, the top of the tank will be square. Let's say the side of this square is x. And let h be the height of the tank. Then the volume is x \times x \times h = 500 and the surface area is A = x \times x + 4 x \times h. Can you combine these equations to find A as a function of x?

2008年11月23日 · We can use these to find the surface area of the can. I'm not sure if your cylinder is open on top or not, but the process for both is similar. So lets suppose that it is open on top then the surface area is A_{surface}=2\pi r h+\pi r^2 but we also know that 10=\pi r^2 h \implies h= \frac{10}{\pi r^2}

2011年9月25日 · Can I just say how confusing this part of the problem is. So 4root3 times radius cubed and 2 times pi times radius times hight describe the surface area of the rectangular cutout and the two hexagons without the two circles, and I guess the length of the sum of the 2 circumferances and the hight are proportional to the surface area when multiplied by the …

2020年10月11日 · A potter may form a cylinder as part of another process, such as the production of a number of disks of equal size, assuming they can be cut from the cylinder with minimal distortion. (Yes I have done a bit of pottery. And, since when are we required to discern the motives of a fictional character in a word problem?

2007年3月15日 · The surface of mountain is modeled by the equation h(x,y)=5000 -0.001x^2-0.004y^2. A mountain climber is at the point (500, 300, 4390). In what direction should the climber move in order to ascend at the greatest rates ? Give direction as a vector only i & j components needed. From that...

2007年4月28日 · Since z=xy+1, thus any point on surface is (x,y,xy+1) The distance of this point from the origin is, sqrt(x^2+y^2+(xy+1)^2) = sqrt(x^2+y^2+x^2y^2+2xy+1) We need to minimize this. Instead let us minize its square, that is to remove the square root. We need to minimize, g(x,y)=x^2+y^2+x^2y^2+2xy+1 Find its partial derivatives and make them zero.

2007年5月28日 · A spherical raindrop evaporates at a rate proportional to its surface area. Write a differential equation for the volume of the raindrop as a function of time. The back of the book says the answer: dV/dt = -kV^(2/3) for some k > 0. Though I have no idea how. Thanks

2009年8月26日 · A chemistry student in lab needs to fill a temperature-control tank with water. The tank measures long by wide by deep. In addition, as shown in the sketch below, the student needs to allow between the top of the tank and the top of …

2013年3月24日 · In any poset (partially ordered set), an element u is an upper bound of a set S iff s\leq u for all s in S. In particular for {a,b,c} both l and m are upper bounds from your diagram.

2011年8月23日 · Let f and g be the functions given by f(x) = 1+sin(2x) and g(x) = eˆx/2. Let R be the shaded region in the first quadrant enclosed by the graphs of f and g as shown in the figure above.