A hole is cut through the center of a sphere of radius r. The height of the remaining spherical ring is h. Find the volume of the ring (two ways), and show that it is independent of the radius of the sphere. (See problem 4, page 505.) (a) as a A????1dxA????1 integral. (b) as a A????1dyA????1 integral. [2] Set up and evaluate the definite integral that gives the length of the graph of f(x)=(e^3x e^-3x)/6 over the interval 0 ln 2 ? ?x . [3] Set up and evaluate the definite integral that .... Read More

1). If the frequency is variable and the length of the closed (at both ends) tube is fixed at 45 cm, sketch the plastic tube showing the positions of the nodes and anti-nodes for the three lowest resonant frequencies. 2). If the frequency is held constant at 1350 Hz and the length of the closed (at both ends) tube is increased from zero, sketch the tube showing this expansion of length and the positions of the nodes and anti nodes for the first three resonances. .... Read More

Show transcribed image text In a snowball melts so that its surface area decreases at a rate of 5 cm2/min, find the rate at which the diameter decreases when the diameter is 9 cm. Water is leaking out of an inverted conical tank at a rate of 9,000 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4m. If the water level is rising at a rate of 20cm/min when the height of the water is 2 m, find the .... Read More

A Rankine oval is formed by combining a sourceâ€“sink pair, each having a strength of 36 ft 2 /s and separated by a distance of 12 ft along the x axis, with a uniform velocity of 10 ft/s Attachments: rankine_oval.pdf .... Read More

Find the alope of the line which passes through points (4, -3) (7,1) .... Read More

Please show work where needed. Feel free to hand write the answers if it will make it easier for you. Attachments: quiz_3-ma107-1.docx .... Read More

1: Watch the Supplemental Week 5 Video, "Math Crash". What other uses for radicals exist? Research through the internet and cite sources as needed. 2: I found this week video interesting, because I always wondered how the cops comes up with how fast a person was going during an accident, and now I see that they use radicals also. Radical numbers are also used in the scientific and engineering world. For example, .... Read More

Simplifying multiplied radicals is pretty simple. We use the fact that the product of two radicals is the same as the radical of the product, and vice versa. The radical symbol (âˆš) represents the square root of a number. You can encounter the radical symbol in algebra or even in carpentry or another trade that involves geometry or calculating relative sizes or distances. You can multiply any two radicals that have the same indices (degrees of a root) together. If the .... Read More