A. calculate the volume of the solid of revolution created by rotating the curve y = 3 + 3 exp(-5 x) about the x-axis, for x between 2 and 4. volume : 56.55 b. the equation of a circle of radius r, centered at the origin (0,0), is given by r^2 = x^2 + y^2 rearrange this equation to find a formula for y in terms of x and r. (take the positive root.) what solid of revolution is swept out if this curve is rotated around the x axis, and x is allowed to vary between -r and r suppose we wanted to set the following integral so that v gives the volume of a sphere of radius r v = integral a to b f(x) dx what would a, b and f(x) be? a=b=f(x)=carry out the integration, and calculate the value of v in terms of r. v=

The lee family bought their home for $220,000 this year. the equation =220,000(1.038) v = 220 , 000 ( 1 . 038 ) x can be used to find the value, v, of their home after x years. which will be the value of the lee family's home in 5 years?

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."

Ahypothesis is: a the average squared deviations about the mean of a distribution of values b) an empirically testable statement that is an unproven supposition developed in order to explain phenomena a statement that asserts the status quo; that is, any change from what has been c) thought to be true is due to random sampling order da statement that is the opposite of the null hypothesis e) the error made by rejecting the null hypothesis when it is true