(1 point) Suppose r⃗ (t)=cos(πt)i+sin(πt)j+5tkr→(t)=cos( πt)i+sin(πt)j+5tk represents the position of a particle on a helix, where zz is the height of the particle. (a) What is tt when the particle has height 2525? t=t= (b) What is the velocity of the particle when its height is 2525? v⃗ =v→= (c) When the particle has height 2525, it leaves the helix and moves along the tangent line at the constant velocity found in part (b). Find a vector parametric equation for the position of the particle (in terms of the original parameter tt) as it moves along this tangent line. L(t)=L(t)=

Given the equation y − 4 = three fourths(x + 8) in point-slope form, identify the equation of the same line in standard form. −three fourthsx + y = 10 3x − 4y = −40 y = three fourthsx + 12 y = three fourthsx + 10

Christine wong has asked dave and mike to her move into a new apartment on sunday morning. she has asked them both, in case one of them does not show up. from past experience, christine knows that there is a 40% chance that dave will not show up and a 30% chance that mik a. what is the probability that both dave and mike will show up? (round your answer to 2 decimal places.) b. what is the probability that at least one of them will show up? c. what is the probability that neither dave nor mike will show up? (round your answer to 2 decimal places.)e will not show up. dave and mike do not know each other and their decisions can be assumed to be independent.

Mike wants to make meatloaf. his recipe uses a total of 8 pounds of meat. if he uses a 3 to 1 ratio of beef to pork, how much pork will he use? enter your answer as a mixed number in simplest terms.