1.Findequationsforthelinesthroughthepoint(a,b)thatareparalleltoandperpendiculartotheliney=mx+c,assumingm≠0.Parallel:y=Perpendicular:y=2.Writeaformulaforthedistancebetweenapoint(x,y)onthegraphofy=x6andthep

Question

1.Find equations for the lines through the point (a,b) that are parallel to and perpendicular to the line
y = mx + c,assuming m ≠ 0.
Parallel:y=
Perpendicular:y=
2.Write a formula for the distance between a point (x,y) on the graph of y = x6 and the point (4,8).Express your answer in terms of x.
D(x)=
3.The power P of a jet of water is jointly proportional to the cross sectional area A and to the cube of the velocity v.
(a) Write the formula for P.Use k as the proportionality constant.
P=
(b) If the velocity is quadrupled and the cross sectional area is halved,by what factor will the power increase?

Answer 1

1.
parellel的话 y = mx - am + b
perpendicular的话 y = -x/m + a/m + b
2.求点到直线的距离:D(x) = (8+4*6)/√(1²+6²)
3.
(a) P = kAv³
(b) 速度是原来的4倍 cross sectional area是一半,所以 P2 = k (A/2) (4v)³ = 32kAv³
所以答案是 by a factor of 32