4 x 225 = 900
17500 / 900 = 19.44
Therefore he will need 20 volunteers
The required plane Π contains the line
L: (-1,1,2)+t(7,6,2)
means that Π is perpendicular to the direction vector of the line L, namely
vl=<7,6,2>
It is also required that Π be perpendicular to the plane
Π 1 : 5y-7z+8=0
means that Π is also perpendicular to the normal vector of the given plane, vp=<0,5,-7>.
Thus the normal vector of the required plane, Π can be obtained by the cross product of vl and vp, or vl x vp:
i j k
7 6 2
0 5 -7
=<-42-10, 0+49, 35-0>
=<-52, 49, 35>
which is the normal vector of Π
Since Π has to contain the line, it must pass through the point (-1,1,2), so the equation of the plane is
Π : -52(x-(-1))+49(y-1)+35(z-2)=0
=>
Π : -52x+49y+35z = 171
Check that normal vector of plane is orthogonal to line direction vector
<-52,49,35>.<7,6,2>
=-364+294+70
=0 ok
Answer:
The amount of sugar needed to make 1 quart of lemonade is <u>1/12 cup</u>.
Step-by-step explanation:
Given:
Alex made 4 quarts of lemonade using 1/3 cup of sugar.
Now, to determine the amount of sugar needed to make 1 quart of lemonade.
Let the amount of sugar needed to make 1 quart of lemonade = 
.
So, by using the proportion we solve it:
<em>On solving we get:</em>
So, cup of sugar = 
Therefore, the amount of sugar needed to make 1 quart of lemonade is 1/12 cup.
