The three vectors 
, 
, and 
each terminate on the plane. We can get two vectors that lie on the plane itself (or rather, point in the same direction as vectors that do lie on the plane) by taking the vector difference of any two of these. For instance,
Then the cross product of these two results is normal to the plane:
Let 
be a point on the plane. Then the vector connecting to a known point on the plane, say (0, 0, 1), is orthogonal to the normal vector above, so that
which reduces to the equation of the plane,
Let 
. Then the volume of the region above 
and below the plane is
Answer: x=90
Step-by-step explanation: 11 x 7.5 =90
24/52 because there are 6 even number in a 13 card section
2,4,6,8,10,12
and there are four of them so you multiply 6 by 4 to get 24
since you know there are 52 cards then you will place 24 over 52
you can simplify this fraction to 6/13 depending what you want
Answer:
5
Step-by-step explanation:
The value of <em>y</em> is five times the value of <em>x</em>. In symbols, this relationship is
Compare this with the slope-intercept form of the equation of a line.
where <em>m</em> is the slope and <em>b</em> is the <em>y</em>-intercept.
The value of <em>m</em> is 5. The slope is 5.
Answer:
Step-by-step explanation:
The equation of a line in slope-intercept form is
y = mx + b
We need to find the slope, m, and the y-intercept, b.
The line we need is perpendicular to the line 2x + y = 8.
<em>The slopes of perpendicular lines are negative reciprocals.</em>
We solve the given equation for y to find the slope of the given line.
2x + y = 8
y = -2x + 8
The given line has slope -2.
The negative reciprocal of -2 is 1/2.
Our line has slope, m = 1/2.
Now we have
y = 1/2 x + b
Now we use the given point, (-2, 3), for x and y, using x = -2, and y = 3, and we solve for b.
y = 1/2 x + b
3 = 1/2 * (-2) + b
3 = -1 + b
4 = b
b = 4
Now we have
y = 1/2 x + 4
Answer:
