3D Graphing
An equation of the form ax+by+cz=d forms what shape graphically?
A plane
What is the minimum number of equations needed to solve a system of equations with three unknowns?
3
Rewrite x2y=16 in logarithm form.
logx16=2y
Fully expand log xyz
log x + log y + log z
Solve log 5x = log (2x + 9)
x = 3
What shape is formed by the intersection of a line and a plane?
A point
What is the first step one should always take when solving a system of equations?
Choose which variable to eliminate.
Rewrite log5x = y in exponential form.
5y = x
Fully condense log m - log n - log a
log (m/na)
Solve −6log 3 (x − 3) = −24
x = 42
Give an equation of a plane parallel to
3x-4y+10z= 60
3x-4y+10z = d
Solve the following:
x + y + z = 2
2x + 3y + 5z = 3
-4x - y + 2z = -8
(1,2,-1)
When a log has no base listed, what is the base's value?
10
Fully expand log (x2/y5z4)
2log x - 5logy - 4logz
Solve 52x+1=125
x=1
What shape is formed by two planes intersecting each other?
A line.
Solve he following:
2x + 3y - z = -16
5x - y + 2z = 34
3x + 2y - 2z = -15
(3,-5,7)
Find the inverse of y = log2x and put in y= form.
y = 2x
Fully condense 3log a - 2log b + 5log c
log (a3c5/b2)
Solve −10 + log 3 (n + 3) = −10
n = -2
What is the minimum number of planes needed in order to form a point at their intersection?
3
Jeopardy (bet up to your max score or 500 pts)
Find the equation of the parabola that passes through (2,16), (3,59) and (4,102)
y = 5x2 + 8x - 10
Find the inverse of y = 145x and put into y= form.
y = log145x
Fully expand log 5sqrt(x/y)
log 5 + 1/2 log x + 1/2 log y
Solve 6 + 2log 2 (2r) = 0
r = 1/16