Answer:
6³ = 216
9² = 81
3⁴ = 81
18² = 324
Step-by-step explanation:
6³ = 6 · 6 · 6 = 36 · 6 = 216
9² = 9 · 9 = 81
3⁴ = 3 · 3 · 3 · 3 = 9 · 3 · 3 = 27 · 3 = 81
18² = 18 · 18 = 324
To solve this problem you have to convert the percentage to a decimal which would
be .40.
40% =40/100=.40
After doing so all you need to do is divide the amount needed by the percentage which gives you the amount she has saved.
225/.40= $90
Lauren has $90 saved
Given plane Π : f(x,y,z) = 4x+3y-z = -1
Need to find point P on Π that is closest to the origin O=(0,0,0).
Solution:
First step: check if O is on the plane Π : f(0,0,0)=0 ≠ -1 => O is not on Π
Next:
We know that the required point must lie on the normal vector <4,3,-1> passing through the origin, i.e.
P=(0,0,0)+k<4,3,-1> = (4k,3k,-k)
For P to lie on plane Π , it must satisfy
4(4k)+3(3k)-(-k)=-1
Solving for k
k=-1/26
=>
Point P is (4k,3k,-k) = (-4/26, -3/26, 1/26) = (-2/13, -3/26, 1/26)
because P is on the normal vector originating from the origin, and it satisfies the equation of plane Π
Answer: P(-2/13, -3/26, 1/26) is the point on Π closest to the origin.
