Answer:
(4,7) and (0,1)
Step-by-step explanation:
(7-4)/(4-2) = 3/ 2, and (4-1)/(2-0) = 3/2.
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.
Answer:
The missing value is 19.
Step-by-step explanation:
The equation is increasing by 2 and 17+2 equals 19.
Mr. Jackson invested $800 at 6% per year and $ 2400 at 4 % per year
<h3><u>Solution:</u></h3>
Mr. Jackson invested a sum of money at 6% per year, and 3 times as much at 4% per year.
Let the sum invested be ‘a’ and ‘3a’ at 6% per year and 4 % per year respectively
Also, his annual return totaled $144
We can form following equation on the basis of question:-
a = $800
The amount of money invested at 6% = a = 800
The amount of money invested at 4 % = 3a = 3(800) = 2400
So, the amount of money invested at 6% is $800 and the amount of money invested at 4% is $ 2400
