Hello! First we should note that the shape of the figure can be broken down into two rectangular prisms, so that the expression will look like:
Volume = (w • h • l) vertical rectangular prism + (w •h • l) horizontal rectangular prism
Thus Volume = (7 • 3 • 3) + (9 • 3 • 4)
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.
There would be about 0.82 lbs of candy in the jar.
Explanation: 7.41 divided by 9= .82333
The answer is 320 to find the product you can just do 4 times 8 and then add a zero
Prime numbers 2 through 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97. Even numbers greater than two are composite.
