Answer:
Type of exercise
Step-by-step explanation:
Answer:
56
Step-by-step explanation:
You add 91 and 33 and you get 124. Subtract 180 and 124 to get 56.
Answer:
It's positive when you have 6^-2 it's the same as having 
. So 6^-2 it's 1/36.
Step-by-step explanation:
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.
Split this figure into 3 shapes: 2 triangles and 1 trapezoid
Area of top triangle = 1/2(7)(2) = 7 square units
Area of bottom triangle = 1/2(3)(7) = 10.5 square units
Area of trapezoid = 1/2(3 + 6)(4) = 18 square units
Area of the polygon = 7 + 10.5 + 18 = 35.5 square units
