Answer:
x = 60°
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
- Equality Properties
<u>Geometry</u>
- A box on an angle signifies a 90° angle
- All angles in a triangle add up to 180°
Step-by-step explanation:
<u>Step 1: Set up equation</u>
x° + 90° + 30° = 180°
<u>Step 2: Solve for </u><em><u>x</u></em>
- Combine like terms: x + 120 = 180
- Subtract 120 on both sides: x = 60°
Triangle has 3 equal sides so it is equilateral triangle.
<A = <B = <C = 60 degrees
Answer
C. 60°
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.
