The property displayed here is the distributive property.
If you have a variable or unknown number inside or outside of parentheses, you can distribute it to each term and add the terms together, and it will remain true.
Example:
4(x + 5)
After distributing, it'll look like this:
4x + 20
The longest side
Think about it. The widest angle would leave a resulting long side to reach the ends of the angle
If you look at the picture, the side across from the widest angle has the longest length
The unit normal for the given plane is <5,2,-1>.
The equation of the plane parallel to the given plane passing through (5,5,4) is therefore
5(x-5)+2(y-5)-1(z-4)=0
simplify =>
5x+2y-z=25+10-4=31
Answer: the plane through (5,5,4) parallel to 5x+2y-z=-6 is 5x+2y-z=31
By Pythagorean theorem
x²+GF²=EF² ( where G is the point of intersection of perpendicular lines)
now, GF=1/2 EF= 12
x²+12²=24²
x²=24²-12²
x²=432
x=√432
x=12√3
x≈20.78
Answer:
X = 0, π/2 in the interval [0, 2pi).
Step-by-step explanation:
Use the auxiliary angle method:
R sin(x + a) = Rsin x cos a + Rcos x sin a = 1
sin x + cos x = 1
Comparing coefficients:
R cos a = 1 and R sin a = 1, so
tan a = R sin a / R cos a = 1
So a = π/4 radians.
Also R^2(sin^2 a + cos^2 a) = 1^2 + 1^2 = 2
Therefore R = √2.
So √2 sin (x +π/4 = 1
sin x + π/4 = 1/√2
x + π/4 = π/4
x = 0 radians
Also
x = 0 + π/2 = π/2.
