Answer:
ü=2i+2j+0k
Step-by-step explanation:
The given plane 2x + 2y + 2 = 3 can also be written as:
2x+2y=3-2
2x+2y=1
The general equation for a plane is Ax+By+Cz=D and by definition the normal vector of that plane is n=Ai+Bj+Ck
Where i,j,k are the unit vectors
In order to demostrate that the vector n is normal to the plane, let R1=(a1,b1,c1) and R2=(a2,b2,c2) be two vectors that are in the plane.
If R1 ∈ Ax+By+Cz=D then Aa1+Bb1+Cc1=D
If R2 ∈ Ax+By+Cz=D then Aa2+Bb2+Cc2=D
Therefore, the vector R1R2=R2-R1=(a2-a1)i+(b2-b1)j+(c2-c1)k
You can apply the dot product. <em>If the dot product of the two vectors is zero then the vectors are normal.</em>
So, the vector which components are A,B,C is normal to the plane becase it is normal to any vector contained in the plane.
In this case:
A=2, B=2, C=0
ü=2i+2j+0k
Answer: x < 11.9
Step-by-step explanation:
Answer:
Problem 1:
Problem 2:
Problem 3:
The radius is cm.
Problem 4:
The width is 15 cm.
Step-by-step explanation:
Problem 1:
We want to solve for .
Multiply both sides by 3:
Rearrange the multiplication using commutative property:
We want to get by itself so divide both sides by what is being multiplied by which is .
Problem 2:
We want to solve for in .
Multiply both sides by 3:
We want by itself so divide both sides by what is being multiply by; that is divide both sides by .
Problem 3:
The circumference formula for a circle is . We are asked to solve for the radius when the circumference is cm.
Divide both sides by what r is being multiply by; that is divide both sides by :
Reduce fraction:
The radius is cm.
Problem 4:
The perimeter of a rectangle is where is the width and is the length.
We are asked to find w, the width, for when L, the length, is 5, and the perimeter is 40.
So we have this equation to solve for w:
Simplify the 2(5) part:
Subtract both sides by 10:
Divide both sides by 2:
Simplify the fraction:
The width is 15 cm.
Answer:
x>3
Step-by-step explanation:
Answer:
10th term
Step-by-step explanation:
3ⁿ⁻¹ > 7000
log₃ 7000 = 8.05
n - 1 > 8
n > 9
10th term
check: 1, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683