Answer:

Step-by-step explanation:
<u>Area of a Circle</u>
A circle is a geometric shape where all the points on its circumference are at the same distance to a fixed point called center. The radius is the distance from the center to any point of the circumference.
The relation of the length of the circumference to the radius is an irrational number called pi (
).
Another interesting relation in a circle is the area it occupies in a 2D space. Being r the radius of the circle, the area is computed by the formula

The party hat has a radius of r= 3 inches. The area of the circular base is computed as follows


Answer: C
Step-by-step explanation:
Answer:
Slope = 7/4
Step-by-step explanation:
You are given coordinate values and a formula that tells you what to do with them. All you need to do is put the values in the formula and do the arithmetic.
<h3>Points</h3>
You are given points (2, -3) and (6, 4). The slope formula refers to the two points as (x1, y1) and (x2, y2). It does not matter which is which.
If we use the points in the same order they are given, then we can see that ...
- x1 = 2
- y1 = -3
- x2 = 6
- y2 = 4
<h3>Formula</h3>
Using these values in the given formula, we find the slope to be ...

The slope of the line through the given points is 7/4.
Given:
Length of rectangle = (x+10) cm
Width of the rectangle = x cm
Perimeter = 32 cm
To find:
The length of the rectangle.
Solution:
We know that,

Where, l is length and w is width.
Substituting the values, we get



Subtract 20 from both sides.


Divide both sides by

So, the length is

Therefore, the length of the rectangle is 13 cm.
Answer with explanation:
For, a Matrix A , having eigenvector 'v' has eigenvalue =2
The order of matrix is not given.
It has one eigenvalue it means it is of order , 1×1.
→A=[a]
Determinant [a-k I]=0, where k is eigenvalue of the given matrix.
It is given that,
k=2
For, k=2, the matrix [a-2 I] will become singular,that is
→ Determinant |a-2 I|=0
→I=[1]
→a=2
Let , v be the corresponding eigenvector of the given eigenvalue.
→[a-I] v=0
→[2-1] v=[0]
→[v]=[0]
→v=0
Now, corresponding eigenvector(v), when eigenvalue is 2 =0
We have to find solution of the system
→Ax=v
→[2] x=0
→[2 x] =[0]
→x=0, is one solution of the system.