Okay, First, Lets Remember The Formulas. Area Of A Rectangle :
B*H.
Area Of A Circle:
R*2*3.14.
16*12 Is The Area Of The Rectangle. 16*12 = 192.
Area Of The Two Semicircles = 6*6*3.14. 6*6 = 36. 36*3.14 =113.04.
Now, 192-113.04 = 78.96 in ^2. Hope This Helps!
Answer:
a
<em>a </em><em>is </em><em>the </em><em>correct </em><em>answer</em>
Step-by-step explanation:
0.8/1 = x/1.5
Cross multiplication is applied here
0.8 × 1.5 = 1 × x
1.2 = x
Therefore, x = 1.2
Hope it helps.
Stay safe and blessed.
<h2>
Answer:</h2>
<em><u>Recursive equation for the pattern followed is given by,</u></em>
![a_{n}=a_{n-1}+(n-1)^{2}](https://tex.z-dn.net/?f=a_%7Bn%7D%3Da_%7Bn-1%7D%2B%28n-1%29%5E%7B2%7D)
<h2>
Step-by-step explanation:</h2>
In the question,
The number of interaction for 1 child = 0
Number of interactions for 2 children = 1
Number of interactions for 3 children = 5
Number of interaction for 4 children = 14
So,
We need to find out the pattern for the recursive equation for the given conditions.
So,
We see that,
![a_{1}=0\\a_{2}=1\\a_{3}=5\\a_{4}=14\\](https://tex.z-dn.net/?f=a_%7B1%7D%3D0%5C%5Ca_%7B2%7D%3D1%5C%5Ca_%7B3%7D%3D5%5C%5Ca_%7B4%7D%3D14%5C%5C)
Therefore, on checking, we observe that,
![a_{n}=a_{n-1}+(n-1)^{2}](https://tex.z-dn.net/?f=a_%7Bn%7D%3Da_%7Bn-1%7D%2B%28n-1%29%5E%7B2%7D)
On checking the equation at the given values of 'n' of, 1, 2, 3 and 4.
<u>At, </u>
<u>n = 1</u>
![a_{n}=a_{n-1}+(n-1)^{2}\\a_{1}=a_{1-1}+(1-1)^{2}\\a_{1}=0+0=0\\a_{1}=0](https://tex.z-dn.net/?f=a_%7Bn%7D%3Da_%7Bn-1%7D%2B%28n-1%29%5E%7B2%7D%5C%5Ca_%7B1%7D%3Da_%7B1-1%7D%2B%281-1%29%5E%7B2%7D%5C%5Ca_%7B1%7D%3D0%2B0%3D0%5C%5Ca_%7B1%7D%3D0)
which is true.
<u>At, </u>
<u>n = 2</u>
![a_{n}=a_{n-1}+(n-1)^{2}\\a_{2}=a_{2-1}+(2-1)^{2}\\a_{2}=a_{1}+1\\a_{2}=1](https://tex.z-dn.net/?f=a_%7Bn%7D%3Da_%7Bn-1%7D%2B%28n-1%29%5E%7B2%7D%5C%5Ca_%7B2%7D%3Da_%7B2-1%7D%2B%282-1%29%5E%7B2%7D%5C%5Ca_%7B2%7D%3Da_%7B1%7D%2B1%5C%5Ca_%7B2%7D%3D1)
Which is also true.
<u>At, </u>
<u>n = 3</u>
![a_{n}=a_{n-1}+(n-1)^{2}\\a_{3}=a_{3-1}+(3-1)^{2}\\a_{3}=a_{2}+4\\a_{3}=5](https://tex.z-dn.net/?f=a_%7Bn%7D%3Da_%7Bn-1%7D%2B%28n-1%29%5E%7B2%7D%5C%5Ca_%7B3%7D%3Da_%7B3-1%7D%2B%283-1%29%5E%7B2%7D%5C%5Ca_%7B3%7D%3Da_%7B2%7D%2B4%5C%5Ca_%7B3%7D%3D5)
Which is true.
<u>At, </u>
<u>n = 4</u>
![a_{n}=a_{n-1}+(n-1)^{2}\\a_{4}=a_{4-1}+(4-1)^{2}\\a_{4}=a_{3}+9\\a_{4}=14](https://tex.z-dn.net/?f=a_%7Bn%7D%3Da_%7Bn-1%7D%2B%28n-1%29%5E%7B2%7D%5C%5Ca_%7B4%7D%3Da_%7B4-1%7D%2B%284-1%29%5E%7B2%7D%5C%5Ca_%7B4%7D%3Da_%7B3%7D%2B9%5C%5Ca_%7B4%7D%3D14)
This is also true at the given value of 'n'.
<em><u>Therefore, the recursive equation for the pattern followed is given by,</u></em>
![a_{n}=a_{n-1}+(n-1)^{2}](https://tex.z-dn.net/?f=a_%7Bn%7D%3Da_%7Bn-1%7D%2B%28n-1%29%5E%7B2%7D)
Answer:
140 degrees
Step-by-step explanation:
180-20+20 =140