Answer:
Step-by-step explanation:
3X-2=0
3X=2
X=2/3 OR X=0.66
<h3><u>Answer:</u></h3>
- First term = 6
- Common difference= 4
<h3><u>Solution</u><u>:</u></h3>
Let's take the first term as <u>a</u> and the common difference be <u>d</u>
The formula to find the nth term of an arithmetic progression is given by :
<u>According to question, we have :</u>
- 16th term of an AP is three times the 5th term.
➝ a16 = 3 ( a5 )
➝ a + ( 16 - 1 )d = 3 ( a + ( 5 - 1 )d )
➝ a + 15d = 3 ( a + 4d )
➝ a + 15d = 3a + 12d
➝ 15d - 12d = 3a - a
➝ 3d = 2a
➝ 2a = 3d
➝ <u>a = 3d/2</u><u></u>ㅤㅤㅤ⸻ ( 1 )
- And, the 12th term is 20 more the 7th term.
➝ a12 - ( a7 ) = 20
➝ a + ( n - 1 )d -( a + ( n - 1 )d ) = 20
➝ a + ( 12 - 1 )d - + a + ( 7 - 1 )d ) = 20
➝ a + 11d - ( a + 6d ) = 20
➝ a - a + 11d - 6d = 20
➝ 5d = 20
➝ d = 20/ 5
➝<u> d = 4</u>
- <u>Using</u><u> equation</u><u> (</u><u> </u><u>1</u><u> </u><u>)</u>
➝ a = 3d / 2
➝ a = ( 3 × 4 ) / 2
➝ a = 12 / 2
➝<u> a = 6</u>
Answer:
.
Step-by-step explanation:
The first derivative of the denominator 
is 
. Rewrite the fraction to obtain that expression on the numerator.
.
In other words,
.
Apply 
-substitution on the integral 
:
Let 
. 
.
.
.
Therefore
.
