Answer: 25
<u>Step-by-step explanation:</u>
7(x - y) - 3(2 + 2x)
= 7x - 7y - 6 - 6x
= x - 7y - 6
for x = 3, y = -4
3 - 7(-4) - 6
= 3 + 28 - 6
= 31 - 6
= 25
243.87 and 132.37 thts the answer
Answer:
∫▒〖arctan(x).1 dx=arctan(x).x〗-1/2 ln(1+x^2 )+C
Step-by-step explanation:
∫▒〖1st .2nd dx=1st∫▒〖2nd dx〗-∫▒〖(derivative of 1st) dx∫▒〖2nd dx〗〗〗
Let 1st=arctan(x)
And 2nd=1
∫▒〖arctan(x).1 dx=arctan(x) ∫▒〖1 dx〗-∫▒〖(derivative of arctan(x))dx∫▒〖1 dx〗〗〗
As we know that
derivative of arctan(x)=1/(1+x^2 )
∫▒〖1 dx〗=x
So
∫▒〖arctan(x).1 dx=arctan(x).x〗-∫▒〖(1/(1+x^2 ))dx.x〗…………Eq1
Let’s solve ∫▒(1/(1+x^2 ))dx by substitution now
Let 1+x^2=u
du=2xdx
Multiply and divide ∫▒〖(1/(1+x^2 ))dx.x〗 by 2 we get
1/2 ∫▒〖(2/(1+x^2 ))dx.x〗=1/2 ∫▒(2xdx/u)
1/2 ∫▒(2xdx/u) =1/2 ∫▒(du/u)
1/2 ∫▒(2xdx/u) =1/2 ln(u)+C
1/2 ∫▒(2xdx/u) =1/2 ln(1+x^2 )+C
Putting values in Eq1 we get
∫▒〖arctan(x).1 dx=arctan(x).x〗-1/2 ln(1+x^2 )+C (required soultion)
2 | <u>5</u><u>5</u><u>0</u><u>,</u><u>7</u><u>5</u><u>0</u><u>,</u><u>9</u><u>0</u><u>0</u>
2 | <u>2</u><u>7</u><u>5</u><u>,</u><u>3</u><u>7</u><u>5</u><u>,</u><u>4</u><u>5</u><u>0</u>
3 |<u> </u><u>2</u><u>7</u><u>5</u><u>,</u><u>3</u><u>7</u><u>5</u><u>,</u><u>2</u><u>2</u><u>5</u>
<u>3</u><u> </u>| <u>2</u><u>7</u><u>5</u><u>,</u><u>1</u><u>2</u><u>5</u><u>,</u><u>7</u><u>5</u>
5 | <u>2</u><u>7</u><u>5</u><u>,</u><u>1</u><u>2</u><u>5</u><u>,</u><u>2</u><u>5</u>
5 | <u>55,25,5</u>
5 | <u>1</u><u>1</u><u>,</u><u>5</u><u>,</u><u>5</u>
11 | <u>1</u><u>1</u><u>,</u><u>1</u><u>,</u><u>1</u>
LCM:-2×2×3×3×5×5×5×11=49500
Answer:
BC = 22
Step-by-step explanation:
BD = 67
Bc = 3x - 2
CD = 4x + 13
BC + CD = BD (Given)
3x - 2 + 4x + 13 = 67
3x + 4x -2 + 13 = 67
7x + 11 = 67
7x = 67 - 11
7x = 56
x = 56 ÷ 7
x = 8
now instead of x put 8
Bc = 3x - 2
BC = 3(8) -2
BC = 24 -2
BC = 22