Answer:
406
Step-by-step explanation:
Given: product of two positive integers us 2005.
Let the two positive integers be a and b
Now prime factorization of 2005 = 401×5
where both 401 and 5 are prime number and non of them is 1.
So, and b will be 401 and 5 respectively.
Therefore, sum of the two integers a+b = 401+5 = 406
6.
![y^2\sqrt[8]{8}](https://tex.z-dn.net/?f=y%5E2%5Csqrt%5B8%5D%7B8%7D)
Step-by-step explanation:
![\sqrt[8]{8*y*y*y*y*y*y*y*y*y*y*y*y*y*y*y*y}](https://tex.z-dn.net/?f=%5Csqrt%5B8%5D%7B8%2Ay%2Ay%2Ay%2Ay%2Ay%2Ay%2Ay%2Ay%2Ay%2Ay%2Ay%2Ay%2Ay%2Ay%2Ay%2Ay%7D)
Since there are eight y's in two groups we can take them out which turns into
:)
3.
Answer:
0.05
Step-by-step explanation:
divide 100 by 20
Answer:
∫((cos(x)*dx)/(√(1+sin(x)))) = 2√(1 + sin(x)) + c.
Step-by-step explanation:
In order to solve this question, it is important to notice that the derivative of the expression (1 + sin(x)) is present in the numerator, which is cos(x). This means that the question can be solved using the u-substitution method.
Let u = 1 + sin(x).
This means du/dx = cos(x). This implies dx = du/cos(x).
Substitute u = 1 + sin(x) and dx = du/cos(x) in the integral.
∫((cos(x)*dx)/(√(1+sin(x)))) = ∫((cos(x)*du)/(cos(x)*√(u))) = ∫((du)/(√(u)))
= ∫(u^(-1/2) * du). Integrating:
(u^(-1/2+1))/(-1/2+1) + c = (u^(1/2))/(1/2) + c = 2u^(1/2) + c = 2√u + c.
Put u = 1 + sin(x). Therefore, 2√(1 + sin(x)) + c. Therefore:
∫((cos(x)*dx)/(√(1+sin(x)))) = 2√(1 + sin(x)) + c!!!
