Answer:
4 dozens
Step-by-step explanation:
<em>Find Eleanor and Joanna's ratio of eggs to milk</em>
Eleanor:
<em>Dozen eggs : gallons of milk</em>
9 : 3
3 : 1
Joanna:
<em>Dozen eggs : gallons of milk</em>
2 : 2
1 : 1
<em>They gather one gallon of milk each which means Joanna has 1 dozen eggs and Eleanor has 3 dozens of eggs.</em>
Total dozen of eggs = 3 + 1 = 4
Therefore, total dozen of eggs the family have per week is 4 dozens.
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!!!
<h2>
Explanation:</h2>
Here we have the following expression:
So we need to simplify that radical expression. By property of radicals we know that:
![\sqrt[n]{a}\sqrt[n]{b}=\sqrt[n]{ab}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Ba%7D%5Csqrt%5Bn%5D%7Bb%7D%3D%5Csqrt%5Bn%5D%7Bab%7D)
So:
The prime factorization of 22968 is:
Hence:
By property:
![\sqrt[n]{a^n}=a](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Ba%5En%7D%3Da)
So:
Finally:
<h2>Learn more:</h2>
Radical expressions: brainly.com/question/13452541
#LearnWithBrainly
Answer:
52
Step-by-step explanation:
When asked such a question, try to use trial and error.
For example, the total is 202 and is made of of 4 integers which are <u>consecutive</u>(follow each other)
If you were to divide 202 by 4, you would get approximately 50
So, it would be best to try and add certain consecutive numbers(making sure 50 is one of them) till you get a total of 202
In this case, the integers would be, <em>49, 50, 51</em> and <em>52</em>
The question then further asks you ti find out which is the greatest of these integers. That would be <em>52</em>
