We write the equation in terms of dy/dx,
<span>y'(x)=sqrt (2y(x)+18)</span>
dy/dx = sqrt(2y + 18)
dy/dx = sqrt(2) ( sqrt(y + 9))
Separating the variables in the equation, we will have:
<span>1/sqrt(y + 9) dy= sqrt(2) dx </span>
Integrating both sides, we will obtain
<span>2sqrt(y+9) = x(sqrt(2)) + c </span>
<span>where c is a constant and can be determined by using the boundary condition given </span>
<span>y(5)=9 : x = 5, y = 9
</span><span>sqrt(9+9) = 5/sqrt(2) + C </span>
<span>C = sqrt(18) - 5/sqrt(2) = sqrt(2) / 2</span>
Substituting to the original equation,
sqrt(y+9) = x/sqrt(2) + sqrt(2) / 2
<span>sqrt(y+9) = (2x + 2) / 2sqrt(2)
</span>
Squaring both sides, we will obtain,
<span>y + 9 = ((2x+2)^2) / 8</span>
y = ((2x+2)^2) / 8 - 9
The inference shows that the correct options that will fill the information will be:
- I need to study harder to understand the lesson.
- I realize that my knowledge will improve in this lesson..
- I need to study more to be able to explore more in the activity.
<h3>What is an inference?</h3>
An inference means the conclusion that can be deduced from the information given in a literary work.
In this case, it's important that one checks the information and correctly put in the options.
The learner communicates the explanation of their personal assessment as indicated in the Learner’s Assessment Card. • The learner, in their notebook, will write their personal insights about the lesson using the prompts below. I understand that ___________________. I realize that ________________________. I need to learn more about __________.
Learn more about inference on:
brainly.com/question/25280941
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Answer:
they are equivalent to 4
Step-by-step explanation:
CL ≈ AE and HG≈ZR and ∠L≈∠E as both triangles are isosceles so CL=HL and AE=EZ
so HL≈AE≈ZR≈EZ so according to side angle side ΔCLH andΔ AZE both are congruent so side CH≈AZ
