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quester [9]
2 years ago
10

Consider the differential equation

Mathematics
2 answers:
Minchanka [31]2 years ago
7 0

Answer: For this problem I used the separation method instead of plugging in each one. I thought this would be easiereasier.to

Step-by-step explanation:

Gennadij [26K]2 years ago
4 0

The first solution is quadratic, so its derivative y' on the left side is linear. But the right side would be a polynomial of degree greater than 1, so this is not the correct choice.

The third solution has a similar issue. The derivative of √(x² + 1) will be another expression involving √(x² + 1) on the left side, yet on the right we have y² = x² + 1, so that the entire right side is a polynomial. But polynomials are free of rational powers, so this solution can't work.

This leaves us with the second choice. Recall that

1 + tan²(x) = sec²(x)

and the derivative of tangent,

(tan(x))' = sec²(x)

Also notice that the ODE contains 1 + y². Now, if y = tan(x³/3 + 2), then

y' = sec²(x³/3 + 2) • x²

and substituting y and y' into the ODE gives

sec²(x³/3 + 2) • x² = x² (1 + tan²(x³/3 + 2))

x² sec²(x³/3 + 2) = x² sec²(x³/3 + 2)

which is an identity.

So the solution is y = tan(x³/3 + 2).

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Choices:<br><br> One-sixth cups<br> Five-sixths cups<br> 1 and two-thirds cups<br> 1 and 5 / 6 cups
navik [9.2K]

Answer:

Patel will require more orange juice = \frac{371}{660} cups

Step-by-step explanation:

Patel needs the orange juice for his family = 3 cups

He needs more orange juice = 3 cups - Sum of juice squeezed from different oranges

=3-(\frac{13}{15}+\frac{1}{5}+\frac{9}{20}+\frac{5}{11}+\frac{7}{15})

L.C.M. of the denominators = 660

=3-\frac{572+132+297+300+308}{660}

=3-\frac{1609}{660}

= \frac{1980-1609}{660}

= \frac{371}{660}

Therefore, amount of orange juice required more = \frac{371}{660} cups

3 0
3 years ago
Find the inverse function for y=3/4+x
Sonja [21]

The inverse of this function is y = x - \frac{3}{4}


You can find the inverse of any function by switching the x and y values and then solving for the new y value. Once you've done that, what will be left over is the inverse function.


y = \frac{3}{4} + x ----> Swap x and y

x = \frac{3}{4} + x -----> Subtract 3/4 from both sides.

x - \frac{3}{4} = y ----> rearrange to appropriate order

y = x - \frac{3}{4}


And that is your inverse function.

8 0
3 years ago
Bryce has a rug that is 14 decimeters by 16 decimeters. Draw a sketch of Bryce'srug. Then find the area of his rug. Show your wo
yuradex [85]

Answer:

the answer is 224 decimeters

Step-by-step explanation:

first you need to draw a box than label the length and with which is 14 by 16 and then you can use the formula A=L*W. Know you can plug the numbers in 14*16 which equals 224 and that would be your answer

4 0
3 years ago
Pls help me with this question
ankoles [38]

Answer:

I'm not sure the answer to this

8 0
3 years ago
What is the common ratio of the geometric<br> sequence below?<br> -5, -10, -20, -40, -..
andrew11 [14]
2
Hope this helps!!!!
3 0
3 years ago
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