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3 years ago

Solve the given differential equation by separation of variables. csc(y) dx sec2(x) dy

Mathematics

1 answer:

Elden [556K]3 years ago

3 0

Try this solution:
dx/siny=dy/cos2x;
sinydy=cos2xdx;
cosy=-1/2 sin2x+C.

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Find the range of the function. Use interval notation. g(x)=log↓3(x-2)

Marizza181 [45]

Answer:

10x=log6-3

Step-by-step explanation:

5 0

2 years ago

Please help, I've been doing math since the time I woke up, with no breaks. I'm brain dead rn. It's all timed.

Yuki888 [10]

The correct answer is A and D

8 0

3 years ago

Could someone help me rnnn?

GuDViN [60]

Answer:

vertex = (0, -4)

equation of the parabola: $y=3x^2-4$

Step-by-step explanation:

Given:

y-intercept of parabola: -4
parabola passes through points: (-2, 8) and (1, -1)

Vertex form of a parabola: $y=a(x-h)^2+k$

(where (h, k) is the vertex and $a$ is some constant)

Substitute point (0, -4) into the equation:

$\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}$

Substitute point (-2, 8) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}$

Substitute point (1, -1) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}$

Equate to find h:

$\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}$

Substitute found value of h into one of the equations to find a:

$\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}$

Substitute found values of h and a to find k:

$\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}$

Therefore, the equation of the parabola in vertex form is:

$\implies y=3(x-0)^2-4=3x^2-4$

So the vertex of the parabola is (0, -4)

5 0

2 years ago

Read 2 more answers

Hi i just wanna know if i'm right on this math question<br><br> Thank you.

Stolb23 [73]

Answer:

Correct my guy or gal.

Step-by-step explanation:

6 0

3 years ago

two people were doing yard work for 1 hour and 35 minutes then they stopped for lunch at 1:20pm at what time did they start doin

MrMuchimi

Answer: The answer would be at 11:45.

Step-by-step explanation: First I though, if they stoppedd for lunch at 1:20 and they've been doing yard work for 1 hour and 35 minutes, I would subtract. 1 hour taken away from 1:20 would be 12:20. Then, since it would be hard to subtract 35 minutes from 12:20, 35 minutes - 20 minutes = 15 minutes. 12:20 subtract 20 minutes = 12:00. 12:00 - 15 minutes equal to 11:45. I hope this helps. I know this explanation can be confusing but it's the best I can do at the moment.

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4 0

3 years ago