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spayn [35]
2 years ago
15

What is the measure of the angle formed by the minute hand and the hour hand of a clock when the clock shows 5:00

Mathematics
1 answer:
ollegr [7]2 years ago
6 0

Answer:

It makes  150°

Step-by-step explanation:

So, I'll explain on the document.

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Dy/dx = 2xy^2 and y(-1) = 2 find y(2)
Anarel [89]
If you're using the app, try seeing this answer through your browser:  brainly.com/question/2887301

—————

Solve the initial value problem:

   dy
———  =  2xy²,      y = 2,  when x = – 1.
   dx


Separate the variables in the equation above:

\mathsf{\dfrac{dy}{y^2}=2x\,dx}\\\\
\mathsf{y^{-2}\,dy=2x\,dx}


Integrate both sides:

\mathsf{\displaystyle\int\!y^{-2}\,dy=\int\!2x\,dx}\\\\\\
\mathsf{\dfrac{y^{-2+1}}{-2+1}=2\cdot \dfrac{x^{1+1}}{1+1}+C_1}\\\\\\
\mathsf{\dfrac{y^{-1}}{-1}=\diagup\hspace{-7}2\cdot \dfrac{x^2}{\diagup\hspace{-7}2}+C_1}\\\\\\
\mathsf{-\,\dfrac{1}{y}=x^2+C_1}

\mathsf{\dfrac{1}{y}=-(x^2+C_1)}


Take the reciprocal of both sides, and then you have

\mathsf{y=-\,\dfrac{1}{x^2+C_1}\qquad\qquad where~C_1~is~a~constant\qquad (i)}


In order to find the value of  C₁  , just plug in the equation above those known values for  x  and  y, then solve it for  C₁:

y = 2,  when  x = – 1. So,

\mathsf{2=-\,\dfrac{1}{1^2+C_1}}\\\\\\
\mathsf{2=-\,\dfrac{1}{1+C_1}}\\\\\\
\mathsf{-\,\dfrac{1}{2}=1+C_1}\\\\\\
\mathsf{-\,\dfrac{1}{2}-1=C_1}\\\\\\
\mathsf{-\,\dfrac{1}{2}-\dfrac{2}{2}=C_1}

\mathsf{C_1=-\,\dfrac{3}{2}}


Substitute that for  C₁  into (i), and you have

\mathsf{y=-\,\dfrac{1}{x^2-\frac{3}{2}}}\\\\\\
\mathsf{y=-\,\dfrac{1}{x^2-\frac{3}{2}}\cdot \dfrac{2}{2}}\\\\\\
\mathsf{y=-\,\dfrac{2}{2x^2-3}}


So  y(– 2)  is

\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{2\cdot (-2)^2-3}}\\\\\\
\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{2\cdot 4-3}}\\\\\\
\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{8-3}}\\\\\\
\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{5}}\quad\longleftarrow\quad\textsf{this is the answer.}


I hope this helps. =)


Tags:  <em>ordinary differential equation ode integration separable variables initial value problem differential integral calculus</em>

7 0
3 years ago
I will mark brainly, help me with this question please.​
Anna [14]

Step-by-step explanation:

Since x varies directly as \sqrt{y} we can write the relation as

x = k\sqrt{y}

where k is the constant of proportionality.

a) To solve for the k, we substitute the given values:

5 = k\sqrt{13} = k(13)

\Rightarrow k = \dfrac{5}{13}

b) The equation relation x and y can be written as

x = \dfrac{5}{13}\sqrt{y}

c) When y = 9,

x = \dfrac{5}{13}\sqrt{9} = \dfrac{5}{13}(3) = \dfrac{15}{13}

3 0
2 years ago
There are 7 oak trees in Aidan's yard. The other 2 trees in his yard are maple trees.
Radda [10]
7/9 of his trees are oak trees

6 0
3 years ago
Estimate.<br> 36 x 92 ~ ?
Jet001 [13]

Answer:

3,312

lets be real who arctually looks at the step by step just use a calculator for this one

7 0
3 years ago
Answers for adding and subtracting polynomials
lakkis [162]
Please explain more :))

Oh nvm this
(4+9) + (2-1) = 12
5 0
2 years ago
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