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zaharov [31]
3 years ago
6

∠1 ​ and ∠2 are supplementary.

Mathematics
2 answers:
Rasek [7]3 years ago
8 0
By definition, supplementary angles are those whose sum is 180°

Therefore, ∠2 = 180 - ∠1
2x + 4 = 180 - 124
2x = 52
x = 26°
ivolga24 [154]3 years ago
8 0
124° + 2 x + 4° = 180° ( angles are supplementary )
2 x = 180° - 124° - 4°
2 x = 52°
x = 52° : 2
Answer:
x = 26°
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(X^2+y^2+x)dx+xydy=0<br> Solve for general solution
aksik [14]

Check if the equation is exact, which happens for ODEs of the form

M(x,y)\,\mathrm dx+N(x,y)\,\mathrm dy=0

if \frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}.

We have

M(x,y)=x^2+y^2+x\implies\dfrac{\partial M}{\partial y}=2y

N(x,y)=xy\implies\dfrac{\partial N}{\partial x}=y

so the ODE is not quite exact, but we can find an integrating factor \mu(x,y) so that

\mu(x,y)M(x,y)\,\mathrm dx+\mu(x,y)N(x,y)\,\mathrm dy=0

<em>is</em> exact, which would require

\dfrac{\partial(\mu M)}{\partial y}=\dfrac{\partial(\mu N)}{\partial x}\implies \dfrac{\partial\mu}{\partial y}M+\mu\dfrac{\partial M}{\partial y}=\dfrac{\partial\mu}{\partial x}N+\mu\dfrac{\partial N}{\partial x}

\implies\mu\left(\dfrac{\partial N}{\partial x}-\dfrac{\partial M}{\partial y}\right)=M\dfrac{\partial\mu}{\partial y}-N\dfrac{\partial\mu}{\partial x}

Notice that

\dfrac{\partial N}{\partial x}-\dfrac{\partial M}{\partial y}=y-2y=-y

is independent of <em>x</em>, and dividing this by N(x,y)=xy gives an expression independent of <em>y</em>. If we assume \mu=\mu(x) is a function of <em>x</em> alone, then \frac{\partial\mu}{\partial y}=0, and the partial differential equation above gives

-\mu y=-xy\dfrac{\mathrm d\mu}{\mathrm dx}

which is separable and we can solve for \mu easily.

-\mu=-x\dfrac{\mathrm d\mu}{\mathrm dx}

\dfrac{\mathrm d\mu}\mu=\dfrac{\mathrm dx}x

\ln|\mu|=\ln|x|

\implies \mu=x

So, multiply the original ODE by <em>x</em> on both sides:

(x^3+xy^2+x^2)\,\mathrm dx+x^2y\,\mathrm dy=0

Now

\dfrac{\partial(x^3+xy^2+x^2)}{\partial y}=2xy

\dfrac{\partial(x^2y)}{\partial x}=2xy

so the modified ODE is exact.

Now we look for a solution of the form F(x,y)=C, with differential

\mathrm dF=\dfrac{\partial F}{\partial x}\,\mathrm dx+\dfrac{\partial F}{\partial y}\,\mathrm dy=0

The solution <em>F</em> satisfies

\dfrac{\partial F}{\partial x}=x^3+xy^2+x^2

\dfrac{\partial F}{\partial y}=x^2y

Integrating both sides of the first equation with respect to <em>x</em> gives

F(x,y)=\dfrac{x^4}4+\dfrac{x^2y^2}2+\dfrac{x^3}3+f(y)

Differentiating both sides with respect to <em>y</em> gives

\dfrac{\partial F}{\partial y}=x^2y+\dfrac{\mathrm df}{\mathrm dy}=x^2y

\implies\dfrac{\mathrm df}{\mathrm dy}=0\implies f(y)=C

So the solution to the ODE is

F(x,y)=C\iff \dfrac{x^4}4+\dfrac{x^2y^2}2+\dfrac{x^3}3+C=C

\implies\boxed{\dfrac{x^4}4+\dfrac{x^2y^2}2+\dfrac{x^3}3=C}

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3 years ago
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Nana76 [90]
Are you a K12 student? Which quiz is this? I recognize this question. <span />
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3 years ago
Whats -12j &gt; 156 , and n+4 +2n &lt; -20 and also -1/2 k - 14 &lt;11
yKpoI14uk [10]
For the first one it is, j<<span>−<span>13
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8 0
3 years ago
7. Marco is making beaded bracelets. Each
stiks02 [169]

One way to find the least common multiple of two numbers is to first list the prime factors of each number.

8 = 2 x 2 x 2

Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs.

2: three occurrences

3: one occurrence

So, our LCM should be

2 x 2 x 2 x 3 = 24.

So, Marco can buy, at the very least, 24 beads of each color to have equal colors of beads.

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3 years ago
PLeAsE sEnD hElP !!!!!!!!!!!!!!!!
Luba_88 [7]

Answer:

5 units

Step-by-step explanation:

If DG, EG and FG are perpendicular bisectors of the sides of triangle ABC, then point G is the circumcenter of the triangle ABC and

BG = AG = CG as radii of the circumcirle.

Consider right triangle BEG. By the Pythagorean theorem,

BG^2=EG^2+BE^2\\ \\BG^2=4^2+3^2\\ \\BG^2 =16+9\\ \\BG^2=25\\ \\BG=5\ units

This gives us that

AG = BG = 5 units

3 0
3 years ago
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