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3 years ago

If A= [-5,7] and B= [6,10], then find A u B

Mathematics

1 answer:

lesantik [10]3 years ago

7 0

Answer:

$\large\boxed{A\ \cup\ B=[-5,\ 10]}$

Step-by-step explanation:

Look at the picture.

The union of two sets A and B (A ∪ B) is the set of elements which are in A, in B, or in both A and B

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Please please please help me

zzz [600]

Answer:

Step-by-step explanation:

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3 years ago

A total of 3 cards are chosen at random, without replacing them, from a standard deck of 52 playing cards. What is the probabili

Minchanka [31]

Answer: $\dfrac{1}{5525}$

Step-by-step explanation:

The total number of cards =52

The number of kings in the cards = 4

If repetition is not allowed , then the total number of ways of choosing 3 cards will be :-

$52\times51\times50=132600$

The number of ways of choosing 3 kings will be :-

$4\times3\times2=24$

Now, the probability of choosing 3 king cards will be :-

$\dfrac{24}{132600}=\dfrac{1}{5525}$

Hence, the probability of choosing 3 king cards = $\dfrac{1}{5525}$

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3 years ago

Circles - Radius, Diameter, Area and Circumference

NemiM [27]

176.71
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8 0

3 years ago

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Determine the values of the constants r and s such that i(x, y) = x rys is an integrating factor for the given differential equa

garri49 [273]

$\underbrace{y(7xy^2+6)}_{M(x,y)}\,\mathrm dx+\underbrace{x(xy^2-1)}_{N(x,y)}\,\mathrm dy=0$

For the ODE to be exact, we require that $M_y=N_x$ , which we'll verify is not the case here.

$M_y=21xy^2+6$
$N_x=2xy^2-1$

So we distribute an integrating factor $i(x,y)$ across both sides of the ODE to get

$iM\,\mathrm dx+iN\,\mathrm dy=0$

Now for the ODE to be exact, we require $(iM)_y=(iN)_x$ , which in turn means

$i_yM+iM_y=i_xN+iN_x\implies i(M_y-N_x)=i_xN-i_yM$

Suppose $i(x,y)=x^ry^s$ . Then substituting everything into the PDE above, we have

$x^ry^s(19xy^2+7)=rx^{r-1}y^s(x^2y^2-x)-sx^ry^{s-1}(7xy^3+6y)$
$19x^{r+1}y^{s+2}+7x^ry^s=rx^{r+1}y^{s+2}-rx^ry^s-7sx^{r+1}y^{s+2}-6sx^ry^s$
$19x^{r+1}y^{s+2}+7x^ry^s=(r-7s)x^{r+1}y^{s+2}-(r+6s)x^ry^s$
$\implies\begin{cases}r-7s=19\\r+6s=-7\end{cases}\implies r=5,s=-2$

so that our integrating factor is $i(x,y)=x^5y^{-2}$ . Our ODE is now

$(7x^6y+6x^5y^{-1})\,\mathrm dx+(x^7-x^6y^{-2})\,\mathrm dy=0$

Renaming $M(x,y)$ and $N(x,y)$ to our current coefficients, we end up with partial derivatives

$M_y=7x^6-6x^5y^{-2}$
$N_x=7x^6-6x^5y^{-2}$

as desired, so our new ODE is indeed exact.

Next, we're looking for a solution of the form $\Psi(x,y)=C$ . By the chain rule, we have

$\Psi_x=7x^6y+6x^5y^{-1}\implies\Psi=x^7y+x^6y^{-1}+f(y)$

Differentiating with respect to $y$ yields

$\Psi_y=x^7-x^6y^{-2}=x^7-x^6y^{-2}+\dfrac{\mathrm df}{\mathrm dy}$
$\implies\dfrac{\mathrm df}{\mathrm dy}=0\implies f(y)=C$

Thus the solution to the ODE is

$\Psi(x,y)=x^7y+x^6y^{-1}=C$

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3 years ago

One week Alaina ran 12 miles in 131.25 minutes. The next, Alaina ran 12 miles in 119.5 minutes. If she ran in a constant pace du

vlabodo [156]

Ou should not increase to more than 12 miles next week; ... 25 miles a week, usually a 7 milerun ... before I run a half. Using that method

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3 years ago

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