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2 years ago

Which number is composite A 19 B 23 C 33 D 37

Mathematics

2 answers:

raketka [301]2 years ago

7 0

Option C is correct.

Step-by-step explanation:

We need to identify the composite numbers from the given options

<u>Composite Numbers</u>

A number is composite number if it has factors other than 1 and the number itself i.e the number is not prime.

The numbers 19, 23 and 37 are prime numbers because they have factors 1 and the number itself while 33 is composite number because it has factors 1,3,11,33.

So, Option C is correct.

Keywords: Composite Numbers

Learn more about Composite Numbers at:

#learnwithBrainly

pishuonlain [190]2 years ago

3 0

Answer:

C. 33

Step-by-step explanation:

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3 years ago

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Step-by-step explanation:

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3 years ago

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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2 years ago

For each hour he babysits, Anderson earns $1 more than half of Carey's hourly rate. Anderson earns $6 per hour. Which equation c

MAVERICK [17]

Answer:

The total earnings of Carey in t tours is 12 t - 2 .

Step-by-step explanation:

For each hour he babysits, Anderson earns $1 more than half of Carey's hourly rate. Anderson earns $6 per hour. Which equation can be used to solve for Carey's hourly rate, c? 18 + ?T = 24 What number should be the coefficient of t?

Anderson earns $1 more than half of Carey's hourly rate.

Anderson hourly rate = $ 6

Let Carey's hourly rate is p. Let the time is t hours.

So, Anderson rate is

$6 t = \frac{p t}{2} +1\\\\2\times 6 t = p t + 2 \\\\p t = 12 t - 2$

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2 years ago

Which number is composite A 19 B 23 C 33 D 37​

Which number is composite A 19 B 23 C 33 D 37