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3 years ago

What kind (type) of decimal number cannot be perfectly converted to fraction form? It can only be estimated by a fraction?

Mathematics

1 answer:

OverLord2011 [107]3 years ago

8 0

Answer:

Repeating decimals

Step-by-step explanation:

They go on forever, the never stop

Hope this helps :)

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PLS HELP! If f(x) = -9x + 12, and f(x) = -6, find x.

aivan3 [116]

Answer:

Step-by-step explanation:

You can rewrite thosee two equations as -9x+12=-6, because f(x)=f(x)

Now isolate x

-9x+12=-6

-9x+12-12=-6-12 (subtract 12, subtraction property of equality)

-9x=-6-12

-9x=-18 (simplify)

-9x/-9=-18/-9 (divide by 9, division property of equality)

x=2

5 0

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

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

4 0

3 years ago

If a baker doubles a recipe that calls for 6-2/3 cups of flour , how many cups of flour will be needed in all ?

Assoli18 [71]

13 1/3 cups needed in all

5 0

3 years ago

Read 2 more answers

Can someone help me please

nataly862011 [7]

Answer:

D is 90 E is 81 F is 99

Step-by-step explanation:

D is 90 because a straight angle equals 180 degrees. E is 81 because it is directly across from 81. F is 99 because 180-81 is 99

7 0

2 years ago

a group raised $276 for its favorite charity. this is 23% of the amount it hopes to raise. how much money does the group want to

OverLord2011 [107]

Answer: The group wants to raise $1,200.

Step-by-step explanation:

We can use a proportion to solve.

part/whole = percent/100

If we insert the values:

276/x = 23/100

We can cross multiply.

276 x 100 = 27,600

27,600 / 23 = 1,200

$1,200 is the answer.

6 0

2 years ago