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3 years ago

I need help and steps please

Mathematics

1 answer:

kkurt [141]3 years ago

3 0

-2/3 b + 4 = 0

Add -4 to both sides to eliminate the 4 on the left:

-2/3 b + 4 - 4 = - 4

-2/3 b = -4

Multiply both sides by -3/2 to eliminate the -2/3 on the left:

-3/2 • (-2/3 b) = -3/2 • 4

b = -12/2

Simplify the solution:

b = -6

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jeka94

$\underbrace{35x^4y+14x^5y-2y^3-4xy^3}_M\,\mathrm dx+\underbrace{7x^5-6xy^2}_N\,\mathrm dy=0$

$M_y=35x^4+14x^5-6y^2-12xy^2$
$N_x=35x^4-6y^2$

$\dfrac{N_x-M_y}N=\dfrac{-14x^5+12xy^2}{7x^5-6xy^2}=-2$

This suggests an integrating factor depending on $x$ only is possible, and given by

$\mu(x)=\exp\left(-\displaystyle\int\frac{N_x-M_y}N\,\mathrm dx\right)=e^{2x}$

Distributing across the ODE, we end up with

$\underbrace{(35x^4y+14x^5y-2y^3-4xy^3)e^{2x}}_{M^*}\,\mathrm dx+\underbrace{(7x^5-6xy^2)e^{2x}}_{N^*}\,\mathrm dy=0$

The equation is now exact, with

${M^*}_y={N^*}_x=(35x^4+14x^5-6y^2-12xy^2)e^{2x}$

Now we find the solution:

$F_x=M^*$
$F=\displaystyle\int(35x^4+14x^5-2y^3-4xy^3)e^{2x}\,\mathrm dx$
$F=(7x^5y-2xy^3)e^{2x}+f(y)$

$F_y=N^*$
$(7x^5-6xy^2)e^{2x}+f'(y)=(7x^5-6xy^2)e^{2x}$
$f'(y)=0$
$\implies f(y)=C$

The general solution is then

$F(x,y)=(7x^5y-2xy^3)e^{2x}=C$

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3 years ago

A package of 4 pairs of insulated socks costs $27.96. What is the unit price of the pairs of socks?

harkovskaia [24]

Answer:

1 pair of socks cost $6.99

Step-by-step explanation:

$27.96 divided by 4 = $6.99

Hope I helped :)

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3 years ago

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B b b b b b b b b b b

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3 years ago

Select the point that satisfies y less than or equal to x^2-3x+2

solong [7]

Answer:

Point (4,4) satisfies the required condition.

Step-by-step explanation:

x²-3x+2 = x²-2x-x+2

= x(x-2)-1(x-2)

= (x-2)(x-1)

According to the given information

y ≤ (x-2)(x-1) ...(1)

So lets consider one point having coordinates (4,4).

Substitute (4,4) in equation (1), we get

4≤ (4-2)(4-1)

4 ≤ 6

Hence point (4,4) satisfies the above condition. It's only one example there will be more points which satisfies the required condition.

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3 years ago

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