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2 years ago

2. What are the next three terms in the geometric sequence below?

1 answer:

7 0

-0.5 and 2 the difference is 2.5. 2.5 times 4 equals 10. 2 and -8 the difference is 10. 10 times 4 equals 40. -8 and 32 the difference is 40

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Solve the equation <img src="https://tex.z-dn.net/?f=%2835%20x%5E%7B4%7D%20y%2B14%20x%5E%7B5%7D%20y-2%20y%5E%7B3%7D-4x%20y%5E%7B

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

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

7 0

3 years ago

What is 36 rounded to the nearest hundred?

BARSIC [14]

Its 40
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............

7 0

2 years ago

7. What is the final paragraph of an informational essay or article called?

viva [34]

Answer:

the conclusion

Step-by-step explanation:

The final paragraph of an informational essay or article is called the conclusion.

6 0

2 years ago

Describe a situation in your life when what you know about probability may have helped you make a decision. How could you have u

Andrei [34K]

Answer:

Knowledge > Probability

Step-by-step explanation:

In the moment knowledge would be useful because you are thinking about the decision you are making but after days, months or years probability would be in your mind. Also probability is just another word for chance so there would be no confirmation of said thing happening but when you have knowledge your brain knows that said thing is 100% going to happen, so for me personally knowledge is more useful than probability

8 0

1 year ago

Solve for lenght y. Show work PLease help

dolphi86 [110]

You have a right triangle here so we are going to use a trig identity to solve for y. Y is the side opposite the angle given to us, and then we also have the hypotenuse. Opposite / hypotenuse tells us that we have to use the sin ratio to find y. $sin(52)=\frac{y}{37}$ .

In order to isolate the y, we will multiply both sides by 37 to get

37sin(52)=y. We can do this on our calculator in degree mode and will get that y = 29.156 inches

6 0

3 years ago