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3 years ago

Explain why you would make one of the addends a tens number when solving an addition problem

1 answer:

4 0

<span> You refer to a multiple of ten. As a multiple of ten you can just add it to another number easier than a "ones number".</span>

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Show that ( 2xy4 + 1/ (x + y2) ) dx + ( 4x2 y3 + 2y/ (x + y2) ) dy = 0 is exact, and find the solution. Find c if y(1) = 2.

fredd [130]

$\dfrac{\partial\left(2xy^4+\frac1{x+y^2}\right)}{\partial y}=8xy^3-\dfrac{2y}{(x+y^2)^2}$

$\dfrac{\partial\left(4x^2y^3+\frac{2y}{x+y^2}\right)}{\partial x}=8xy^3-\dfrac{2y}{(x+y^2)^2}$

so the ODE is indeed exact and there is a solution of the form $F(x,y)=C$ . We have

$\dfrac{\partial F}{\partial x}=2xy^4+\dfrac1{x+y^2}\implies F(x,y)=x^2y^4+\ln(x+y^2)+f(y)$

$\dfrac{\partial F}{\partial y}=4x^2y^3+\dfrac{2y}{x+y^2}=4x^2y^3+\dfrac{2y}{x+y^2}+f'(y)$

$f'(y)=0\implies f(y)=C$

$\implies F(x,y)=x^2y^3+\ln(x+y^2)=C$

With $y(1)=2$ , we have

$8+\ln9=C$

$\boxed{x^2y^3+\ln(x+y^2)=8+\ln9}$

8 0

3 years ago

Three airlines serve a small town in Ohio. Airline A has 52% of all scheduled flights, airline B has 27% and airline C has the r

julia-pushkina [17]

Answer:

Step-by-step explanation:

Given that three airlines serve a small town in Ohio. Airline A has 52% of all scheduled flights, airline B has 27% and airline C has the remaining 21%.

Their on-time rates are 83%, 66%, and 36%, respectively.

Airlines A B C

Flights 52% 27% 21% 100%

On time rates 83% 66% 36%

Flight*online rates 43.1600% 17.8200% 7.5600% 68.5400%

Thus the above table shows the product of no of flights and on time rates.

Prob it was airline A given it left on time

= $\frac{43.16}{68.54} \\=0.6297$

4 0

3 years ago

Please help me! I need help. Please help me, I need help, please help me!

stiv31 [10]

Answer:

17x

Step-by-step explanation:

3x+4+4x+4+3x-4+3x-4+4x

Collect liketerms

5 0

2 years ago

Sam took out an 80/20 mortgage on a $125,000 home. What is the amount financed under the first mortgage?

SIZIF [17.4K]

Answer:100,000

Step-by-step explanation:

7 0

3 years ago

1, 3,4,5,11, answer is 65 _ + (_-_)^2 +_x_

Y_Kistochka [10]

Answer:

1 + (11-4)^2 +3x5

Step-by-step explanation:

1 + (11-4)^2 +3x5

1 + (7)^2 + 3 x 5

1 + 49 + 15

50 + 15 = 65

5 0

3 years ago