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NARA [144]
3 years ago
15

(1 point) In this problem we consider an equation in differential form M dx + N dy = 0. (8x + 8y)dx + (8x + 4y)dy = 0 Find My =

8 Nx = 8 If the problem is exact find a function F(x, y) whose differential, dF(x, y) is the left hand side of the differential equation. That is, level curves F(x, y) = C, give implicit general solutions to the differential equation. If the equation is not exact, enter NE otherwise find F(x, y) (note you are not asked to enter C) F(x, y) =
Mathematics
1 answer:
OLga [1]3 years ago
3 0

The ODE is exact because M_y=N_x. Then

F_x=8x+8y\implies F(x,y)=4x^2+8xy+g(y)

F_y=8x+g'(y)=8x+4y\implies g'(y)=4y\implies g(y)=2y^2+C

So we have

F(x,y)=4x^2+8xy+2y^2=C

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Solve the equation. Show all work.<br> -2 (4 - x) = 12x – 3<br> (I think this is 9th grade algebra)
Genrish500 [490]

Answer:

-1/2

Step-by-step explanation:

-2 (4 - x) = 12x – 3

-8+2x=12x-3

+8            +8

2x=12x+5

-12x  -12x

-10x=5

/-10  /-10

= -1/2

4 0
3 years ago
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If you need one gallon of gas for 20miles how many gallon do you need for 364 miles?
ad-work [718]

Divide total miles by miles per gallon:

364 miles / 20 miles per gallon = 18.2 gallons

7 0
3 years ago
A person breathes 2.5 x 10^-4 in about cubic meters of air per second. How long does it take to breathe in 2.5 cubic meters of a
Ipatiy [6.2K]

Answer:

10⁴ seconds

Step-by-step explanation:

Given that,

A person breathes 2.5\times 10^{-4} in about cubic meters of air per second.

We need to find time taken to breathe 2.5 cubic meters of air.

In 1 sec = 2.5\times 10^{-4} m³ of air breathe

Let in x seconds, 2.5 m³ of air taken by the person.

x=\dfrac{2.5}{2.5\times 10^{-4}}\\\\x=10^4\ s

Hence, in 10⁴ seconds 2.5 m³ of air is taken by the person.

5 0
3 years ago
1.<br> Work<br> 8m + 5 = 6m + 17<br> Reason<br> Given Statement
snow_tiger [21]

Answer:

m = 6

Step-by-step explanation:

6 0
3 years ago
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Find g[h(x)] if g(x)=x^2 and h(x)=x+3
svetlana [45]

Answer:

g(h(x)) = [x + 3]^2 or x^2 + 6x + 9

Step-by-step explanation:

g[h(x)] signifies that h(x) is the input to g(x).

Writing out g(x) = x^2 and replacing "x" with [x + 3], we get:

g(h(x)) = [x + 3]^2 or x^2 + 6x + 9

8 0
3 years ago
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