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devlian [24]
3 years ago
11

Find the solution to the differential equation dx/dy+y/3=0 subject to the initial conditions y(0)=12.

Mathematics
1 answer:
ycow [4]3 years ago
8 0
\dfrac{\mathrm dx}{\mathrm dy}+\dfrac y3=0\iff\mathrm dx=-\dfrac y3\,\mathrm dy
\implies\displaystyle\int\mathrm dx=-\frac13\int\mathrm y\,dy
\implies x=-\dfrac16y^2+C

Given that y(0)=12, we have

0=-\dfrac16(12)^2+C\implies C=24

So the particular solution to the initial value problem is

x=-\dfrac16y^2+24\iff y^2=144-6x
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From the set (76, 77, 78), use substitution to determine which value of x makes the equation true
jeyben [28]

Answer:

The answer is C.

Step-by-step explanation:

Multiply 4 by 76, 77, and 78.

4 * 76 = 304

4 * 77 = 308

4 * 78 = 312

304 = 304, so C is the correct answer.

Hope this helps!

7 0
3 years ago
The product of (3 − 4i) and____is 25.
LiRa [457]

(3-4i)(a+bi)=25\qquad\text{use FOIL method}\\\\(3)(a)+(3bi)+(-4i)(a)+(-4i)(bi)=25+0i\\\\3a+3bi-4ai-4bi^2=25+0i\\\\3a+3bi-4ai-4b(-1)=25+0i\\\\3a+3bi-4ai+4b=25+0i\\\\(3a+4b)+(3b-4a)i=25+0i\\.\qquad\qquad\qquad\qquad\Downarrow\\\\3a+4b=25\ and\ 3b-4a=0\\\\3b-4a=0\qquad\text{add 4a to both sides}\\\\3b=4a\qquad\text{divide both sides by 3}\\\\b=\dfrac{4}{3}a\qquad\text{substitute it to the first equation}\\\\3a+4\left(\dfrac{4}{3}a\right)=25\\\\3a+\dfrac{16}{3}a=25\qquad\text{multiply both sides by 3}

9a+16a=75\\\\25a=75\qquad\text{divide both sides by 25}\\\\\boxed{a=3}\qquad\text{put the value of a to}\ b=\dfrac{4}{3}a:\\\\b=\dfrac{4}{3}(3)\\\\\boxed{b=4}\\\\Answer:\ \boxed{(3-4i)\underline{(3+4i)}=25}

6 0
3 years ago
Write the equation of a line that is perpendicular to the given line and that passes through the given point.
OverLord2011 [107]

Answer:

y=5x+17

Step-by-step explanation:

perpendicular slope is 5

y-7=5(x+2) convert this equation into slope intercept and that's your answer


5 0
3 years ago
Answer?......................
erica [24]

Answer:

22

Step-by-step explanation:

6( n^2 +2)

-----------------

n

Let n = 3

6( 3^2 +2)

-----------------

3

Parentheses first

6( 9 +2)

-----------------

3

6( 11)

-----------------

3

Top of the fraction next

66

-----

3

Divide

22

7 0
2 years ago
You have 35 yards of ribbon for your gift boxes. Each box gets the same amount of ribbon. How much ribbon will each of your 30 g
Lubov Fominskaja [6]
1.16 of a yard, don’t know if this is correct but worth a shot
6 0
3 years ago
Read 2 more answers
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