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3 years ago

In a school, the ratio of boys to girls is 4:3. There are 216 boys. How many girls are there?

Mathematics

1 answer:

tankabanditka [31]3 years ago

5 0

Answer:

162

Step-by-step explanation:

Divide 216 by 4

Then multiply 3 times

That's the answer

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Find a linear second-order differential equation f(x, y, y', y'') = 0 for which y = c1x + c2x3 is a two-parameter family of solu

Alisiya [41]

Let $y=C_1x+C_2x^3=C_1y_1+C_2y_2$ . Then $y_1$ and $y_2$ are two fundamental, linearly independent solution that satisfy

$f(x,y_1,{y_1}',{y_1}'')=0$
$f(x,y_2,{y_2}',{y_2}'')=0$

Note that ${y_1}'=1$ , so that $x{y_1}'-y_1=0$ . Adding $y''$ doesn't change this, since ${y_1}''=0$ .

So if we suppose

$f(x,y,y',y'')=y''+xy'-y=0$

then substituting $y=y_2$ would give

$6x+x(3x^2)-x^3=6x+2x^3\neq0$

To make sure everything cancels out, multiply the second degree term by $-\dfrac{x^2}3$ , so that

$f(x,y,y',y'')=-\dfrac{x^2}3y''+xy'-y$

Then if $y=y_1+y_2$ , we get

$-\dfrac{x^2}3(0+6x)+x(1+3x^2)-(x+x^3)=-2x^3+x+3x^3-x-x^3=0$

as desired. So one possible ODE would be

$-\dfrac{x^2}3y''+xy'-y=0\iff x^2y''-3xy'+3y=0$

(See "Euler-Cauchy equation" for more info)

6 0

3 years ago

Add (2x+5) + (3x-7) plsssssss SBUIAXSBADJASN

MArishka [77]

2x+3x= 5x
5-7= -2

so its 5x-2 since all like terms are added

6 0

3 years ago

Which line has a slope of 1/2 and goes through the point (2,4)?

Pani-rosa [81]

The line equation for its slope and one point is:
y - y1 = m(x - x1)
m is the slope, x1, y1 are the point coordinates, so lets substitute:
y - 4 = (1/2)(x - 2)
y = (1/2)x + 3

7 0

3 years ago

The picture is my question.

Dominik [7]

The second one because domain refers to x, and since at (-3,-4) the point is hollow, the sign should be < without the line under it

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3 years ago

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Solve for x: 2x-1/3 - 3x/4 = 5/6

bogdanovich [222]

Answer:

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2 years ago