Find the first 2 equivalent fraction by division (complete all)a)9/18b)20/30

Mathematics

2 answers:

Alla [95]2 years ago

7 0

Answer:

a) 9/18 = 1/2
b) 20/30 = 2/3

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Explanations:

a) Divide both parts of the fraction by the GCF 9. The numerator becomes 9/9 which simplifies to 1. The denominator becomes 18/9 which simplifies to 2.
b) Divide both parts by the GCF 10. We have 20/10 become 2, and 30/10 become 3.

Igoryamba2 years ago

5 0

Answer:

Below in bold.

Step-by-step explanation:

a) 9/3 / 18/3 = 3/6

3/3 / 6/3 = 1/2

b) 20/ 5 / 30/5 = 4/6

4/2 / 6/2 = 2/3.

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Find the solution of the given initial value problem in explicit form. y′=(1−5x)y2, y(0)=−12 Enclose numerators and denominators

Nata [24]

Answer:

The solution is $y=-\frac{12}{12x-30x^2+1}$ .

Step-by-step explanation:

A first order differential equation $y'=f(x,y)$ is called a separable equation if the function $f(x,y)$ can be factored into the product of two functions of $x$ and $y$ :

$f(x,y)=p(x)h(y)$

where $p(x)$ and $h(y)$ are continuous functions.

We have the following differential equation

$y'=(1-5x)y^2, \quad y(0)=-12$

In the given case $p(x)=1-5x$ and $h(y)=y^2$ .

We divide the equation by $h(y)$ and move $dx$ to the right side:

$\frac{1}{y^2}dy\:=(1-5x)dx$

Next, integrate both sides:

$\int \frac{1}{y^2}dy\:=\int(1-5x)dx\\\\-\frac{1}{y}=x-\frac{5x^2}{2}+C$

Now, we solve for $y$

$-\frac{1}{y}=x-\frac{5x^2}{2}+C\\-\frac{1}{y}\cdot \:2y=x\cdot \:2y-\frac{5x^2}{2}\cdot \:2y+C\cdot \:2y\\-2=2yx-5yx^2+2Cy\\y\left(2x-5x^2+2C\right)=-2\\\\y=-\frac{2}{2x-5x^2+2C}$