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Vadim26 [7]
2 years ago
11

Write the converse of the conditional statement. Determine whether the converse is true or false. If it is false, find a counter

example. Collinear points are on the same line. a. If the points are on the same line, then the points are collinear. True. b. If the points are collinear, then the points are on the same line. True. c. If the points are on the same line, then the points are on the same line. True. d. Collinear points are on the same line. True. Please select the best answer from the choices provided A B C D
Mathematics
1 answer:
Bumek [7]2 years ago
7 0

Answer:

a. is True.

Step-by-step explanation:

Collinear points are on the same line.

The converse is:

If the points are on the same line the the points are collinear. This is True.

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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}

We use the initial condition y(0)=-12 to find the value of C.

-12=-\frac{2}{2\left(0\right)-5\left(0\right)^2+2C}\\-12=-\frac{1}{c}\\c=\frac{1}{12}

Therefore,

y=-\frac{2}{2x-5x^2+2(\frac{1}{12})}\\y=-\frac{12}{12x-30x^2+1}

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3 years ago
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Parallel lines have the same slope.

So the graph of  [ y = 3x + any number ] is parallel
to the graph of  [ y = 3x - 10 ] .
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3 years ago
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