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3 years ago

This is for today someone help me!!!

Mathematics

1 answer:

Dmitry [639]3 years ago

7 0

Answer:

Centre = (2, -3)

radius = 5units

Step-by-step explanation:

The standard form of a circle is expressed as;

x²+y²+2gx+2fy+c = 0

Centre = (-g, -f)

radius r = √g²+f²-c

Given the equation;

x²+y²-4x+6y-12 = 0

Compare

2gx = -4x

2g = -4

g = -2

Similarly;

2fy = 6y

2f = 6

f = 3

Centre = (-(-2), -3)

Centre = (2, -3)

Radius = r = √(-2)²+3²+12

r = √4+9+12

r = √25

r = 5 units

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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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3 years ago

How to complete equation and tell property with 21*blank =9*21

LenaWriter [7]

21*x=9*21

9*21=189

21*x=189

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5 0

3 years ago

Will give 25 points and brainliest answer if correct

Norma-Jean [14]

Let $d$ be the common difference between terms in the sequence $\{a_n\}_{n\ge1}$ . Then

$a_{19}=-58$
$a_{20}=a_{19}+d$
$a_{21}=a_{19}+2d$
$\implies-164=-58+2d\implies d=-53$

The first term in the sequence, $a_1$ , satisfies

$a_2=a_1+d$
$a_3=a_1+2d$
$a_4=a_1+3d$
...
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So the explicit formula for the $n$ -th term in the sequence is

$a_n=a_1+(n-1)d\implies a_n=896-53(n-1)$

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3 years ago

What is the value of X?

algol [13]

Answer:

x = 3

Step-by-step explanation:

ΔABC is 45 45 90 right triangle

The ratio of leg: hypo = a : a√2

Given: hypo AC = 6√2; so AB = BC = 6

ΔBCD is 30 60 90 right triangle

The ratio of short leg : long leg : hypo = x : x√3 : 2x

Hypo. BC = 6 = 2 (3)

So short leg BD = x = 3

7 0

3 years ago