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2 years ago

Find the LCD for the list of rational expressions. 2 7x +4 x2 + 5x - 14' x2 + 3x – 28

Mathematics

1 answer:

andre [41]2 years ago

7 0

the equation is made and the included values are indicated.

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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,

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

4 0

3 years ago

3. PLZZZZ HELP MEEE!.!.!

andre [41]

Answer:

60in²

Step-by-step explanation:

Since lateral surface area means all the shapes except the base, we will ignore the square in the middle.

A=1/2(b*h)

A=1/2(10*3)

A=15in²

Now we will multiply the area by 4 or the number of other shapes besides the base.

60in²

3 0

2 years ago

Which shows a perfect square trinomial?

Tju [1.3M]

The third one. Because it factors to (4x+3y)^2

7 0

3 years ago

Read 2 more answers

The scores of individual students on the American College Testing (ACT) Program composite college entrance examination have a No

jeyben [28]

Answer:

The sample size must be atleast 3600

Step-by-step explanation:

We are given the following in the question:

The scores of individual students on the American College Testing (ACT) Program is a bell shaped distribution that is a normal distribution.

Population standard deviation = 6.0

We want that the sample standard deviation should not be more than 0.1.

Thus, the standard error should not be more than 0.1.

Standard error =

$=\dfrac{\sigma}{\sqrt{n}}$

Putting values, we get,

$\dfrac{\sigma}{\sqrt{n}}\leq 0.1\\\\ \dfrac{6}{\sqrt{n}} \leq 0.1\\\\ \sqrt{n}\geq 60\\n\geq 3600$

Thus, the sample size must be atleast 3600

3 0

3 years ago

2| x - 3 | > 8, 2| x - 3 | < -8 Sovle the inequality involving absolute value? I don't understand how to get the right ans

frutty [35]

Divide both sides by 2

|x-3|>4 and |x-3|<-4
ok so |x-3|<-4 is false, since |x|≥0 always

so we have
|x-3|>4
now assume
x-3>4 and
x-3<-4

x-3>
add 3
x>7

x-3<-4
add 3
x<-1

so
-1>x and x>7

so basically it is all numbers from -∞ to +∞ except from -1 to 7
in interval notaion
(-∞,-1)U(7,∞)

S={x|x<-1 or x>7}

4 0

3 years ago

Read 2 more answers