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klemol [59]
3 years ago
11

A newspaper has more than 30 pages and fewer than 40 pages. The newspaper is divided into sections and each section has 8 pages.

How many sections does the newspaper have
Mathematics
1 answer:
VashaNatasha [74]3 years ago
4 0
8 * 4  = 32    which is a number in between 30 and 40 
So the newspaper has 4 sections.
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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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andriy [413]

Answer:

-2x + 5

Step-by-step explanation:

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The function f(x) = 25(4)^x represents the growth of a bird population every year in a national park. Kyle wants to manipulate t
Natasha_Volkova [10]

f(x)=25(4)^{\frac{x}{2}} will be the function to calculate population every half year.

Further explanation:

The given formula is:

f(x) = 25(4)^x

In the given formula, x represents the amount of time in years. So, in order to convert the given function for yearly calculation of population, to find the population every half year the time will be converted into half. This means that instead of x, x/2 will be used.

So the new function will be:

f(x) = 25(4)^{\frac{x}{2}}

Keywords: Population growth, Population growth function

Learn more about population growth at:

  • brainly.com/question/10689103
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#LearnwithBrainly

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Answer:

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Step-by-step explanation:

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