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Arisa [49]
2 years ago
10

What is the expression for -3(x-5)2+1 in descending order

Mathematics
1 answer:
ruslelena [56]2 years ago
4 0

The expression in descending order is -6x + 31

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She can make 36 banners. Hope this helps!
7 0
3 years ago
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What is the area of a square, if a side measures 12 cm?
Westkost [7]
Area of a square is length times by itself (length x width) so 12 cm x 12 cm
144cm squared
hope i helped :)
3 0
3 years ago
I'm thinking of a number. This number is 12 less than its square. What could my number be?
omeli [17]

let nwmber to be X

the number is 12 less than it's square,

so X=12-X^2

=> X^2+X-12=0

=> (X+4)(X-3)=0

=>X= 3, or X=-4

in math we don't usually take negative numbers into account so your number would be 3

5 0
2 years ago
1) Use power series to find the series solution to the differential equation y'+2y = 0 PLEASE SHOW ALL YOUR WORK, OR RISK LOSING
iogann1982 [59]

If

y=\displaystyle\sum_{n=0}^\infty a_nx^n

then

y'=\displaystyle\sum_{n=1}^\infty na_nx^{n-1}=\sum_{n=0}^\infty(n+1)a_{n+1}x^n

The ODE in terms of these series is

\displaystyle\sum_{n=0}^\infty(n+1)a_{n+1}x^n+2\sum_{n=0}^\infty a_nx^n=0

\displaystyle\sum_{n=0}^\infty\bigg(a_{n+1}+2a_n\bigg)x^n=0

\implies\begin{cases}a_0=y(0)\\(n+1)a_{n+1}=-2a_n&\text{for }n\ge0\end{cases}

We can solve the recurrence exactly by substitution:

a_{n+1}=-\dfrac2{n+1}a_n=\dfrac{2^2}{(n+1)n}a_{n-1}=-\dfrac{2^3}{(n+1)n(n-1)}a_{n-2}=\cdots=\dfrac{(-2)^{n+1}}{(n+1)!}a_0

\implies a_n=\dfrac{(-2)^n}{n!}a_0

So the ODE has solution

y(x)=\displaystyle a_0\sum_{n=0}^\infty\frac{(-2x)^n}{n!}

which you may recognize as the power series of the exponential function. Then

\boxed{y(x)=a_0e^{-2x}}

7 0
3 years ago
Walter invests $100,000 in an account that compounds interest continuously and earns 12%. How long will it take for his money to
prohojiy [21]

Answer:

300000= 100000 e^{0.12 t}

We divide both sides by 100000 and we got:

3 = e^{0.12 t}

Now we can apply natural logs on both sides;

ln(3) = 0.12 t

And then the value of t would be:

t = \frac{ln(3)}{0.12}= 9.16 years

And rounded to the nearest tenth would be 9.2 years.

Step-by-step explanation:

For this case since we know that the interest is compounded continuously, then we can use the following formula:

A =P e^{rt}

Where A is the future value, P the present value , r the rate of interest in fraction and t the number of years.

For this case we know that P = 100000 and r =0.12 we want to triplicate this amount and that means A= 300000 and we want to find the value for t.

300000= 100000 e^{0.12 t}

We divide both sides by 100000 and we got:

3 = e^{0.12 t}

Now we can apply natural logs on both sides;

ln(3) = 0.12 t

And then the value of t would be:

t = \frac{ln(3)}{0.12}= 9.16 years

And rounded to the nearest tenth would be 9.2 years.

5 0
3 years ago
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