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2 years ago

11

Carlos is tiling a kitchen counter that is 12 feet by 3 feet.The counter has a rectangular hole 3 feet by 2 feet cut in it for a

sink.What is the area of the kitchen counter that Carlos will tile? Help

1 answer:

alina1380 [7]2 years ago

3 0

Answer:

Carlos has to tile 30 sq ft

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riadik2000 [5.3K]

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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

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

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2 years ago

the average price of a gallon of gas was $3.22 and 2014 and $2.40 in 2015 what is the percent decrease in the price of gas

kakasveta [241]

Answer:

25.47%

Step-by-step explanation:

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2 years ago

Can someone tell me answers I’m really confused

Luba_88 [7]

No is the answer. You cannot split 5ft evenly.

Hope this helps!!!

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2 years ago

The length of a rectangle is 24 units.can the preimteter p of the rectangle be 60 units when it’s width w is 11 units?

Alenkinab [10]

No it can’t because calculating the perimeter, you would have to add all sides of the rectangle. If you added 11 + 11 + 24 +24, the perimeter would be 70 not 60.

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3 years ago