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3 years ago

15

A scale drawing of a rectangular park is 5 inches wide and 7 inches long. The actual park is 280 yards long. What is the area of

the actual park, in square yards?

1 answer:

jekas [21]3 years ago

7 0

Answer:

area=56000 yards²

Step-by-step explanation:

first divide 280 by 7 and get 40

scale factor is 40

5x40=200

200x280=56000

area=56000 yards²

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Which description best compares the graphs of these two functions?

s2008m [1.1K]

Answer:

1st option, they have the same y-intercept

Step-by-step explanation:

they do not have the same x-intercept

'A' is linear

'B' has a less steep slope

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2 years ago

Factor 21a–27.

Ganezh [65]

Answer:

3(7a - 9)

Step-by-step explanation:

21a–27

3*7*a - 3*9

Factor out 3

3(7a - 9)

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2 years ago

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How many solutions can be found for the equation −4x − 11 = 2(x − 3x) + 13? (4 points) none or one or two or infinitrly many

Nadya [2.5K]

There is one solution

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3 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

Jackie and a classmate spent a total of 20 hrs working on a chemistry project. Jackie’s classmate spent 2 hrs less time working

valina [46]

Answer:

x = 11

Step-by-step explanation:

x + (x - 2) = 20

2x - 2 = 20

2x - 2 + 2 = 22 + 2

2x = 22

x = 11

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2 years ago