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irina1246 [14]
3 years ago
11

Identify the location of the point (-3, -2).

Mathematics
1 answer:
Lisa [10]3 years ago
7 0
Point S is where (-3, -2)
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An 18 fluid ounces bottle of lotion costs $10.99, what is the prices per fluid ounce?
anzhelika [568]

Answer:

35

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
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
Which of the following expressions correctly uses the properties of summations to represent
madam [21]

Answer:

Option C is correct.

7 \cdot \sum_{i=1}^{18} i^2 + 9 \cdot 18

Step-by-step explanation:

Given the expression:  \sum_{i=1}^{18} (7i^2+9)

Using properties of summation:

  • \sum_{i=1}^{n} (a+bi) =\sum_{i=1}^{n} a + \sum_{i=1}^{n} bi
  • \sum_{i=1}^{n} a = an

Using properties of summation in the given expression we have;

\sum_{i=1}^{18} (7i^2+9)

= \sum_{i=1}^{18} 7i^2 + \sum_{i=1}^{18} 9

=7 \cdot \sum_{i=1}^{18} i^2 + 9 \cdot 18

Therefore, the following given expression uses the properties of summation to represents is, 7 \cdot \sum_{i=1}^{18} i^2 + 9 \cdot 18


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3 years ago
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What is the length and width of the rectangle if the area is 72 squre meters?
cupoosta [38]

Answer:

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Step-by-step explanation:

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a game is played by drawing 4 cards from a standard playing deck and replacing each card after it is drawn. find the probability
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It is a 1 in 13 chance of drawing at least 1 ace. 
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