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likoan [24]
3 years ago
5

Mary sells lemonade at $1.50 a glass.  She spent $8.00 on supplies.  She ended with more than $28.00

Mathematics
2 answers:
inna [77]3 years ago
4 0

Answer:

(C.) 1.50n - 8.00 > 28.00

Step-by-step explanation:

Mary sells lemonade at $1.50 a glass

She spent $8.00 on supplies

She ended with more than $28.00

The cost of n lemonade glasses - the cost of supplies is more than $28.00

i.e $1.50n - $8.00 > $28.00

Elena-2011 [213]3 years ago
3 0

Answer:

(C.) 1.50n – 8.00 > 28.00

Hope this helped you!!!

<u><em>Love,</em></u>

<u><em>Morgan Taylor!</em></u>

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y′′ −y = 0, x0 = 0 Seek power series solutions of the given differential equation about the given point x 0; find the recurrence
sukhopar [10]

Let

\displaystyle y(x) = \sum_{n=0}^\infty a_nx^n = a_0 + a_1x + a_2x^2 + \cdots

Differentiating twice gives

\displaystyle y'(x) = \sum_{n=1}^\infty na_nx^{n-1} = \sum_{n=0}^\infty (n+1) a_{n+1} x^n = a_1 + 2a_2x + 3a_3x^2 + \cdots

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

When x = 0, we observe that y(0) = a₀ and y'(0) = a₁ can act as initial conditions.

Substitute these into the given differential equation:

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

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

Then the coefficients in the power series solution are governed by the recurrence relation,

\begin{cases}a_0 = y(0) \\ a_1 = y'(0) \\\\ a_{n+2} = \dfrac{a_n}{(n+2)(n+1)} & \text{for }n\ge0\end{cases}

Since the n-th coefficient depends on the (n - 2)-th coefficient, we split n into two cases.

• If n is even, then n = 2k for some integer k ≥ 0. Then

k=0 \implies n=0 \implies a_0 = a_0

k=1 \implies n=2 \implies a_2 = \dfrac{a_0}{2\cdot1}

k=2 \implies n=4 \implies a_4 = \dfrac{a_2}{4\cdot3} = \dfrac{a_0}{4\cdot3\cdot2\cdot1}

k=3 \implies n=6 \implies a_6 = \dfrac{a_4}{6\cdot5} = \dfrac{a_0}{6\cdot5\cdot4\cdot3\cdot2\cdot1}

It should be easy enough to see that

a_{n=2k} = \dfrac{a_0}{(2k)!}

• If n is odd, then n = 2k + 1 for some k ≥ 0. Then

k = 0 \implies n=1 \implies a_1 = a_1

k = 1 \implies n=3 \implies a_3 = \dfrac{a_1}{3\cdot2}

k = 2 \implies n=5 \implies a_5 = \dfrac{a_3}{5\cdot4} = \dfrac{a_1}{5\cdot4\cdot3\cdot2}

k=3 \implies n=7 \implies a_7=\dfrac{a_5}{7\cdot6} = \dfrac{a_1}{7\cdot6\cdot5\cdot4\cdot3\cdot2}

so that

a_{n=2k+1} = \dfrac{a_1}{(2k+1)!}

So, the overall series solution is

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

\boxed{\displaystyle y(x) = a_0 \sum_{k=0}^\infty \frac{x^{2k}}{(2k)!} + a_1 \sum_{k=0}^\infty \frac{x^{2k+1}}{(2k+1)!}}

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mixer [17]
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3 years ago
Help, i just need the answers and no need for explanations.
maria [59]

Answer:

The equation of the quadratic function shown is;

x^2+ 2x -3

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Here in this question, we need to know the quadratic equation whose graph was shown.

The key to answering this lies in knowing the roots of the equation.

The roots of the equation are the solution to the quadratic equation and can be seen from the graph at the point where the quadratic equation crosses the x-axis.

The graph crosses the x-axis at two points.

These are at the points x = -3 and x = 1

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x + 3 and x -1

Multiplying both will give us the quadratic equation we are looking for.

(x + 3)(x-1) = x(x -1) + 3(x-1)

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Answer:

i feel as if in the United States, both the metric system and the English system of measurement are used, although the English system predominates. This discussion question has three parts:

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Give an example of how you think the metric system will be used in your future career.

Do you think the U.S. should switch to metric system exclusively? Why or why not?

This week we learned about the metric and U.S. customary measurement systems. Please upload and submit your responses to the following questions in at least 150 words:

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Expert Answer

Step-by-step explanation:

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