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3 years ago

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90 marbles were stored in two boxes, box A and box B. After 5 marbles were removed from box A to box B, both boxes had the same

number of of marble. How many marbles were in box A originally?
(Please help- I really don't understand)

2 answers:

KIM [24]3 years ago

6 0

Answer:

50 marbles in box a

Step-by-step explanation:

if one box has 50 and another 40, when you take away 5 from box a there will be 45 and 45 and in total there are still 90 marbles. Your welcome. Pls mark brainliest

arsen [322]3 years ago

4 0

Answer:

There were originally 50 marbles in box A.

Step-by-step explanation:

If you have 50 marbles in box A and put five of them into box B, they would both have 45 marbles.

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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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3 years ago

Plz prove the given equation!!!

elixir [45]

Answer:

Please see the attached picture for the full solution.

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3 years ago

12 What is the solution to this equation?

Levart [38]

Answer:

x=-5

Step-by-step explanation:

add 7 to 53 then divide -12 to itself and 60.

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3 years ago

A store sells rope by the meter. The equation p=0.8L represents the price p(in dollars) of a piece of nylon rope that is L meter

Margaret [11]

Answer:

1. $0.80 or 80 cents

2. 1.25 meters

Step-by-step explanation:

The equation p=0.8L represents the price p (in dollars) of a piece of nylon rope that is L meters long.

1. To find how much the nylon costs per meter, take L = 1 (this means you are calculating the price of a piece of nylon rope that is 1 meter long):

$L=1,\\ \\p=\$0.8\cdot 1=\$0.80$

2. To find how long a piece of nylon rope that costs $1.00 is, substitute into the equation p = 1:

$p=1,\\ \\1=0.8L\\ \\L=\dfrac{1}{0.8}=\dfrac{10}{8}=\dfrac{5}{4}=1.25\ meters$

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3 years ago

Terry bought 2 1/2 dozen chocolate chip cookies. She paid $15 for her purchase. If there are 12 cookies in each dozen, what is t

Kruka [31]

Answer:

you have to divide 12 by 15

Step-by-step explanation:

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