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Licemer1 [7]
2 years ago
11

Mr.smith has 238 eggs in the warehouse. He collected all another 122 eggs from his chickens yesterday. As he arranged all the eg

gs in trays, he accidentally dropped 28 eggs on the ground how many unbroken eggs were left?among the eggs left, there were 126 brown eggs how many were white eggs
Mathematics
1 answer:
Aleksandr [31]2 years ago
5 0

Answer:

238 + 122 – 28 = 332

There were 332 unbroken eggs left.

332 – 126 = 206

There were 206 white eggs left

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If the complex number x = 3 + bi and |x|2 = 13, which is a possible value of b?
Naddika [18.5K]

Answer:

A: 2

Step-by-step explanation:

EDGE 2021

3 0
2 years ago
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)!}}

4 0
3 years ago
Expand, and simplify the following expressions a. (2x+y)(x+y) + (2x-y)(x+y)​
tankabanditka [31]

Step-by-step explanation:

2x²+2xy+yx+y²+2x²+2xy-yx+y²

2x²+2x²+2xy+2xy+yx-yx+y²+y²

2x²+2x²+2xy+2xy

4x²+4xy

7 0
3 years ago
Read 2 more answers
Lydia makes $7,000 per month in New York City at her interior design company. She can't spend more than 25% of her income on the
Nataly [62]

Answer:

The maximum amount that Lydia can spend on a one-bedroom apartment is $ 1,750.

Step-by-step explanation:

Given that Lydia makes $ 7,000 per month in New York City at her interior design company, and that she can't spend more than 25% of her income on the one bedroom apartment, to determine the maximum amount of money that she can spend must be made the following calculation:

7,000 x 0.25 = X

1,750 = X

Thus, the maximum amount that Lydia can spend on a one-bedroom apartment is $ 1,750.

7 0
3 years ago
Write an equation in​ slope-intercept form of the line that passes through the given point and is parallel to the graph of the g
Shtirlitz [24]

Answer:

The equation in the slope-intercept form is

y = -5x - 41

Step-by-step explanation:

The given equation in the question is;

y = -5x + 2

The equation of a straight line graph can be written in the form;

y = mx + c

where m is the slope and c is the intercept

From here, we can see that the slope m is -5

Since the line is parallel to the new line we are trying to write its equation, it means that they have the same value of intercept.

Hence, the slope of the new line is also -5

Now, we can write the equation of the new line as;

y = -5x + c

we need to get the value of c here however

To get the value of c, we need to input the value of x and y

From the graph, x = -7 and y = -6

Substituting these values, we have;

-6 = -5(-7) + c

-6 = 35 + c

c = -6 -35

c = -41

So the equation of the new line will be;

y = -5x - 41

7 0
3 years ago
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