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3 years ago

2.

Mathematics

2 answers:

777dan777 [17]3 years ago

7 0

Your answer choice should be ( B )

Darina [25.2K]3 years ago

5 0

Answer: B

0.07274

Step-by-step explanation:

Length

72.74

Millimeter

0.07274

Meter

Formula

divide the length value by 1000

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15 liters increased by 60%

kicyunya [14]

15 liters increased by 60% is 24 liters.

8 0

3 years ago

A retail company estimates that if it spends x thousands of dollars on advertising during the year, it will realize a profit of

Gwar [14]

Answer:

Step-by-step explanation:

If the profit realized by the company is modelled by the equation

P (x) = −0.5x² + 120x + 2000, marginal profit occurs at dP/dx = 0

dP/dx = -x+120

P'(x) = -x+120

Company's marginal profit at the $100,000 advertising level will be expressed as;

P '(100) = -100+120

P'(100) = 20

Marginal profit at the $100,000 advertising level is $20,000

Company's marginal profit at the $140,000 advertising level will be expressed as;

P '(140) = -140+120

P'(140) = -20

Marginal profit at the $140,000 advertising level is $-20,000

<u>Based on the marginal profit at both advertising level, I will recommend the advertising expenditure when profit between $0 and $119 is made. At any marginal profit from $120 and above, it is not advisable for the company to advertise because they will fall into a negative marginal profit which is invariably a loss.</u>

7 0

3 years ago

A merchant buys a television for $125 and sells it for $75 more. what is the percent of markup?

guajiro [1.7K]

Since he sold it for $75 more,

% Mark Up = Mark Up/ Cost Price * 100%

% Mark Up = 75 / 125 * 100%

= 0.6 * 100% = 60%

Percent Mark Up = 60%.

Hope this explains it.

4 0

3 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

Kiera already has 12 plants in her backyard and she can also grow 1 plant with every seed packet she uses. How many seed packets

Elza [17]

Answer: 12

Step-by-step explanation: 24 - 12 times 1

7 0

3 years ago