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2 years ago

Great freight a local shipping company charges .40 per pound for shipping if your shipping 20 pounds what would the cost be

Mathematics

1 answer:

masya89 [10]2 years ago

4 0

Answer:

$8.00

Step-by-step explanation:

For every pound shipped, $0.40 is charged. This can be represented by the mathematical equation: y=0.4x, where x is the pounds to ship and y is the total cost. If we plug in 20 as x to find what the total cost would be, we would have the equation, y=0.4*20, and y would equal 8, meaning that the total cost is $8.00.

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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

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

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

4 0

2 years ago

Haruka hiked several kilometers in the morning. She only hiked 6 kilometers in the afternoon, which was 25 percent less she had

Allisa [31]

6km is 3/4 of her morning speed so 6/(3/4)=6×4/3=8km. Total distance=6+8=14km.

5 0

2 years ago

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Please help me I'm on a time crunch

Neporo4naja [7]

You multiple it by 20....
1:20
2:40
3:60
4:80
5:100
So it’s 80 inches by 100 inches (80x100) =800 square feet

8 0

2 years ago

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For which value of b can the expression x2 + bx + 18 be factored?

WINSTONCH [101]

An expression is defined as a set of numbers, variables, and mathematical operations. The value of b for which the expression x² + bx + 18 can be factored is 9.

<h3>What is an Expression?</h3>

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The value of b for which the given expression x² + bx + 18 can be factored is 9. This will make the expression factored as (x+3) and (x+6).

Thus, the value of b for which the expression x² + bx + 18 can be factored is 9.

Learn more about Expression:

brainly.com/question/13947055

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6 0

1 year ago

Evaluate when n = 3.<br> (244 − n)×n<br> -3<br> 9<br> 55<br> 72

HACTEHA [7]

Answer:

$(244 - n)n \\ n = 3 \\ (244 - 3) \times 3 \\ = (241) \times 3 \\ = 723$

3 0

2 years ago