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3 years ago

4×8 is it positive or negative

Mathematics

2 answers:

Nitella [24]3 years ago

7 0

Answer:

4 × 8 = 32 so it is positive

Step-by-step explanation:

andrey2020 [161]3 years ago

5 0

Answer:

Hi, 4x8 is positive.

Step-by-step explanation:

4x8=?

4+4+4+4+4+4+4+4=?

4x8=32

Since both numbers are positive, the answer will also be positive.

Hope this helps!!

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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

3 years ago

How do simplify 4(x-3)+5(x-3)

vesna_86 [32]

Answer:

9x-27

Step-by-step explanation:

4(x-3)+5(x-3)=4x-12+5x-15=4x+5x-12-15=9x-27

4 0

3 years ago

James rode k kilometers on his bike this week. Express the number of kilometers that Ivan rode on his bike in terms of k if he r

Amiraneli [1.4K]

Answer:

13 km/hr

Step-by-step explanation:

Speed = (distance covered) / (time to cover the distance)

( 8.45 km) / (0.65 hr)

(8.45 / 0.65) km/hr

4 0

2 years ago

Select all the sets of numbers that are possible values for x in the inequality, x>- 2.

lana66690 [7]

Answer:

{-1, 0,5}

Step-by-step explanation:

3 0

2 years ago

3 3/5 x 1 2/3 x 4 2/3

lukranit [14]

The answer would be 32/5 or 6 2/5 or 6.4

Hope this helps

Have a great day/night

3 0

3 years ago

4×8 is it positive or negative​

4×8 is it positive or negative