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3 years ago

An air plane moves at a constant speed of 120 miles per hour for 3 hours. How far does it go?

Mathematics

2 answers:

Anvisha [2.4K]3 years ago

7 0

Answer: 360

Step-by-step explanation: All you got to do is multiply 120 by 3

Licemer1 [7]3 years ago

3 0

Answer:

360 miles

Step-by-step explanation:

120 x 3 = 360

120 + 120+ 120 = 360

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Help quick please!!!! I'll mark your answer as the brainliest if it's correct!

muminat

Answer:

(8,2)

Step-by-step explanation:

The solution is where the two graphs intersect.

The two graphs intersect at x=8 and y=2

(8,2)

3 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

Worth 12 points and please actually help me

Dmitrij [34]

Answer:

B = (-5, 4)

B' = (-5+3, 4-2) = (-2, 2)

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3 years ago

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Santa's Wonderland is an extravagant holiday light display that is open from early November through January each year. The entry

Fofino [41]

Ok,
f(0.35)= 7f/20

f(-5.2)=-26f/5

f(10)= 10f

f(-0.5)= -f/2

as for the last question I am not quite sure, sorry....hope I helped a little :)

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3 years ago

HELP ASAP! PLS!! The Water Department checks the city water supply on a regular basis for

aleksandr82 [10.1K]

Answer:

B. 95% confident the average concentration of PCBs in the water supply is between 2.9 ppb and 3.5 ppb

Step-by-step explanation:

You are given the total number of samples, the concentration of lead, and the standard deviation. The standard deviation represents how inaccurate the estimation of the concentration of lead in the drinking water. This means that there can only possibly be a 0.3 ppb error in the estimation. 3.2-0.3=2.9, and 3.2+0.3=3.5

8 0

3 years ago

Read 2 more answers