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2 years ago

Please help meee! thanks

Mathematics

2 answers:

Sergio039 [100]2 years ago

5 0

Answer:

Step-by-step explanation:

Mark me brainlest plzz

Vladimir [108]2 years ago

4 0

Answer:

C. -2 and -1

Step-by-step explanation:

-1.5 is bigger than -2 but smaller than -1.

Thus, it is between these two number

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a coin weighs 3/4, debra picked up 6 of these coins, what is the total weight of coins she picked up?

Keith_Richards [23]

Answer:

4.5

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2 years ago

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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

2 years ago

Question 1

Tanzania [10]

Answer:

Mortality rate is 0.5 per 1000 habitant

the number of deaths have increased (from 210 to 250)

Step-by-step explanation:

Hello

Mortality rate is the number of deaths in a specific population,usually expressed in units of deaths per 1,000 individuals per year

$Mortality\ rate\ (S)= \frac{(D)}{(P)} *10^{n} \\\\\\\\$

where

S=Mortality rate

D=deaths

P= population

n= is a conversion form ,such as multiplying by 10^{3}=1000, to get mortality rate per 1,000 individuals( we will use n=3)

step 1

asign

S=unknown

D=250

P=500000

n=3, (for each 1000 people)

step 2

Replace

$S=\frac{250}{500000}*1000\\S=\ 0.5\ per\ 1000$

Mortality rate is 0.5 per 1000 habitant

step 3

what if S=0.42

S=0.42(assuming it is 0.42 per 1000,n=3)

D=unknown

P=500000

$(S)= \frac{(D)}{(P)} *10^{n}\\\\isolatin D\\\\S*P=D*10^{n}\\ D=\frac{S*P}{10^{n} } \\\\and\ replacing\\\\D=\frac{(0.42)*(500000)}{10^{3} }\\\\ Deaths=210\\$

the number of deaths have increased (from 210 to 250)

Have a great day

5 0

3 years ago

Need answer for this please.

balu736 [363]

Answer:

y= - 5x+40

Step-by-step explanation:

I graphed this out. Remember that in parallel lines, the slopes are always the same.

4 0

2 years ago

Please help meee! thanks​

Please help meee! thanks