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3 years ago

6

A student uses four different tape measures to estimate the length of a meter-stick manufactured to be exactly 1 meter. Which me

asurement is most accurate?
A. 99 cm
B. 105.98 cm
C. 90 cm
D. 104.5 cm

1 answer:

Shkiper50 [21]3 years ago

7 0

A. 99 cm because 1 meter =100 cm
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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

Use the net to find the approximate surface area of the cylinder to the nearest square meter.

ch4aika [34]

The awnser is 367.38 to the 3rd power only if its volume but if its surface area then it would be to the 3rd power. do u get it?

4 0

3 years ago

Instructions: Given the following constraints, find the maximum and minimum values for z.

loris [4]

Answer:

$x+3y\leq 0$

$x-y\geq 0$

$1) x+3y=0$

$x-y=0$

$-----$

$4y=0$

$y=0$

$x=0$

$(0,0)$

$2)(x+3y=0)3$

$3x-7y=16$

$3x+9y=0$

$3x-7y=16\\------\\16y=-16$

$y=-1$

$(3,-1)$

$3)(x-y=0)3$

$3x-7y=16$

$3x-3y=16$

$3x-3y=0$

$3x-7y=16\\------\\4y=-16$

$y=-4$

$x=4$

$(4,-4)$

$Z=-x+5y$

$(0,0):z=0$

$(3,-1):z=-8$

$(4,-4):z=-24$

$Maximum \:Value\: of\: z:0$

$Minimum\: Value\: of\: z:-24$

<u>OAmalOHopeO</u>

8 0

3 years ago

A resident of Bayport claims to the City Council that the proportion of Westside residents

Kazeer [188]

Answer:

The test statistics is $z = -1.56$

The p-value is $p-value = 0.05938$

Step-by-step explanation:

From the question we are told

The West side sample size is $n_1 = 578$

The number of residents on the West side with income below poverty level is $k = 76$

The East side sample size $n_2=688$

The number of residents on the East side with income below poverty level is $u = 112$

The null hypothesis is $H_o : p_1 = p_2$

The alternative hypothesis is $H_a : p_1 < p_2$

Generally the sample proportion of West side is

$\^{p} _1 = \frac{k}{n_1}$

=> $\^{p} _1 = \frac{76}{578}$

=> $\^{p} _1 = 0.1315$

Generally the sample proportion of West side is

$\^{p} _2 = \frac{u}{n_2}$

=> $\^{p} _2 = \frac{112}{688}$

=> $\^{p} _2 = 0.1628$

Generally the pooled sample proportion is mathematically represented as

$p = \frac{k + u}{ n_1 + n_2 }$

=> $p = \frac{76 + 112}{ 578 + 688 }$

=> $p =0.1485$

Generally the test statistics is mathematically represented as

$z = \frac{\^ {p}_1 - \^{p}_2}{\sqrt{p(1- p) [\frac{1}{n_1 } + \frac{1}{n_2} ]} }$

=> $z = \frac{ 0.1315 - 0.1628 }{\sqrt{0.1485(1-0.1485) [\frac{1}{578} + \frac{1}{688} ]} }$

=> $z = -1.56$

Generally the p-value is mathematically represented as

$p-value = P(z < -1.56 )$

From z-table

$P(z < -1.56 ) = 0.05938$

So

$p-value = 0.05938$

3 0

4 years ago

How do you find 25% of 92

Lilit [14]

Answer:

23

Step-by-step explanation:

4 0

3 years ago