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3 years ago

Identify the pattern rule for this sequence: 20, 80, 40, 160, 80, 320…

Mathematics

2 answers:

Elena-2011 [213]3 years ago

8 0

Answer:

multiplies by 4 then divides by 2

Step-by-step explanation:

cupoosta [38]3 years ago

4 0

Answer:

See step by step.

Step-by-step explanation:

20 * 4 = 80

80 / 2 = 40

40 * 4 = 160

160 / 2 = 80

80 * 4 =320

if x is Nth number in the sequence:

if N is odd:

$x = 20 * 4^{(N-1)/2} / 2^{(N-1)/2}$

if N is even:

$x = 20 * 4^{(N)/2} / 2^{(N)/2-1}$

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Use the surface integral in Stokes' Theorem to calculate the circulation of the field Bold Upper F equals x squared Bold i plus

Alinara [238K]

Answer:

The circulation of the field f(x) over curve C is Zero

Step-by-step explanation:

The function $f(x)=(x^{2},4x,z^{2})$ and curve C is ellipse of equation

$16x^{2} + 4y^{2} = 3$

Theory: Stokes Theorem is given by:

$I= \int \int\limits {{Curl f\cdot \hat{N }} \, dx$

Where, Curl f(x) = $\left[\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\\frac{∂}{∂x} &\frac{∂}{∂y} &\frac{∂}{∂z} \\F1&F2&F3\end{array}\right]$

Also, f(x) = (F1,F2,F3)

$\hat{N} = grad(g(x))$

Using Stokes Theorem,

Surface is given by g(x) = $16x^{2} + 4y^{2} - 3$

Therefore, tex]\hat{N} = grad(g(x))[/tex]

$\hat{N} = grad(16x^{2} + 4y^{2} - 3)$

$\hat{N} = (32x,8y,0)$

Now, $f(x)=(x^{2},4x,z^{2})$

Curl f(x) = $\left[\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\\frac{∂}{∂x} &\frac{∂}{∂y} &\frac{∂}{∂z} \\F1&F2&F3\end{array}\right]$

Curl f(x) = $\left[\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\\frac{∂}{∂x} &\frac{∂}{∂y} &\frac{∂}{∂z} \\x^{2}&4x&z^{2}\end{array}\right]$

Curl f(x) = (0,0,4)

Putting all values in Stokes Theorem,

$I= \int \int\limits {Curl f\cdot \hat{N} } \, dx$

$I= \int \int\limits {(0,0,4)\cdot(32x,8y,0)} \, dx$

I=0

Thus, The circulation of the field f(x) over curve C is Zero

3 0

2 years ago

Michael's bank account opened with $100. 5 weeks after opening, his account balance was $250.

cupoosta [38]

I am pretty sure it is $400. sorry if i’m wrong

8 0

2 years ago

Find the minimum sample size needed to estimate the percentage of Democrats who have a sibling. Use a 0.1 margin of error, use a

Brums [2.3K]

Answer:

The minimum sample size is $n =135$

Step-by-step explanation:

From the question we are told that

The confidence interval is $( lower \ limit = \ 0.44,\ \ \ upper \ limit = \ 0.51)$

The margin of error is $E = 0.1$

Generally the sample proportion can be mathematically evaluated as

$\r p = \frac{ upper \ limit + lower \ limit }{2}$

$\r p = \frac{ 0.51 + 0.44}{2}$

$\r p = 0.475$

Given that the confidence level is 98% then the level of significance can be mathematically evaluated as

$\alpha = 100 - 98$

$\alpha = 2\%$

$\alpha =0.02$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table

The value is

$Z_{\frac{\alpha }{2} } = 2.33$

Generally the minimum sample size is evaluated as

$n =[ \frac { Z_{\frac{\alpha }{2} }}{E} ]^2 * \r p (1- \r p )$

$n =[ \frac { 2.33}{0.1} ]^2 * 0.475(1- 0.475 )$

$n =135$

6 0

3 years ago

1) B. Which method of finding the distance is<br><br> the best? Explain

sveticcg [70]

Answer and Step-by-step explanation:

Distance is the numerical measurement to find the space or interval between two objects. Distance also refers to physical length. Point x to point y distance is denoted as |xy|

There are many ways to find out the distance, distance between two objects or two points. The efficient way of finding the distance between two points is given below. Mathematically, the distance between two points on a coordinate plane can be determined by using the distance formula, which is:

d =√((x2-x1)2+(y2-y1)2),

Where (x1, y1) and (x2, y2) coordinates, and d is the distance.

The middle point between these two points is known as midpoint and can find out by using the formula

Midpoint = a + b /2.

The distance between two points number line can also be calculated by using the formula:

AB =|b –a| or |a-b|.

3 0

2 years ago

1.The sum of 4 and three times a number is 19

fredd [130]

1) 4 + 3(x) = 19

3x=15

x=5

2) 2x -7 = 9

2x=16

x=8

3) not sure

4) 5 (x + 4) = -15

5x+20=-15

5x=-35

x=-7

6 0

3 years ago