Which two consecutive integers does the square root of 200 fall between

Leona [35]

Got you
S' = 4,-3
Y'= 7,-2
U' = 8,--5
V' = 2,-6

3 0

3 years ago

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

3 years ago

The table of values represents a continuous function. Which type of function describes g(x)?

Troyanec [42]

Answer:

Logarithmic

Step-by-step explanation:

For this exmaple, x is the one increasing by a third power for every y

Logarithmic is the opposite of exponential

Exponential is when y is the one increasing by a power for every x.

Therefore this one is logarithmic.

6 0

2 years ago

Sharon’s turtle escaped from her backyard sometime in the last few hours. According to her calculations, the farthest the turtle

myrzilka [38]

The farthest distance of the turtle can be solved with the following equations:

x = 112 + 4
x = 112 - 4

By solving the equations, we conclude that t<span>he turtle can be found either in the 116th block or the 108th block.</span>

8 0

3 years ago

A recursive rule for an arithmetic sequence is a1=4;an=an−1−3 . What is the explicit rule for this sequence? Enter your answer i

Westkost [7]

Answer:

The explicit rule for the arithmetic sequence is given by:

$a_n = a_1+(n-1)d$ ......[1]

where,

$a_1$ is the first term

n is the number of terms and

d is the common difference for two consecutive terms.

As per the statement:

A recursive rule for an arithmetic sequence is:

$a_1 = 4$

$a_n = a_{n-1}-3$

The recursive formula for the arithmetic sequence is given by:

$a_n = a_{n-1}+d$

then;

On comparing we get;

d = -3

Substitute the given values in [1] we have;

$a_n = 4+(n-1)(-3)$

⇒ $a_n = 4 -3n+3 = 7-3n$

Therefore, the explicit rule for this sequence is, $a_n = 7 -3n$

5 0

3 years ago