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melisa1 [442]
3 years ago
7

Consider a cube that measures 1 inch on each side. We can think of a cubic foot as a dilation of the cubic inch by a factor of 1

2. What is the volume, in cubic inches, of a cubic foot? *
Mathematics
1 answer:
Irina-Kira [14]3 years ago
3 0

Answer:

ii

Step-by-step explanation:

Add the length, width, height, and then multiply by 2 so you have the cube, then multiply by 12 so you should have an equation of 2(3 X 12)

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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= \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
Each week, you drive 150 miles. Your car gets 25 miles to the gallon, and gas prices are $3 per gallon. How much gas money will
Marat540 [252]

           (150 miles/week) x (1 gallon / 25 miles) x (3 $/gallon)

       =    (150 x 1 x 3) / (25)   (miles-gallon-$ / week-miles-gallon)

       =                      18            $/week .
6 0
3 years ago
Read 2 more answers
What combination of variables could you analyze using correlation?
Anon25 [30]

Answer:

YOu have to add them i think

Step-by-step explanation:

First add the 3-4 and then finish it

3 0
3 years ago
Answer this and i’ll give you extra points
snow_tiger [21]

Answer:

Option (5)

Step-by-step explanation:

Graph of a function f(x) = x represents a straight straight line (y = x), passing through the origin (0, 0).

As shown in the graph,

Let the equation of the given line is,

y = mx + b

Here, m = slope of the line

b = y-intercept

Since, the given line passes through two points (0, -1) and (-1, 2)

Slope of the line 'm' = \frac{y_2-y_1}{x_2-x_1}=\frac{2+1}{-1-0}

                                              = -3

y-intercept 'b' = -1

Therefore, equation of the line will be,

y = -3x - 1

And the function is,

g(x) = -3x - 1

Here, (-3) represents the reflection of parent function over the x axis, vertical stretch of the parent function by 3 units.

Followed by the shifting of parent function by 1 unit down.

Therefore, Option (5) is the answer.

5 0
3 years ago
1/4 pizza for 5 dollars, how much can you purchase for 8 dollars
Vlada [557]
ONE 
to buy more than one you would need at least 10 dollars 
8 0
4 years ago
Read 2 more answers
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