Answer:
![13.5\sqrt{3}\:\text{ft}^{2}](https://tex.z-dn.net/?f=13.5%5Csqrt%7B3%7D%5C%3A%5Ctext%7Bft%7D%5E%7B2%7D)
Step-by-step explanation:
Given: The side of a regular hexagon is 3 feet.
To find: Area of the hexagon
Solution:
It is given that the side of a regular hexagon is 3 feet.
We know that the area of a regular hexagon whose side is a units is
Here, the side is 3 feet
So, area of the regular hexagon
![=\frac{3\sqrt{3} }{2} \times3^{2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B3%5Csqrt%7B3%7D%20%7D%7B2%7D%20%5Ctimes3%5E%7B2%7D)
![=\frac{3\sqrt{3} }{2} \times9](https://tex.z-dn.net/?f=%3D%5Cfrac%7B3%5Csqrt%7B3%7D%20%7D%7B2%7D%20%5Ctimes9)
![=\frac{27\sqrt{3} }{2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B27%5Csqrt%7B3%7D%20%7D%7B2%7D)
![=13.5\sqrt{3}\:\text{ft}^{2}](https://tex.z-dn.net/?f=%3D13.5%5Csqrt%7B3%7D%5C%3A%5Ctext%7Bft%7D%5E%7B2%7D)
Hence, area of the regular hexagon is ![13.5\sqrt{3}\:\text{ft}^{2}](https://tex.z-dn.net/?f=13.5%5Csqrt%7B3%7D%5C%3A%5Ctext%7Bft%7D%5E%7B2%7D)
1). Her walking pace is (1.75 miles) / (50 minutes).
If you want it in units of (miles per hour), do it like this:
(1.75 miles / 50 minutes) x (60 minutes / 1 hour)
= ( 1.75 x 60 / 50 ) miles per hour.
2). The average change was
(30 - 45) degrees / (5 minutes) .
I'm sure you can do the division and make an integer out of that.
3). Each bracelet cost $3.10.
Caroline bought five of them, so she spent $3.10 five times.
Either do the multiplication, or else write down $3.10 five times
and do the addition.
4). In order to factor the expression, the two terms would need
to have some common factor ... both terms need either a power
of 'x', or they need two numbers that have a common factor.
They don't both have an 'x', and 13 and 10 have no common factor.
5). Todd earned 'T' dollars.
Twice what Todd earned is 2T .
$350 more than that is 2T+350 .
The question says that 2,500 is exactly that amount,
so you can write
2T + 350 = 2,500
Subtract 350 from each side: 2T = 2,150
Divide each side by 2: (you can finish it now)
Answer:
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the correct option is answer choice D, because there are multiple 2's in the x column with different f(x) values.
Integrate the force field along the given path (call it <em>C</em>):
![W=\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=\int_0^{2\pi}\mathbf F(x(t),y(t))\cdot\frac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt](https://tex.z-dn.net/?f=W%3D%5Cdisplaystyle%5Cint_C%5Cmathbf%20F%28x%2Cy%29%5Ccdot%5Cmathrm%20d%5Cmathbf%20r%3D%5Cint_0%5E%7B2%5Cpi%7D%5Cmathbf%20F%28x%28t%29%2Cy%28t%29%29%5Ccdot%5Cfrac%7B%5Cmathrm%20d%5Cmathbf%20r%7D%7B%5Cmathrm%20dt%7D%5C%2C%5Cmathrm%20dt)
![=\displaystyle\int_0^{2\pi}\bigg((t-\sin t)\,\mathbf i+(6-\cos t)\,\mathbf j\bigg)\cdot\bigg((1-\cos t)\,\mathbf i+\sin t\,\mathbf j\bigg)\,\mathrm dt](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle%5Cint_0%5E%7B2%5Cpi%7D%5Cbigg%28%28t-%5Csin%20t%29%5C%2C%5Cmathbf%20i%2B%286-%5Ccos%20t%29%5C%2C%5Cmathbf%20j%5Cbigg%29%5Ccdot%5Cbigg%28%281-%5Ccos%20t%29%5C%2C%5Cmathbf%20i%2B%5Csin%20t%5C%2C%5Cmathbf%20j%5Cbigg%29%5C%2C%5Cmathrm%20dt)
![=\displaystyle\int_0^{2\pi}(t-t\cos t+5\sin t)\,\mathrm dt=\boxed{2\pi^2}](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle%5Cint_0%5E%7B2%5Cpi%7D%28t-t%5Ccos%20t%2B5%5Csin%20t%29%5C%2C%5Cmathrm%20dt%3D%5Cboxed%7B2%5Cpi%5E2%7D)