Pounds is the correct unit of measure
Answer:0
Step-by-step explanation:
its right
The equation of the line through (0, 1) and (<em>c</em>, 0) is
<em>y</em> - 0 = (0 - 1)/(<em>c</em> - 0) (<em>x</em> - <em>c</em>) ==> <em>y</em> = 1 - <em>x</em>/<em>c</em>
Let <em>L</em> denote the given lamina,
<em>L</em> = {(<em>x</em>, <em>y</em>) : 0 ≤ <em>x</em> ≤ <em>c</em> and 0 ≤ <em>y</em> ≤ 1 - <em>x</em>/<em>c</em>}
Then the center of mass of <em>L</em> is the point
with coordinates given by
![\bar x = \dfrac{M_x}m \text{ and } \bar y = \dfrac{M_y}m](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cdfrac%7BM_x%7Dm%20%5Ctext%7B%20and%20%7D%20%5Cbar%20y%20%3D%20%5Cdfrac%7BM_y%7Dm)
where
is the first moment of <em>L</em> about the <em>x</em>-axis,
is the first moment about the <em>y</em>-axis, and <em>m</em> is the mass of <em>L</em>. We only care about the <em>y</em>-coordinate, of course.
Let <em>ρ</em> be the mass density of <em>L</em>. Then <em>L</em> has a mass of
![\displaystyle m = \iint_L \rho \,\mathrm dA = \rho\int_0^c\int_0^{1-\frac xc}\mathrm dy\,\mathrm dx = \frac{\rho c}2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%20%3D%20%5Ciint_L%20%5Crho%20%5C%2C%5Cmathrm%20dA%20%3D%20%5Crho%5Cint_0%5Ec%5Cint_0%5E%7B1-%5Cfrac%20xc%7D%5Cmathrm%20dy%5C%2C%5Cmathrm%20dx%20%3D%20%5Cfrac%7B%5Crho%20c%7D2)
Now we compute the first moment about the <em>y</em>-axis:
![\displaystyle M_y = \iint_L x\rho\,\mathrm dA = \rho \int_0^c\int_0^{1-\frac xc}x\,\mathrm dy\,\mathrm dx = \frac{\rho c^2}6](https://tex.z-dn.net/?f=%5Cdisplaystyle%20M_y%20%3D%20%5Ciint_L%20x%5Crho%5C%2C%5Cmathrm%20dA%20%3D%20%5Crho%20%5Cint_0%5Ec%5Cint_0%5E%7B1-%5Cfrac%20xc%7Dx%5C%2C%5Cmathrm%20dy%5C%2C%5Cmathrm%20dx%20%3D%20%5Cfrac%7B%5Crho%20c%5E2%7D6)
Then
![\bar y = \dfrac{M_y}m = \dfrac{\dfrac{\rho c^2}6}{\dfrac{\rho c}2} = \dfrac c3](https://tex.z-dn.net/?f=%5Cbar%20y%20%3D%20%5Cdfrac%7BM_y%7Dm%20%3D%20%5Cdfrac%7B%5Cdfrac%7B%5Crho%20c%5E2%7D6%7D%7B%5Cdfrac%7B%5Crho%20c%7D2%7D%20%3D%20%5Cdfrac%20c3)
but this clearly isn't independent of <em>c</em> ...
Maybe the <em>x</em>-coordinate was intended? Because we would have had
![\displaystyle M_x = \iint_L y\rho\,\mathrm dA = \rho \int_0^c\int_0^{1-\frac xc}y\,\mathrm dy\,\mathrm dx = \frac{\rho c}6](https://tex.z-dn.net/?f=%5Cdisplaystyle%20M_x%20%3D%20%5Ciint_L%20y%5Crho%5C%2C%5Cmathrm%20dA%20%3D%20%5Crho%20%5Cint_0%5Ec%5Cint_0%5E%7B1-%5Cfrac%20xc%7Dy%5C%2C%5Cmathrm%20dy%5C%2C%5Cmathrm%20dx%20%3D%20%5Cfrac%7B%5Crho%20c%7D6)
and we get
![\bar x = \dfrac{M_x}m = \dfrac{\dfrac{\rho c}6}{\dfrac{\rho c}2} = \dfrac13](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cdfrac%7BM_x%7Dm%20%3D%20%5Cdfrac%7B%5Cdfrac%7B%5Crho%20c%7D6%7D%7B%5Cdfrac%7B%5Crho%20c%7D2%7D%20%3D%20%5Cdfrac13)
Answer: There are 418 sheets needed to cut all the required apples and leaves.
Explanation:
Since we have given that
Number of apples = 1045
Number of leaves = 1463
From a sheet of paper,
Number of apples can be cut = 5
Number of leaves can be cut = 7
Let the number of sheets of paper be x
So,
Number of sheets of paper required to cut 1045 apples is given by
![\frac{1045}{5}=209](https://tex.z-dn.net/?f=%5Cfrac%7B1045%7D%7B5%7D%3D209)
Similarly,
Number of sheets of paper required to cut 1463 leaves is given by
![\frac{1463}{7}=209](https://tex.z-dn.net/?f=%5Cfrac%7B1463%7D%7B7%7D%3D209)
So, total number of sheets is required to cut 1045 apples and 1463 leaves is given by
![209+209=418](https://tex.z-dn.net/?f=209%2B209%3D418)
Hence, there are 418 sheets needed to cut all the required apples and leaves.
The temperature which has best degree of precision would
actually be the temperature reading which has similar decimal place with the
error. So the best answer would have 1 decimal and from the choices above, this
would be:
D. 16.0°C