<span> For this case the volume of the box is given by:
</span>
![V = lwh ](https://tex.z-dn.net/?f=V%20%3D%20lwh%0A)
<span> Substituting values we have:
</span>
![V = (2a + 11) (5a - 12) (a + 6) ](https://tex.z-dn.net/?f=V%20%3D%20%282a%20%2B%2011%29%20%285a%20-%2012%29%20%28a%20%2B%206%29%0A)
<span> Rewriting we have:
</span>
![V = (10a ^ 2-24a + 55a-132) (a + 6) V = 10a ^ 3-24a ^ 2 + 55a ^ 2-132a + 60a ^ 2-144a + 330a-792](https://tex.z-dn.net/?f=V%20%3D%20%2810a%20%5E%202-24a%20%2B%2055a-132%29%20%28a%20%2B%206%29%0A%0AV%20%3D%2010a%20%5E%203-24a%20%5E%202%20%2B%2055a%20%5E%202-132a%20%2B%2060a%20%5E%202-144a%20%2B%20330a-792)
<span> Grouping terms of equal degree we have:
</span>
![V = 10a ^ 3 + 60a ^ 2 -24a ^ 2 + 55a ^ 2 -132a -144a + 330a-792](https://tex.z-dn.net/?f=V%20%3D%2010a%20%5E%203%20%2B%2060a%20%5E%202%20-24a%20%5E%202%20%2B%2055a%20%5E%202%20-132a%20-144a%20%2B%20330a-792%20%20)
<span> Adding terms of equal degree we have:
</span>
![V = 10 ^ 3 + 91a ^ 2 + 54a-792 ](https://tex.z-dn.net/?f=V%20%3D%2010%20%5E%203%20%2B%2091a%20%5E%202%20%2B%2054a-792%0A)
<span>
Answer: the volume of the box is: All the expressions given.</span>
A. Energy is transmitted by all waves.
I'm trying to make an electromagnet that's strength is constantly getting incremented by small amounts every second. I need to know, which would have a greater effect on the electromagnet's strength, amps or volts? (I know increasing the turns and/or density of the magnet wire will increase the strength, but I am looking for answers other than that particular one.)
If we have the angle and magnitude of a vector A we can find its Cartesian components using the following formula
![A_x = |A|cos(\alpha)\\\\A_y = |A|sin(\alpha)](https://tex.z-dn.net/?f=A_x%20%3D%20%7CA%7Ccos%28%5Calpha%29%5C%5C%5C%5CA_y%20%3D%20%7CA%7Csin%28%5Calpha%29)
Where | A | is the magnitude of the vector and
is the angle that it forms with the x axis in the opposite direction to the hands of the clock.
In this problem we know the value of Ax and Ay and we need the angle
.
Vector A is in the 4th quadrant
So:
![A_x = 6\\\\A_y = -6.5](https://tex.z-dn.net/?f=A_x%20%3D%206%5C%5C%5C%5CA_y%20%3D%20-6.5)
So:
![|A| = \sqrt{6^2 + (-6.5)^2}\\\\|A| = 8.846](https://tex.z-dn.net/?f=%7CA%7C%20%3D%20%5Csqrt%7B6%5E2%20%2B%20%28-6.5%29%5E2%7D%5C%5C%5C%5C%7CA%7C%20%3D%208.846)
So:
![Ay = -6.5 = 8.846cos(\alpha)\\\\sin(\alpha) = \frac{-6.5}{8.846}\\\\sin(\alpha) = -0.7348\\\\\alpha = sin^{- 1}(- 0.7348)](https://tex.z-dn.net/?f=Ay%20%3D%20-6.5%20%3D%208.846cos%28%5Calpha%29%5C%5C%5C%5Csin%28%5Calpha%29%20%3D%20%5Cfrac%7B-6.5%7D%7B8.846%7D%5C%5C%5C%5Csin%28%5Calpha%29%20%3D%20-0.7348%5C%5C%5C%5C%5Calpha%20%3D%20sin%5E%7B-%201%7D%28-%200.7348%29)
= -47.28 ° +360° = 313 °
= 313 °
Option 4.
The process of changing from one phase of matter to another is a physical matter.