Answer:![12.74 ft^2/s](https://tex.z-dn.net/?f=12.74%20ft%5E2%2Fs)
Step-by-step explanation:
Given
Two sides of triangle of sides 5 ft and 7 ft
and angle between them is increasing at a rate of 0.9 radians per second
let
is the angle between them thus
Area of triangle when two sides and angle between them is given
![A=\frac{ab\sin C}{2}](https://tex.z-dn.net/?f=A%3D%5Cfrac%7Bab%5Csin%20C%7D%7B2%7D)
![A=\frac{5\times 7\times \sin \theta }{2}](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B5%5Ctimes%207%5Ctimes%20%5Csin%20%5Ctheta%20%7D%7B2%7D)
Differentiate w.r.t time
![\frac{\mathrm{d} A}{\mathrm{d} t}=\frac{35\cos theta }{2}\times \frac{\mathrm{d} \theta }{\mathrm{d} t}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20A%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D%5Cfrac%7B35%5Ccos%20theta%20%7D%7B2%7D%5Ctimes%20%5Cfrac%7B%5Cmathrm%7Bd%7D%20%5Ctheta%20%7D%7B%5Cmathrm%7Bd%7D%20t%7D)
at ![\theta =\frac{\pi }{5}](https://tex.z-dn.net/?f=%5Ctheta%20%3D%5Cfrac%7B%5Cpi%20%7D%7B5%7D)
![\frac{\mathrm{d} A}{\mathrm{d} t}=\frac{35\times cos(\frac{\pi }{5})}{2}\times 0.9](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20A%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D%5Cfrac%7B35%5Ctimes%20cos%28%5Cfrac%7B%5Cpi%20%7D%7B5%7D%29%7D%7B2%7D%5Ctimes%200.9)
![\frac{\mathrm{d} A}{\mathrm{d} t}=12.74 ft^2/s](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20A%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D12.74%20ft%5E2%2Fs)
<h3>
Answer: B) real number</h3>
Explanation:
Something like 3.5 = 7/2 is a rational number because its a fraction of two integers.
While on the other hand, the constant pi = 3.14159... is irrational because we cannot write pi as a fraction of two integers. We can get approximations like 22/7, but not a perfect exact match.
Both types of numbers, rational and irrational, are under the umbrella of the real number system. Any real number is a string of decimal digits. Sometimes it might be a whole number, but fractional values can be included as well. The decimal number may terminate, or it may repeat, or it may go on forever without a pattern.
In short, any number you can think of is a real number assuming your teacher hasn't covered complex numbers (or imaginary numbers) just yet.
18.03 inches
Put the dimensions into the pythagorean theorem, that will give you the answer.
Answer:
it has infinite solutions because the lines wont end.
Step-by-step explanation:
Answer:
2/3
Step-by-step explanation:
rise over run is 2 over 3, and it is positive because the y increases as the x increases!