Answer:
60
Explanation:
The volume of the water carried will be proportional to the cross-sectional area. The cross-section is a trapezoid with height 10sint, where t represents theta. The top of the trapezoid is 10+(2)(10cost), i.e. 10 + 20cost. The base of the trapezoid is 10.
Area of trapezoid = (average of bases) times (height)
= ([10 + (10 +20cost)] / 2 ) 10 sint
= (10 + 10cost)(10sint)
= 100sint + 100sintcost, call this A(t). You need to maximize. So differentiate and set equal to zero.
dA/dt = -100sin(t)^2+100cos(t)+100cos(t)^2 = 0, divide by 100:
-sin(t)^2 + cos(t) + cos(t)^2 = 0, replace sin^2 by 1-cos^2
2cos(t)^2 + cos(t) - 1 = 0, factor
(1+cos(t))(2cos(t)-1)=0, so
cos(t)=1, t=0 that give a min (zero area) not a max, or
cos(t) = 1/2, so t=60 degrees. This gives the max.
Answer:
Thus, including a control condition allows researchers to compare the way things are in the presence of an independent variable with the way things would have been in the absence of an independent variable.
Explanation:
Thus, including a control condition allows researchers to compare the way things are in the presence of an independent variable with the way things would have been in the absence of an independent variable.
Principles of relative dating
Uniformitarianism. ...
Intrusive relationships. ...
Cross-cutting relationships. ...
Inclusions and components. ...
Original horizontality. ...
Superposition. ...
Faunal succession. ...
Lateral continuity.
https://en.wikipedia.org/wiki/Relative_dating
decreases.
remains the same.
becomes irregular.