Answer:
0.1 rad/s
Step-by-step explanation:
Since the distance from or to the flagpole is not given, I will assume. And my assumption is 50 ft
Now, the elevation angle A = 45 degrees, converting to radians, we have π/4 radians
Remember that the tan of an angle is OPP/HYP, and so
tan A = h/25, on differentiating, we have
d tan A/dA = sec^2 A = (1/25) dh/dA
Next, we have
25 sec^2 A * dA/dt= dh/dt = 5
Making dA/dt the subject of formula, we have
dA/dt = (1/5) cos^2 A
but cos^2 A from trigonometry = 1/2, this means that
dA/dt = .1 radians/second
If you want to convert to degrees, your have
.1 Rad/s( 180 deg/rad) = 18 degrees/second
See attachment for math work and answer.
I've answered your other question as well.
Step-by-step explanation:
Since the identity is true whether the angle x is measured in degrees, radians, gradians (indeed, anything else you care to concoct), I’ll omit the ‘degrees’ sign.
Using the binomial theorem, (a+b)3=a3+3a2b+3ab2+b3
⇒a3+b3=(a+b)3−3a2b−3ab2=(a+b)3−3(a+b)ab
Substituting a=sin2(x) and b=cos2(x), we have:
sin6(x)+cos6(x)=(sin2(x)+cos2(x))3−3(sin2(x)+cos2(x))sin2(x)cos2(x)
Using the trigonometric identity cos2(x)+sin2(x)=1, your expression simplifies to:
sin6(x)+cos6(x)=1−3sin2(x)cos2(x)
From the double angle formula for the sine function, sin(2x)=2sin(x)cos(x)⇒sin(x)cos(x)=0.5sin(2x)
Meaning the expression can be rewritten as:
sin6(x)+cos6(x)=1−0.75sin2(2x)=1−34sin2(2x)
Since 57x17=969 I did 969-942 and got 27 so there is 16 full rows and then 27 left over so that means it won’t be a full row but 27 extra seats will be filled. (If your wondering where the 17 came from that’s how many rows can be made that’s over 942 because if I did 57x16 it would equal 912 and I would not have had a full row of chairs)
