Step-by-step explanation:
the length <em>s</em><em> </em>of the arc AC is given as :
s = r. 0
where
r = 10 is radius
0 = 90°
= π/2 rad is angle
s = 10. π/2
= 5π
= 5.3.14
= 15.7 ~ 16
Solution :
We know, cot 2θ = 1/tan 2θ
Multiplying tan 2θ both side of the given equation.
tan²2θ - 3tan 2θ - 10 = 0
tan²2θ - 5tan 2θ + 2tan 2θ - 10 = 0
tan 2θ ( tan 2θ - 5 ) + 2 ( tan 2θ - 5 ) = 0
tan 2θ = -2 or tan 2θ = 5
Therefore,
or ![\theta = \dfrac{tan^{-1} (5)}{2}](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20%5Cdfrac%7Btan%5E%7B-1%7D%20%20%285%29%7D%7B2%7D)
Hence, this is the required solution.
Answer:
Third option is correct.
Step-by-step explanation:
The given model is
![h(t)=-16t^2-30t+124](https://tex.z-dn.net/?f=h%28t%29%3D-16t%5E2-30t%2B124)
Where, h(t) is heigth of rock after time t (in seconds).
The initial height of rock is 124 ft.
The leading coefficient is negative. It means it is a downward parabola.
First we have to the x-intercepts of the function.
![0=-16t^2-30t+124](https://tex.z-dn.net/?f=0%3D-16t%5E2-30t%2B124)
Using quadratic formula, we get
![t=\frac{-(-30)\pm \sqrt{(-30)^2-4(124)(-16)}}{2(-16)}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B-%28-30%29%5Cpm%20%5Csqrt%7B%28-30%29%5E2-4%28124%29%28-16%29%7D%7D%7B2%28-16%29%7D)
and ![t=2](https://tex.z-dn.net/?f=t%3D2)
It means rock remains in the air between
.
The value of t can not be negative, therefore rock remains in the air between
.
Third option is correct.
Answer:
60°
Step-by-step explanation:
angle A +angle B +angle C = 180
30° +B+90°= 180
120°+B=180°
B=180°-120°
B=60°