Sin(2θ)+sin(<span>θ)=0
use double angle formula: sin(2</span>θ)=2sin(θ)cos(<span>θ).
=>
2sin(</span>θ)cos(θ)+sin(<span>θ)=0
factor out sin(</span><span>θ)
sin(</span>θ)(2cos(<span>θ)+1)=0
by the zero product property,
sin(</span>θ)=0 ...........(a) or
(2cos(<span>θ)+1)=0.....(b)
Solution to (a): </span>θ=k(π<span>)
solution to (b): </span>θ=(2k+1)(π)+/-(π<span>)/3
for k=integer
For [0,2</span>π<span>), this translates to:
{0, 2</span>π/3,π,4π/3}
L*W= 36
Rewrite to get:
l = 36 / w or w = 36 / l
Either one show =s the inverse relationship between w and l
Equation for x and y graph:
y = 36 / x
Answer:
5,500
Step-by-step explanation:
this is quite simple
multiply his earnings by a tenth
55,000 times 1/10
5,500
Answer:
Third option: ![t=3.5\ seconds](https://tex.z-dn.net/?f=t%3D3.5%5C%20seconds)
Step-by-step explanation:
Given the function:
![H(t)=-16t^2 +56t](https://tex.z-dn.net/?f=H%28t%29%3D-16t%5E2%20%2B56t)
Since the ball never leaves the ground, you need to substitute
in the function in order to determine the time the soccer ball traveled:
![0=-16t^2 +56t](https://tex.z-dn.net/?f=0%3D-16t%5E2%20%2B56t)
Factorizing, you get:
![0=-8t(2t-7)](https://tex.z-dn.net/?f=0%3D-8t%282t-7%29)
Then:
![0=-8t\\\\t=0\ seconds\\\\\\\\0=2t-7\\\\7=2t\\\\t=3.5\ seconds](https://tex.z-dn.net/?f=0%3D-8t%5C%5C%5C%5Ct%3D0%5C%20seconds%5C%5C%5C%5C%5C%5C%5C%5C0%3D2t-7%5C%5C%5C%5C7%3D2t%5C%5C%5C%5Ct%3D3.5%5C%20seconds)
Therefore the time the ball traveled was:
![t=3.5\ seconds](https://tex.z-dn.net/?f=t%3D3.5%5C%20seconds)