Answer:
The answer is B: 226 ft
Step-by-step explanation:
Just did the assignment on edg
Answer:
x=3
Step-by-step explanation:
The equation is x² + 5x = 24, so 3² +15 would be the perfect match. This is because 9+15=24.
You want to end up with
. Expand this using the angle sum identity for sine:
![A\sin(\omega t+\phi)=A\sin(\omega t)\cos\phi+A\cos(\omega t)\sin\phi](https://tex.z-dn.net/?f=A%5Csin%28%5Comega%20t%2B%5Cphi%29%3DA%5Csin%28%5Comega%20t%29%5Ccos%5Cphi%2BA%5Ccos%28%5Comega%20t%29%5Csin%5Cphi)
We want this to line up with
. Right away, we know
.
We also need to have
![\begin{cases}A\cos\phi=2\\A\sin\phi=5\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7DA%5Ccos%5Cphi%3D2%5C%5CA%5Csin%5Cphi%3D5%5Cend%7Bcases%7D)
Recall that
for all
; this means
![(A\cos\phi)^2+(A\sin\phi)^2=2^2+5^2\implies A^2=29\implies A=\sqrt{29}](https://tex.z-dn.net/?f=%28A%5Ccos%5Cphi%29%5E2%2B%28A%5Csin%5Cphi%29%5E2%3D2%5E2%2B5%5E2%5Cimplies%20A%5E2%3D29%5Cimplies%20A%3D%5Csqrt%7B29%7D)
Then
![\begin{cases}\cos\phi=\frac2{\sqrt{29}}\\\sin\phi=\frac5{\sqrt{29}}\end{cases}\implies\tan\phi=\dfrac{\sin\phi}{\cos\phi}=\dfrac52\implies\phi=\tan^{-1}\left(\dfrac52\right)](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D%5Ccos%5Cphi%3D%5Cfrac2%7B%5Csqrt%7B29%7D%7D%5C%5C%5Csin%5Cphi%3D%5Cfrac5%7B%5Csqrt%7B29%7D%7D%5Cend%7Bcases%7D%5Cimplies%5Ctan%5Cphi%3D%5Cdfrac%7B%5Csin%5Cphi%7D%7B%5Ccos%5Cphi%7D%3D%5Cdfrac52%5Cimplies%5Cphi%3D%5Ctan%5E%7B-1%7D%5Cleft%28%5Cdfrac52%5Cright%29)
So we end up with
![2\sin(4\pi t)+5\cos(4\pi t)=\sqrt{29}\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)](https://tex.z-dn.net/?f=2%5Csin%284%5Cpi%20t%29%2B5%5Ccos%284%5Cpi%20t%29%3D%5Csqrt%7B29%7D%5Csin%5Cleft%284%5Cpi%20t%2B%5Ctan%5E%7B-1%7D%5Cleft%28%5Cdfrac52%5Cright%29%5Cright%29)
Answer:
Basic wage rate = $9.375 per hour
Step-by-step explanation:
Given :
Fortnight wage = $750
Basic week, hours worked per week = 40 hours
Weekly basic wage rate :
Fortnight = 2 weeks
Hence, weekly wage = fortnight wage / 2 = 750 /2 = $375
Weekly basic wage rate = $375 / Number of hours worked per week = $375 / 40 = $9.375 per hour
Answer:
1) 18m²
2) 25cm²
Step-by-step explanation:
1)
- a = ½ × b × h
- a = ½ × 9 × 4
- a = ½ × 36
- a = 18m²
2)
- a = ½ × b × h
- a = ½ × 10 × 5
- a = 5 × 5
- a = 25 cm²