Answer:
12 ft
Step-by-step explanation:
The base is a 2*6 because 45-45-90 is a special right triangle. So 12 feet.
The answer is A, because you take the square root of both sides and solve. <span />
Pi divided by five is roughly .63. I say "roughly" because pi is infinitely long so it's impossible to get an exact answer, but a common pi length would be
<span>3.14159. </span>
Answer:
A) ![x=-6](https://tex.z-dn.net/?f=x%3D-6)
Step-by-step explanation:
![2\log_5 (x+1)=2](https://tex.z-dn.net/?f=2%5Clog_5%20%28x%2B1%29%3D2)
We can use logarithm properties to write it as:
![\log_5 (x+1)^2=2](https://tex.z-dn.net/?f=%5Clog_5%20%28x%2B1%29%5E2%3D2)
On removing
it gives:
![(x+1)^2=5^2](https://tex.z-dn.net/?f=%28x%2B1%29%5E2%3D5%5E2)
Taking square root both sides.
![\sqrt{(x+1)^2}=\sqrt{5^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x%2B1%29%5E2%7D%3D%5Csqrt%7B5%5E2%7D)
![(x+1)=\pm 5](https://tex.z-dn.net/?f=%28x%2B1%29%3D%5Cpm%205)
Solving for
we get:
and ![x+1=-5](https://tex.z-dn.net/?f=x%2B1%3D-5)
Subtracting by 1 to both sides of both the above equations.
and ![x+1-1=-5-1](https://tex.z-dn.net/?f=x%2B1-1%3D-5-1)
and ![x=-6](https://tex.z-dn.net/?f=x%3D-6)
So we have got two solutions for the logarithmic equation.
Now we check the validity of the solutions by plugging values in the equation ![2\log_5 (x+1)=2](https://tex.z-dn.net/?f=2%5Clog_5%20%28x%2B1%29%3D2)
Plugging ![x=4](https://tex.z-dn.net/?f=x%3D4)
![2\log_5 (4+1)=2](https://tex.z-dn.net/?f=2%5Clog_5%20%284%2B1%29%3D2)
![2\log_5 5=2](https://tex.z-dn.net/?f=2%5Clog_5%205%3D2)
[As
]
![2=2](https://tex.z-dn.net/?f=%202%3D2)
So, thats a valid solution.
Plugging ![x=-6](https://tex.z-dn.net/?f=x%3D-6)
![2\log_5 (-6+1)=2](https://tex.z-dn.net/?f=2%5Clog_5%20%28-6%2B1%29%3D2)
![2\log_5 (-5)=2](https://tex.z-dn.net/?f=2%5Clog_5%20%28-5%29%3D2)
As
is undefined, so
is not a valid solution which means its extraneous.
SOH CAH TOA.
Sin = Opposite / Hypotenuse
Cos = Adjacent / Hypotenuse
Tan = Opposite / Adjacent