Answer:
![-\frac{4}{5}](https://tex.z-dn.net/?f=-%5Cfrac%7B4%7D%7B5%7D)
Step-by-step explanation:
There is not much that can be done to figure out how to write 0.8 as a fraction, except to literally use what the decimal portion of your number, the .8, means.
Since there are 1 digits in 8, the very last digit is the "10th" decimal place.
So we can just say that .8 is the same as 8/10.
The fraction is not reduced to lowest terms. We can reduce this fraction to lowest terms by dividing both the numerator and denominator by 2.
Why divide by 2? 2 is the Greatest Common Divisor (GCD) or Greatest Common Factor (GCF) of the numbers 8 and 10.
So, this fraction reduced to lowest terms is 4/5
So your final answer is: 0.8 can be written as the fraction 8/10 simplified to 4/5
Given:
Height of the lighthouse = 280 feet
The angle of depression from the top of the lighthouse to a ship = 18°.
To find:
The distance between boat and shore.
Solution:
Draw a diagram by using the given information.
In a right angle triangle,
![\tan \theta=\dfrac{Perpendicular}{Base}](https://tex.z-dn.net/?f=%5Ctan%20%5Ctheta%3D%5Cdfrac%7BPerpendicular%7D%7BBase%7D)
In triangle ABC,
![\tan C=\dfrac{AB}{BC}](https://tex.z-dn.net/?f=%5Ctan%20C%3D%5Cdfrac%7BAB%7D%7BBC%7D)
![\tan 18^\circ=\dfrac{280}{BC}](https://tex.z-dn.net/?f=%5Ctan%2018%5E%5Ccirc%3D%5Cdfrac%7B280%7D%7BBC%7D)
![BC=\dfrac{280}{\tan 18^\circ}](https://tex.z-dn.net/?f=BC%3D%5Cdfrac%7B280%7D%7B%5Ctan%2018%5E%5Ccirc%7D)
Using a calculator, we get
![BC=\dfrac{280}{0.3249}](https://tex.z-dn.net/?f=BC%3D%5Cdfrac%7B280%7D%7B0.3249%7D)
![BC=861.80363...](https://tex.z-dn.net/?f=BC%3D861.80363...)
![BC\approx 862](https://tex.z-dn.net/?f=BC%5Capprox%20862)
Therefore, the boat is 862 feet away from shore.
The answer to this is 2. Ten only has two factors, 5 and 2, and 2 can be decided evenly amongst them all.
Answer:
![y=arc\csc x](https://tex.z-dn.net/?f=y%3Darc%5Ccsc%20x)
Step-by-step explanation:
The given function is
.
The domain refers to all values of x for which this function is defined.
Recall that: the domain of
is ![-1\le x\le1](https://tex.z-dn.net/?f=-1%5Cle%20x%5Cle1)
And we know
is the reciprocal of
.
Therefore the complement of the domain of
which is
is the domain of ![y=arc\csc x](https://tex.z-dn.net/?f=y%3Darc%5Ccsc%20x)
Your answer would be c. 18,6