Answer:
Area of the circle = ![95.33feet^2](https://tex.z-dn.net/?f=95.33feet%5E2)
Step-by-step explanation:
Circumference of the circle=34.6 feet
Circumference of a circle= ![2\pi r](https://tex.z-dn.net/?f=2%5Cpi%20r)
![34.6=2\pi r\\\\](https://tex.z-dn.net/?f=34.6%3D2%5Cpi%20r%5C%5C%5C%5C)
As, ![\pi =\frac{22}{7}=3.14](https://tex.z-dn.net/?f=%5Cpi%20%3D%5Cfrac%7B22%7D%7B7%7D%3D3.14)
![34.6=2*3.14*r\\\\34.6=6.28*r\\\\34.6/6.28=r\\\\r=5.51feet](https://tex.z-dn.net/?f=34.6%3D2%2A3.14%2Ar%5C%5C%5C%5C34.6%3D6.28%2Ar%5C%5C%5C%5C34.6%2F6.28%3Dr%5C%5C%5C%5Cr%3D5.51feet)
Area of the circle=![\pi r^2](https://tex.z-dn.net/?f=%5Cpi%20r%5E2)
![=3.14*5.51*5.51\\\\=3.14*30.36\\\\=95.33feet^2](https://tex.z-dn.net/?f=%3D3.14%2A5.51%2A5.51%5C%5C%5C%5C%3D3.14%2A30.36%5C%5C%5C%5C%3D95.33feet%5E2)
The area of the circle is ![95.33feet^2](https://tex.z-dn.net/?f=95.33feet%5E2)
Answer:
A and C
Step-by-step explanation:
A function has a unique y value for every unique x value
The vertical section disqualifies B
D has 2 y values for many x values.
Answer:
$7153.03
Step-by-step explanation:
To find the total amount after 3 years, we can use the formula for compound tax:
P = Po * (1+r/n)^(t*n)
where P is the final value, Po is the inicial value, r is the rate, t is the amount of time and n depends on how the tax is compounded (in this case, it is semi-annually, so n = 2)
For our problem, we have that Po = 5000, r = 12.3% = 0.123, t = 3 years and n = 2, then we can calculate P:
P = 5000 * (1 + 0.123/2)^(3*2)
P = 5000 * (1 + 0.0615)^6
P = $7153.029
Rounding to the nearest cent, we have P = $7153.03
Answer:
A) x=3 or x=6
Step-by-step explanation:
Factor out the GCF : 2(x^2-9x+18)
Then, set to zero.
2(x^2-9x+18)=0
2(x-3)(x-6)=0
x=3 or x=6
Ah...Trigonometry is fun!
The law of sines states:
![\frac{sinA}{a}= \frac{sinB}{b} = \frac{sinC}{c}](https://tex.z-dn.net/?f=%20%5Cfrac%7BsinA%7D%7Ba%7D%3D%20%5Cfrac%7BsinB%7D%7Bb%7D%20%3D%20%5Cfrac%7BsinC%7D%7Bc%7D%20)
The transitive property (switching the orders of the equations) applies here. Therfore, we can say that
![\frac{sinA}{a}=\frac{sinC}{c}](https://tex.z-dn.net/?f=%5Cfrac%7BsinA%7D%7Ba%7D%3D%5Cfrac%7BsinC%7D%7Bc%7D%20)
We then plug in our given values to find C
![\frac{sin24}{77}=\frac{sinC}{162}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin24%7D%7B77%7D%3D%5Cfrac%7BsinC%7D%7B162%7D%20)
![\frac{162*sin24}{77}=sinC](https://tex.z-dn.net/?f=%5Cfrac%7B162%2Asin24%7D%7B77%7D%3DsinC)
Solving, we get 0.8557316387.
We're not done yet!We are trying to find an angle measure, so we'll do the inverse of the ratio we used (sin).
arcsin0.8557316387 (arcsin is the same as inverse sin)
=
58.8 (approximate)
So the measure of angle C is 58.8. You could check this by reinserting it into the equation
![\frac{sinA}{a}= \frac{sinB}{b} = \frac{sinC}{c}](https://tex.z-dn.net/?f=%20%5Cfrac%7BsinA%7D%7Ba%7D%3D%20%5Cfrac%7BsinB%7D%7Bb%7D%20%3D%20%5Cfrac%7BsinC%7D%7Bc%7D%20)
.
:)