As AB is a diameter, then m∠CBA=180^{0}-75^{0}=105^{0}.
∠CBA is a central angle, so its measure multiplied by radius is the length of arc AC.
Note that
![105^{0}=7\cdot 15^0](https://tex.z-dn.net/?f=105%5E%7B0%7D%3D7%5Ccdot%2015%5E0)
and
![15^{0}= \frac{\pi}{12}](https://tex.z-dn.net/?f=15%5E%7B0%7D%3D%20%5Cfrac%7B%5Cpi%7D%7B12%7D%20)
. Then
![105^{0}= \frac{7\pi}{12} = \frac{7\cdot 3.14}{12}=1.83](https://tex.z-dn.net/?f=105%5E%7B0%7D%3D%20%5Cfrac%7B7%5Cpi%7D%7B12%7D%20%3D%20%5Cfrac%7B7%5Ccdot%203.14%7D%7B12%7D%3D1.83%20)
and length of the arc is
![12\cdot 1.83=21,96](https://tex.z-dn.net/?f=12%5Ccdot%201.83%3D21%2C96)
.The correct answer is 22 in.
Answer:
468
Step-by-step explanation:
26 x 6 x3
Answer:
262 and 263 are consecutive natural numbers whose sum is 525.
Step-by-step explanation:
Natural number are a subset of real numbers consisting in positive integers (i.e. 1, 2, 3, 525) and two natural numbers are consecutive when distance between each other is equal to 1. (
,
) We can interpret the statement mathematically by means of the following expression:
![x + y = 525](https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%20525)
![x = n](https://tex.z-dn.net/?f=x%20%3D%20n)
![y = n+1](https://tex.z-dn.net/?f=y%20%3D%20n%2B1)
Where
,
,
.
This system is reduced to a single equation and solved afterwards:
![n +(n+1) = 525](https://tex.z-dn.net/?f=n%20%2B%28n%2B1%29%20%3D%20525)
![2\cdot n + 1 = 525](https://tex.z-dn.net/?f=2%5Ccdot%20n%20%2B%201%20%3D%20525)
![2\cdot n = 524](https://tex.z-dn.net/?f=2%5Ccdot%20n%20%3D%20524)
![n = 262](https://tex.z-dn.net/?f=n%20%3D%20262)
Now we evaluate
and
to obtain the natural numbers:
![x = 262](https://tex.z-dn.net/?f=x%20%3D%20262)
![y = 263](https://tex.z-dn.net/?f=y%20%3D%20263)
262 and 263 are consecutive natural numbers whose sum is 525.
Answer:
B
Step-by-step explanation:
The amortization period in months is:
30 years * 12 = 360 months
The monthly interest rate would be 5.25%/12 = 0.004375
The payment for monthly mortgage formula would be:
![E=\frac{C*r}{1-(1+r)^{-n}}](https://tex.z-dn.net/?f=E%3D%5Cfrac%7BC%2Ar%7D%7B1-%281%2Br%29%5E%7B-n%7D%7D)
Where
E is the monthly mortgage payment
C is the cost of mortgage, cost is $150,000
r is the monthly rate of interest, which is 0.004375
n is the period, in months, which is 360
Substituting, we get our answer:
![E=\frac{C*r}{1-(1+r)^{-n}}\\E=\frac{150,000*0.004375}{1-(1+0.004375)^{-360}}\\E=\frac{656.25}{1-(1.004375)^{-360}}\\E=\frac{656.25}{0.7923}\\E=828.31](https://tex.z-dn.net/?f=E%3D%5Cfrac%7BC%2Ar%7D%7B1-%281%2Br%29%5E%7B-n%7D%7D%5C%5CE%3D%5Cfrac%7B150%2C000%2A0.004375%7D%7B1-%281%2B0.004375%29%5E%7B-360%7D%7D%5C%5CE%3D%5Cfrac%7B656.25%7D%7B1-%281.004375%29%5E%7B-360%7D%7D%5C%5CE%3D%5Cfrac%7B656.25%7D%7B0.7923%7D%5C%5CE%3D828.31)
So, the correct answer is B