The equation of a circle is written as ( x-h)^2 + (y-k)^2 = r^2
h and k is the center point of the circle and r is the radius.
In the given equation (x+3)^2 + (y-1)^2 = 81
h = -3
k = 1
r^2 = 81
Take the square root of both sides:
r = 9
The center is (-3,1) and the radius is 9
A customer borrowed $2000 and then a further $1000 both repayble in 12 months. What would he have saved if he had taken out one loan for $3000 repayable in 12 months?
He took two different loans, it charged him loan processing fee twice, two-time documentation process, and of course, extra time spent for second loan. Instead, he could take single loan of $3000 with one-time processing fee, one-time documentation process, and time-saving also.
Answer:
0.1187
Step-by-step explanation:
A = P (1 + k)^t
where A is the final amount,
P is the initial amount,
k is the monthly growth rate,
and t is the number of months.
70 = 50 (1 + k)^3
1.4 = (1 + k)^3
∛1.4 = 1 + k
k = -1 + ∛1.4
k = 0.1187
Let's use the variables N and Q for the number of nickels and the number of quarters.
We know there are 49 total coins, so we can write the following equation:
N + Q = 49
We can solve this equation for one variable which will help in the next step. Let's solve for N:
N = 49 - Q
Next, we know that nickels are worth $0.05 and quarters are worth $0.25. We can use these values along with the total value of $8.85 to create another equation.
0.05N + 0.25Q = 8.85
Now we can use substitution to solve our system out equations. We solved the first equation for N, so we can plug 49 - Q in for N.
0.05(49-Q) + 0.25Q = 8.85
Distribute and combine like terms.
2.45 - 0.05Q + 0.25Q = 8.85
2.45 + 0.2Q = 8.85
0.2Q = 6.4
Q = 32
Plug 32 in for Q in N + Q = 49 to find the number of nickels.
N + 32 = 49
N = 17
Dustin has 32 quarters and 17 nickels.