Answer:
18 years
Step-by-step explanation:
The formula for computing accrued amount A for a principal of P at an interest rate of r(in decimal) compounded n times in a year for t years is given by
Note that r is percentage converted to decimal. So 3% = 3/100 = 0.03
We can rearrange the above equation to:
Taking logs on both sides
This gives
In this particular problem, n = 4, , A= 9600, P = 5600, r =0.03, so r/n = 0.03/4 = 0.0075
1 + r/n = 1+0.0075 = 1.0075
4t = log(9600/5600)/log(1.0075) = log(1.714) / log(1.0075) = 0.234 /0.00325 = 72
t = 72/4 = 18 years
Answer:
2n^2 - 11
steep by steep explanation
=(4n^2 + 3n -5) -(2n^2 + 3n +6)
= 4n^2 +3n -5 - 2n^2 - 3n -6
= 2n^ - 11
Answer:
2438.4
Step-by-step explanation:
multiply 96 by 25.4
The domain of f/g
consists of numbers x for which g(x) cannot equal 0 that are in the domains of
both f and g.
Let’s take this equation as an example:
If f(x) = 3x - 5 and g(x)
= square root of x-5, what is the domain of (f/g)x.
For x to be in the domain of (f/g)(x), it must be
in the domain of f and in the domain of g since (f/g)(x) = f(x)/g(x). We also
need to ensure that g(x) is not zero since f(x) is divided by g(x). Therefore,
there are 3 conditions.
x must be in the domain of f:
f(x) = 3x -5 are in the domain of x and all real numbers x.
x must be in the domain of g:
g(x) = √(x - 5) so x - 5 ≥ 0 so x ≥ 5.
g(x) can not be 0: g(x)
= √(x - 5) and √(x - 5) = 0 gives x = 5 so x ≠ 5.
Hence to x x ≥ 5 and x ≠ 5
so the domain of (f/g)(x) is all x satisfying x > 5.
Thus, satisfying <span>satisfy all
three conditions, x x ≥ 5 and x ≠ 5 so the domain of (f/g)(x) is all x
satisfying x > 5.</span>
Answer:
Her speed on the summit was 35 mph.
Step-by-step explanation:
Her speed on the summit was "x" mph while her speed while climbing was "x - 10" mph. The distance she rode uphill was 55 miles and on the summit it was 28 miles. The total time she explored the mountain was 3 hours. Therefore:
time uphill = distance uphill / speed uphill = 55 / (x - 10)
time summit = distance summit / speed summit = 28 / x
total time = time uphill + time summit
3 = [55 / (x - 10)] + 28 / x
3 = [55*x + 28*(x - 10)]/[x*(x - 10)]
3*x*(x - 10) = 55*x + 28*x - 280
3x² - 30*x = 83*x - 280
3x² - 113*x + 280 = 0
x1 = {-(-113) + sqrt[(-113)² - 4*(3)*(280)]}/(2*3) = 35 mph
x2 = {-(-113) - sqrt[(-113)² - 4*(3)*(280)]}/(2*3) = 2.67 mph
Since her speed on the uphill couldn't be negative the speed on the summit can only be 35 mph.
