Alright, so you have the basic formula- good.
You have the A value (400), the interest rate r (7.5% -> .075 in decimal), and the final P value (8500). So, we only need to solve for t.
8500 = (400)(1+.075)^t
/400 /400
21.25 = 1.075^t
logarithms are the inverse of exponents, basically, if you have an example like
y = b^x, then a logarithm inverts it, logy(baseb)=x
Makes sense if you consider a power of ten.
1000 = 10^3
if you put logbase10(1000), you'll get 3.
Anyways, though, to solve the problem make a log with a base of 1.075 in your calculator
log21.25(base 1.075) = t
also, because of rules of change of base (might want to look this up to clarify), you can write this as log(21.25)/log(1.075) = t
Thus, t is 42.26118551.
Rounded to hundredths, t=42.26
Answer:
m∠R = 123°
m∠S = 91°
Step-by-step explanation:
The measure of an inscribed angle is 1/2 the measure of the intercepted arc
m of arc QRS = 2 m∠P = 2(57) = 114
Now m of arc SPQ = 360 - 114 = 246
So, m∠R = 1/2(246) = 123
m of arc RSP = 2 m∠Q = 2(89) = 178
m of arc PQR = 360 - 178 = 182
m∠S = 1/2(182) = 91
The ratio of circumference to diameter is independent of the radius.
Defining C=circumference, r=radius, D=diameter = 2r
Circumference = C = 2 π r = π D
=>
ratio of circumference / diameter
= C/D = π
