Step-by-step explanation:
i = interest 3% for 30 years
This is a simple dynamical system for whom the the solutions are given as
](https://tex.z-dn.net/?f=S%3DR%5B%5Cfrac%7B%28i%2B1%29%5En-1%7D%7Bi%7D%5D%28i%2B1%29)
putting values we get
S=2000[\frac{(1.03)^{30}-1}{0.03}](1.03)
= $98005.35
withdrawal of money takes place from one year after last payment
To determine the result we use the present value formula of an annuity date
we need to calculate R so putting the values and solving for R we get
R= $6542.2356
So there are two triangles here: Smaller one (ADE) and bigger one (ABC) and they both are similar.
So you can use proportions here.
AB / AC = AD / AE
AB = AD + DB = 6 + 1 = 7
AC = AE + 3
AD = 6
So plug in these values:
AB / AC = AD / AE becomes
7 / (AE + 3) = 6 / AE
Now do the cross multiply:
7 AE = 6 (AE + 3)
Now solve for AE:
7AE = 6AE + 18
AE = 18
R = radius of basketball
r = radius of tennis ball
R = 3.6r cube both sides
the ratio of the radii is 1: 3.6
cube both sides to find the ratio of the volumes
1 : 46.656 ( this many times greater)
Answer:
C. x = -12 and x = 2
Step-by-step explanation:
-x²-10x+24=0 Original equation
x²+10x-24=0 Divide everything by -1
(x+12)(x-2)=0 Factor it out
x=-12,2 Solve so that the inside of the parentheses equals 0
An arithmetic sequence takes the form
where
is the common difference between terms. You can solve for
in terms of any of the previous terms of the sequence:
for some integer
Continuing in this way, you know that the sequence can be defined explicitly in terms of the first term
Given that the 4th term is
and the 11th term is
, you have the following system of equations.
Solving this system for the two unknowns yields
and
.
So, the sequence is given explicitly by
