Answer:
amount is 1000 × 
$40762.20 balance of Donna's account will be 1 million dollars when she retires in 40 years
rate 14.97 % when Donna's account will have a balance of 1 million dollars in 40 years when principal is $2500
Step-by-step explanation:
principal = $1000
rate = 8 % = 0.08
to find out
the future value, S(t)
principal when Donna's account will be 1 million dollars when she retires in 40 year
at what rate Donna's account will have a balance of 1 million dollars in 40 years
solution
we know compounded continuously formula i.e.
amount = principal × 
..................1
put the value principal and rate in equation 1 to find amount any time
amount = principal ×
amount = 1000 ×
in 2nd part we have time 40 year and amount 1 million so put rate amount and time in equation 1 to find principal
rt = 0.08 × 40 = 3.2
amount = principal ×
1000000 = principal × 
principal = 1000000 /
principal = 1000000 / 24.5325302
principal = 40762.20397
so $40762.20 balance of Donna's account will be 1 million dollars when she retires in 40 years
in 3rd part we have amount 1 million and principal $2500 and time 40 year put all these in equation 1 to find rate
amount = principal ×
1000000 = 2500 × 
take ln both side
ln = ln (1000000 / 2500 )
40 r = ln 400
r = ln (400) / 40
r = 0.149787
so rate 14.97 % when Donna's account will have a balance of 1 million dollars in 40 years when principal is $2500
Given:
The graph of a function 
.
To find:
The interval where 
.
Solution:
From the given graph graph it is clear that, the function before x=0 and after x=3.6 lies above the x-axis. So, for 
and 
.
The function between x=0 and x=3.6 lies below the x-axis. So, 
for 
.
Now,
For 
, the graph of h(x) is above the x-axis. So, .
For 
, the graph of h(x) is below the x-axis. So, .
For 
, the graph of h(x) is below the x-axis. So, .
Only for the interval , we get .
Therefore, the correct option is A.
Answer:
<h2>231in^3</h2>
Step-by-step explanation:
We know that the volume of a sphere/globe is given as
V=4
/3πr^3
but the circumference is expressed as
C=2πr
solving for r given that C=24
24=2*3.142r
24=6.284r
r=24/6.284
r=3.8in
put r=3.6 in the expression for volume we have
V=4
/3π(3.8)^3
V=4
/3π(55
V=(220.59*3.142)/3
V=693.12/3
V=231in^3
The volume of the globe is 231in^3
Answer:
3 both ways x = 3
EXPLANATION:
plug in inputs and do a little simplifying we get
x = 6 ± √(36-36) all of that over 2
So we simplify and we get 6±sqrt(0) / 2
Then we get 6/2 = 3
x-0 = x+0
thats why there is only one answer
Answer: The correct option is
(d) This is a divergent geometric series. The sum cannot be found.
Step-by-step explanation: The given infinite geometric series is
We are to identify whether the given geometric series is convergent or divergent. If convergent, we are to find the sum of the series.
We have the D' Alembert's ratio test, states as follows:
Let, 
is an infinite series, with complex coefficients 
and we consider the following limit:
Then, the series will be convergent if L < 1 and divergent if L > 1.
For the given series, we have
So, the limit is given by
Therefore, L >1, and so the given series is divergent and hence we cannot find the sum.
Thuds, (d) is the correct option.
