2.5 years required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
Step-by-step explanation:
The given is,
Initial investment - $5000
Future amount - $6000
Interest rate - 7.5% (compounded quarterly)
Step:1
Formula to calculate the Future amount with compound interest,
...................................(1)
Where, F - Future amount
P - Initial amount
r - Rate of interest
n - No. of compounding in a year
t - Time period
From given,
F = $6000
P = $5000
r = 7.5%
n = 4 (compounded quarterly)
Equation (1) becomes,



Take log on both sides,

Substitute log values,
0.07918 = 4(t) (0.0080676)
= (t) (0.0322705)
= 2.45
t ≅ 2.5 years
Result:
2.5 years required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
You're looking for the extreme values of
subject to the constraint
.
The target function has partial derivatives (set equal to 0)


so there is only one critical point at
. But this point does not fall in the region
. There are no extreme values in the region of interest, so we check the boundary.
Parameterize the boundary of
by


with
. Then
can be considered a function of
alone:



has critical points where
:



but
for all
, so this case yields nothing important.
At these critical points, we have temperatures of


so the plate is hottest at (1, 0) with a temperature of 14 (degrees?) and coldest at (-1, 0) with a temp of -12.
Answer:
3 1/2 hours.
Step-by-step explanation:
We subtract>
Number of hours worked on a Saturday
= 7 3/4 - 4 1/4
= (7 - 4) + (3/4 - 1/4)
= 3 + 1/2
= 3 1/2 hours.
The function of f(4) = g(x+1) gives the value of x that is -1/5.
<h3>What is the function addition?</h3>
It is the addition of two functions similar to the addition of any two polynomial functions.
Given;
F(x)=x+1
g(x)=5x+1
We need to find f(4)=g(x+1)
First substitute x = 4 in f(x)
F(x)=x+1
F(4) = 4 + 1
F(4) = 5
Now substitute x = x + 1 in g(x)
g(x)=5x+1
g(x + 1) = 5(x + 1) + 1
g(x + 1) = 5(x + 1) + 1
g(x + 1) = 5x + 5 + 1
g(x + 1) = 5x + 6
Then ,
F(4) = g(x + 1)
5 = 5x + 6
5x = 5 - 6
5x = -1
x = -1/5.
The function of f(4) = g(x+1) gives the value of x that is -1/5.
Learn more about function;
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Answer:
Volume = πr2h
= π×52×9
= 225π
= 706.85 inches3
Step-by-step explanation: