Answer:
$1480.24
Step-by-step explanation:
This will be solved by the formula:
Where
FV is the future value (what we are looking for)
I is the initial amount (which is $1000)
r is the rate of interest per period (8% is annual interest, but the period is SEMI-ANNUAL, that's 6 months, half of yearly. So r would be half of 8%, which is 4% or r = 0.04)
t is the times compounding occurs in the whole time (The whole time period is 5 years, but compounding occurs semi-annually, so 5*2 = 10 times. Thus, t = 10)
<em>plugging the info into the formula we will get our answer.</em>
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I will give you the formula and teach you how to solve this. Let’s start with finding the area of both the right triangles.
The formula is, base x height / 2 = area
Triangle 1 - 2x8/2 = 16/2 = 8
Triangle 2 - 2x8/2 = 16/2 = 8
Rectangle - 8x3 = 24
Add them up: 24 + 8 + 8 = 40 square feet
I hope this wasn’t to confusing
The area of a rectangle is easy to compute.
Area = length times height
Area = 8 cm * 4 cm = 32 square centimeters
3.) An extreme value refers to a point on the graph that is possibly a maximum or minimum. At these points, the instantaneous rate of change (slope) of the graph is 0 because the line tangent to the point is horizontal. We can find the rate of change by taking the derivative of the function.
y' = 2ax + b
Now that we where the derivative, we can set it equal to 0.
2ax + b = 0
We also know that at the extreme value, x = -1/2. We can plug that in as well.
The 2 and one-half cancel each other out.
Now we know that a and b are the same number, and that ax^2 + bx + 10 = 0 at x = -1/2. So let's plug -1/2 in for x in the original function, and solve for a/b.
a(-0.5)^2 + a(-0.5) + 10 = 0
0.25a - 0.5a + 10 = 0
-0.25a = -10
a = 40
b = 40
To determine if the extrema is a minima or maxima, we need to go back to the derivative and plug in a/b.
80x + 40
Our critical number is x = -1/2. We need to plug a number that is less than -1/2 and a number that is greater than -1/2 into the derivative.
LESS THAN:
80(-1) + 40 = -40
GREATER THAN:
80(0) + 40 = 40
The rate of change of the graph changes from negative to positive at x = -1/2, therefore the extreme value is a minimum.
4.) If the quadratic function is symmetrical about x = 3, that means that the minimum or maximum must be at x = 3.
y' = 2ax + 1
2a(3) + 1 = 0
6a = -1
a = -1/6
So now plug the a value and x=3 into the original function to find the extreme value.
(-1/6)(3)^2 + 3 + 3 = 4.5
The extreme value is 4.5
596*25%=149
149 people over the age of 65 years old voted
