Answer:
A. {-1, 2, 7}
Step-by-step explanation:
For a set of ordered pairs, the domain is the set of first-numbers (x). The range is the set of second numbers (y, or g(x)).
The first step here is to find the g(x) values for each of the listed x-values.
The attachment shows a table.
Often, we like to list the domain and/or range values in numerical order, eliminating any duplicates. That is, the set of range values {2, -1, -1, 7} would be listed as ...
{-1, 2, 7} . . . . . . matches choice A
_____
You find the g(x) values by substituting for x and doing the arithmetic.
g(-2) = (-2)² -2 = 4 -2 = 2, for example
Answer:
<em>V = 1,568</em>
Step-by-step explanation:
<u>The Volume of a Square Pyramid</u>
Given a square-based pyramid of base side a and height h, the volume can be calculated with the formula:
We are given a square pyramid with a base side a=14 ft but we're missing the height. It can be calculated by using the right triangle shown in the image attached below, whose hypotenuse is 25 ft and one leg is 7 ft
We use Pythagora's theorem:
Solving for h:
The height is h=24 ft. Now the volume is calculated:
V = 1,568
9p times 100 = 900p or £9
Answer:
11.1 years
Step-by-step explanation:
The formula for interest compounding continuously is:
Where A(t) is the amount after the compounding, P is the initial deposit, r is the interest rate in decimal form, and t is the time in years. Filling in what we have looks like this:
We will simplify this first a bit by dividing 2000 by 1150 to get
To get that t out the exponential position it is currently in we have to take the natural log of both sides. Since a natural log has a base of e, taking the natual log of e cancels both of them out. They "undo" each other, for lack of a better way to explain it. That leaves us with
ln(1.739130435)=.05t
Taking the natural log of that decimal on our calculator gives us
.5533852383=.05t
Now divide both sides by .05 to get t = 11.06770477 which rounds to 11.1 years.
Decimal is 0.12 and fraction is 12/100
