So you may see more than one post abt these bc its due at 11:59 lol
1 answer:
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Answer:
The correct options are:
So, these functions have the same range.
The functions have the same base.
The functions have the same domain.
g(x) is a translation left 1 unit.
Step-by-step explanation:
According to the table, both are exponential functions.
We have that
Lets see each affirmation:
The functions have the same base.
An exponential function has base a.
In this problems, both f and g have base 3.
The functions have the same range.
The range of f are all the values that f can assume. That is, all the positive numbers.
The range of g are all the values that g can assume. That is, also all the positive numbers.
So, these functions have the same range.
The functions have the same exponent.
An exponential function has exponent x.
f has exponent x and g has exponent x + 1. So those functions do not have the same exponent.
The functions have the same domain.
Yes, they both have x = {0,1,2,3} as domain.
g(x) is a translation left 1 unit.
g(x) = f(x+1). So yes, g(x) is a translation left 1 unit.
g(x) is a translation right 2 units.
g(x) is not f(x-2). So g(x) is not a translation right 2 units.
g(x) is a translation up 2 units.
g(x) is not f(x) + 2. So g(x) is not a translation up 2 units.
If we want to simplify Algebraic Fractions:
We have to take a look at the numerator and the denominator
Why? Because to simplify we need to have a common multiple.
When we find the common multiple, we now know by which factor we have to break down the fraction in the numerator and the denominator
I have some examples attached below for help.
We have to take a look at the numerator and the denominator
Why? Because to simplify we need to have a common multiple.
When we find the common multiple, we now know by which factor we have to break down the fraction in the numerator and the denominator
I have some examples attached below for help.
The Halloween conical hat, with given height, circular base and brim
extension has the following calculated parameters;
Part a. The slant height is <u>18.2 inches</u>
Part b. The volume of the cone is in.³
Part c. The area of the brim, <em>A</em> = <u>36·π in.²</u>
Part d. The area of the brim is found by <u>subtracting the area of the base of the cone from the area covered by the perimeter of the brim</u>
Reasons:
Known parameters;
Height of the conical portion, h = 18 inches
Base circumference, C = 5·π inches
Part a. Slant height of the conical portion; Required
Solution:
The circumference of a circle, C = 2·π·r
Therefore;
Which gives;
Radius, r = 2.5 inches
According to Pythagoras's theorem, we have; s² = r² + h²
Where;
s = The slant height of the cone
s² = 2.5² + 18² = 330.25
s = √(330.25) ≈ 18.2
- The slant height, <em>s</em> ≈ <u>18.2 inches</u>
Part b. The measure in cubic inches of candy that exactly fills the conical portion of the hat is the volume of the cone.
Therefore;
- The volume of the cone, V =
·π in.³
Part c. The extension of the brim from the base of the cone = 4 inches
The radius of the brim, R = Radius of the base of the cone + 4 inches
∴ <em>R</em> = 2.5 inches + 4 inches = 6.5 inches
Area of the brim, <em>A</em> = Area of the 6.5 inch circle - Area of the circular base of the cone
∴ A = π × 6.5² - π × 2.5² = 36·π
- The area of the brim, <em>A</em> = <u>36·π in.²</u>
Part d. The procedure for solving the question in part c, is described as follows;
- The area of the brim can be found by finding the entire area of the circle formed by the perimeter of the brim, then subtracting the area of the base of the cone from that area.
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