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<h3>What is the greatest common factor of 15x³y² and 20x⁴y⁴? </h3>
<em>First we have to find the factors of 15x³y²</em>
<em>15x³y² = 3 * 5x³y² </em>
<em>Then we have to find the factors of 20x⁴y⁴</em>
<em>20x⁴y⁴ = 2²x¹y² * 5x³y²</em>
<em>Now we have to find the common factors to both numbers.</em>
<em>The common factors are </em><em>5x³y²</em>
Answer : GCF = (15x³y²,20x⁴y⁴) = 5x³y²
Hope this helps!
Answer:
There is needed around 311 balloons to fulfill Mr. Schordine’s dream of flight.
Step-by-step explanation:
First, we need to calculate the volume of each balloon by considering the balloons as a sphere:
Where:
r: is the radius = 0.4 meters
Knowing that 1 m³ of helium is able to lift about 1 kg, that Mr. Schordine weights 84 kg, and that each ballon has 0.27 m³ of helium, the number of balloons needed are:
Therefore, there is needed around 311 balloons to fulfill Mr. Schordine’s dream of flight.
I hope it helps you!
Answer:
- x-intercept: (-0.1, 0)
- Horizontal Asymptote: y = -3
- Exponential <u>growth</u>
(First answer option)
Step-by-step explanation:
<u>General form of an exponential function</u>
where:
- a is the initial value (y-intercept).
- b is the base (growth/decay factor) in decimal form:
If b > 1 then it is an increasing function.
If 0 < b < 1 then it is a decreasing function. - y=c is the horizontal asymptote.
- x is the independent variable.
- y is the dependent variable.
Given <u>exponential function</u>:
The x-intercept is the point at which the curve crosses the x-axis, so when y = 0. To find the x-intercept, substitute y = 0 into the given equation and solve for x:
Therefore, the x-intercept is (-0.1, 0) to the nearest tenth.
<h3><u>Asymptote</u></h3>An <u>asymptote</u> is a line that the curve gets infinitely close to, but never touches.
The <u>parent function</u> of an <u>exponential function</u> is:
As<em> </em>x approaches -∞ the function f(x) approaches zero, and as x approaches ∞ the function f(x) approaches ∞.
Therefore, there is a horizontal asymptote at y = 0.
This means that a function in the form always has a horizontal asymptote at y = c.
Therefore, the horizontal asymptote of the given function is y = -3.
<h3><u>Exponential Growth and Decay</u></h3>A graph representing exponential growth will have a curve that shows an <u>increase</u> in y as x increases.
A graph representing exponential decay will have a curve that shows a <u>decrease</u> in y as x increases.
The part of an exponential function that shows the growth/decay factor is the base (b).
- If b > 1 then it is an increasing function.
- If 0 < b < 1 then it is a decreasing function.
The base of the given function is 10 and so this confirms that the function is increasing since 10 > 1.
Learn more about exponential functions here:
Answer: