The volume of the cylinder that measures 6 ft tall and 3 ft wide and was triple would be 1,145.6 cubic feet. This is calculated using the formula volume =
(r²)(h). BUt before substitutign the value, we need first to multiply it byt 3 and for the wide it has to be further divided to 2 to have the radius, h = 18 and r = 4.5. Substituting the value it would give us 1,145.6
A)
SLOPE OF f(x)
To find the slope of f(x) we pick two points on the function and use the slope formula. Each point can be written (x, f(x) ) so we are given three points in the table. These are: (-1, -3) , (0,0) and (1,3). We can also refer to the points as (x,y). We call one of the points
and another
. It doesn't matter which two points we use, we will always get the same slope. I suggest we use (0,0) as one of the points since zeros are easy to work with.
Let's pick as follows:
The slope formula is:
We now substitute the values we got from the points to obtain.
The slope of f(x) = 3
SLOPE OF g(x)
The equation of a line is y=mx+b where m is the slope and b is the y intercept. Since g(x) is given in this form, the number in front of the x is the slope and the number by itself is the y-intercept.
That is, since g(x)=7x+2 the slope is 7 and the y-intercept is 2.
The slope of g(x) = 2
B)
Y-INTERCEPT OF g(x)
From the work in part a we know the y-intercept of g(x) is 2.
Y-INTERCEPT OF f(x)
The y-intercept is the y-coordinate of the point where the line crosses the y-axis. This point will always have an x-coordinate of 0 which is why we need only identify the y-coordinate. Since you are given the point (0,0) which has an x-coordinate of 0 this must be the point where the line crosses the y-axis. Since the point also has a y-coordinate of 0, it's y-intercept is 0
So the function g(x) has the greater y-intercept
Answer:
<em>P = 28.57%</em>
Step-by-step explanation:
<u>Probability</u>
The probability of an outcome is defined as the frequency of the number of times the outcome occurs relative to the number of times that it could have occurred.
The equation to calculate the probability is:
Where f is the number of favorable cases and n is the total cases.
The spinner has n=7 equal spaces numbered 1 to 7. We will calculate the probability that the spinner lands on a 4 or a 6.
The set of favorable outcomes is {4,6} which gives a count of f=2.
The required probability is:
P = 28.57%
Answer:
Step-by-step explanation:
f(x) = 6(x+2)²-6
f⁻¹(f(x)) = x
f(x) = t => 6(x+2)²-6 = t =>
=> 6(x+2)² = t+6 =>
=> (x+2)² = t/6 + 1
=> x+2 = ±√(t/6 + 1)
=> x = ±√(t/6 + 1) - 2
=> f⁻¹(x) =
{√(x/6 + 1) - 2, x > -6
{-√(x/6 + 1) - 2, x ≤ -6