Arthur drops a ball from a height of 81 feet above the ground. Its height, h, is given by the equation h = –16t2 + 81, where t i
2 answers:
Answer:
Step-by-step explanation:
We are given the position function and need to find the value of t when h<17.
Create an inequality that represents this situation:
The "less than" sign makes this very specifically a conjunction problem as opposed to a disjunction. That's important to the solution. But we'll get there.
The simplest way to solve this is to subtract 81 from both sides:
then divide both sides by -16:
Notice now that the sign is facing the other way since we had to divide by a negative number. Now it's a disjunction. The solution set to this inequality is that t>2 or t<-2. First and foremost, time will never be negative, so we can disregard the -2. Even if that was t<2, the more time that goes by, the greater the time interval is, not the lesser. It's the "<" that doesn't make sense, not only the -2. The solution to this inequality is
t > 2 sec. That means that after 2 seconds, the height of the ball is less than 17 feet.
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Answer:
<u>Third Option</u>:
Step-by-step explanation:
Given the points on the graph, (4, 5) and (-4, -5):
In order to determine the equation of the given graph in slope-intercept form, y = mx + b:
Use the given points to solve for the slope:
Let (x₁, y₁) = (-4, -5)
(x₂, y₂) = (4, 5)
m = (y₂ - y₁)/(x₂ - x₁)
Therefore, the slope of the line is: .
Next, use one of the given points on the graph, (4, 5) to solve for the y-intercept, b:
y = mx + b
5 = + b
5 = 5 + b
5 - 5 = 5 - 5 + b
0 = b
Therefore, the linear equation in slope-intercept form is: . The correct answer is Option 3.
Answer:
8. Arithmetic Progression
9.
Step-by-step explanation:
Given
Solving (8): Arithmetic or Geometric
We start by checking if it is arithmetic by checking for common difference (d).
This gives:
<em>Because the common difference is equal, then it is an arithmetic progression</em>
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Solving (8):
To find f(9), we substitute 9 for n
We need to solve for f(8); substitute 8 for n
We need to solve for f(7); substitute 7 for n
We need to solve for f(6); substitute 6 for n
We need to solve for f(5); substitute 6 for n
From the function, f(4) = 25 and f(1) = 55.
So:
<u>Answer-</u>
2 is the upper limit for the zeros.
<u>Solution-</u>
The given function f(x) is,
For calculating the zeros,
From all the 4 roots, it can be obtained that 2 is the greatest zero.
