The function is applicable within the segments of x:
(-∞, -1) and [-1, 7), meaning it is valid for x < 7.
Importantly,
the function cannot be evaluated at x = -1 in the left part of the linear graph, while it is valid at x = -1 in the right segment of the same line. Additionally, the function is not defined at x = 7 or any value above it.
Conclusion: x < 7.
The behavior of the spring can be described using either a sine or cosine function. The spring's maximum displacement is 6 inches, occurring at t=0, which we will define as the positive peak. Therefore, we can express the function as:
6sin(at+B). The spring's period is 4 minutes, which means the time factor in the equation must complete a cycle (2π) in 4 minutes. This gives us the equation 4min*a=2π, leading to a=π/2. Generally, a=2π/T where a is the coefficient and T is the period. For B, since sin(π/2)=1, we determine B=π/2 because at t=0, the equation becomes 6sin(B)=6. Therefore, we substitute to form f(t)=6sin(πt/2+π/2)=6cos(πt/2)
due to trigonometric relations.
Answer:
Step-by-step explanation:
To solve for v, reverse the operations performed on it, starting with the equation provided. Here, v is affected by:
- being multiplied by t
- subtracting gt^2 from the result
To start, we first need to add gt^2 back to the equation to counteract the subtraction:
h + gt^2 = vt
Next, we undo the multiplication by dividing the entire expression by the coefficient of v:
(h + gt^2)/t = v
Answer:
We start with the number 337 060.
Expanded form refers to a way of representing a standard form number in more detail.
This number will be converted to expanded form utilizing exponents.
=> 337 060
To begin, let's break down each component.
=> 300 000 = 3 x 10^5
=> 30 000 = 3 x 10^4
=> 7 000 = 7 x 10^3
=> 60 = 6 x 10^1
=> 3 x 10^5 + 3 x 10^4 + 7 x 10^3 + 6 x 10^1 – this is the expanded form of the number using exponents.
Step-by-step explanation:
Sample Answer: To determine the difference between 10 and 13, you apply the concept of additive inverses. Juan is lacking $3 to buy his supplies.
