Answer:
2,3,5,6
Step-by-step explanation:
Every function is a rule which tells you how to associate inputs and outputs. The input, also known as independent variable, is often indicated with the letter , while the output, also known as dependent variable, is often indicated with the letter .
With this notation, we write , read "y is a function of x", in the sense that the value of the variable y depends on the value of the variable x, and f is the function that tells you how y depends on x.
In your example, you have , which means "subtract four times the input (4x) from 2"
So, it doesn't matter which input you chose (i.e. the value for x), because you will always have to behave this way:
- Pick an input value, x
- Multiply it by four to get 4x
- Subtract this number from 2: 2-4x
Here are some examples of explicit calculations: if I choose and input, the workflow will be
- Pick an input value, 2
- Multiply it by four to get 8
- Subtract this number from 2: 2-8=-6
So, if the input is 2, the output is -6
Similarly, if we choose as input, we have:
- Pick an input value, 0
- Multiply it by four to get 0
- Subtract this number from 2: 2-0=2
So, if the input is 0, the output is 2. And so on: for every possible value for x you have the correspondant value for y, with the function f telling you how to associate one with the other.
Answer:
Horizontal distance between lifeguard and the person is 22 feet.
Step-by-step explanation:
Given: A lifeguard sees a person in distress.The eye level of the lifeguard is 15 feet above the ground. Angle of depression is 34°.
To find: Horizontal distance between lifeguard and the person.
Solution : If we draw a triangle then tan∅ =
Here base is the horizontal distance.
Now we put the values in the formula.
tan 34° =
Or Base =
=
So the answer is 22 feet.
Sin51=y/12
y=12sin51 units
y≈9.33 units (to nearest hundredth of a unit)
...
tanα=12/5
α=arctan2.4°
α≈67.38° (to nearest hundredth of a degree)
...
tan13=x/24
x=24tan13 units
x≈5.54 units (to nearest hundredth of a unit)
...
sin20=10/x
x=10/sin20 units
x≈29.24 units (to nearest hundredth of a unit)
Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Coordinates (x, y)
- Functions
- Function Notation
- Terms/Coefficients
- Exponential Rule [Rewrite]:
<u>Calculus</u>
Derivatives
Derivative Notation
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Step-by-step explanation:
<u>Step 1: Define</u>
<u /><u />
<u>Step 2: Differentiate</u>
- [Function] Rewrite [Exponential Rule - Rewrite]:
- Basic Power Rule:
- Simplify:
- Rewrite [Exponential Rule - Rewrite]:
<u>Step 3: Solve</u>
- Substitute in coordinate [Derivative]:
- Evaluate exponents:
- Divide:
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e