The post LaPlace Transform Calculator appeared first on Mikes Calculators with Steps.

]]>Enter your Function and press the “SUBMIT” button.

Example: Enter t^2 to get 2/s^3 as the Laplace Transform.

The Laplace Transform will be displayed in S Domain.

Rule: The LaPlace Transform of a constant is just constant * 1/s .

Thus, the LaPlace Transform of f(t)=6 is 6/s in the S-Domain.

of course we have a LaPlace Transform table for you, see below:

Enter your 2 Functions and their Intervals , next press the “SUBMIT” button.

Example: Enter the 2 Functions 0 and t^2 and their Intervals 0<=t<1 and t>1.

The Laplace Transform of the Piecewise Function will be displayed in the S Domain.

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]]>The post Parabola Graphing Calculator appeared first on Mikes Calculators with Steps.

]]>Different equations may produce the same Parabolas.

For example, these 3 equations will graph the same Parabola. Try it below.

Can you create 3 different equations that result in the same Parabola?

Try it above by typing in 3 different equations into the Parabola Graphing Calculator above.

Hint: All 3 equations would be equal when converted to Standard Form.

Read below on how to convert between the 3 Parabola forms.

Standard Form:

y = x²+6x+8can be rewritten in Vertex Form:

y = (x+3)²-1It tells us that above Parabola has Vertex Coordinates = (3,-1). Verify that above on the Graph of the Parabola Graphing Calculator. You can actually click on the vertex and the coordinates will show.

The process to convert from Standard Form to Vertex Form is called “Completing the Square”. You can Complete the Square for your quadratic equation below. You can read the details and examples on how to convert here.

Factored Form:

y = (x+4)(x+2)It tells us that above Parabola has Zeros -4 and -2 . Again, verify that above on the Graph of the Parabola Graphing Calculator. You can actually click on the zeros and the coordinates will show.

The process to convert from Standard Form to Factored Form can be done below. You can read the details and examples on how to convert here.

Or simply use the head menu when converting between the different Parabola Forms.

Standard Form:

y = ax²+bx+cVertex Form:

y = a(x-h)²+k(h,k) = Vertex Coordinates.

Factored Form:

y = a(x-r)(x-s)r and s = Zeros of the Parabola.

(h,k) = Vertex Coordinates.

Example: Vertex=(1,2) which makes the Parabola Equation

Given Point (3,10) turns the Equation to

Therefore, the Parabola Equation is calculated as

If however you are given two Zeros and a Point you will use the Factored Form:

Example: Zeros are 3 and 5 which makes the Parabola Equation

Given Point (4,-2) makes the Parabola Equation

Therefore, the Parabola Equation is calculated as

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]]>For Questions, Bookings, etc : Chat with us.

Email us : support@mikescalculator.com

Or call us at 301-494-3900

Payment is made below via Paypal to our company SmartSoft LLC.

Note: You don’t have to be a Paypal member to make payment using credit card or check.

1. Lesson ($50) | One Lesson ($100) | Multiple Lessons |
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]]>The post Schedule a Tutoring Session appeared first on Mikes Calculators with Steps.

]]>For Questions, Bookings, etc : Chat with us.

Email us : support@mikescalculator.com

Or call us at 301-494-3900

Payment is made below via Paypal to our company SmartSoft LLC.

Note: You don’t have to be a Paypal member to make payment using credit card or check.

1. Lesson ($50) | One Lesson ($100) | Multiple Lessons |
---|---|---|

The post Schedule a Tutoring Session appeared first on Mikes Calculators with Steps.

]]>The post Domain and Range of a Parabola appeared first on Mikes Calculators with Steps.

]]> 1 – Step by Step Solver: Find the Range of a Parabola

2 – What is the Domain of a Parabola?

3 – How do I write the Range in Interval Notation?

4 – Example: Domain and Range of a Parabola

5 – Is there a Domain and Range Parabola Calculator?

The reason for that is quadratic equations fall in the category of polynomials and thus don’t contain fractions, roots or radicals nor logarithms. Those 3 categories of functions have restrictions with regard to their domain.

Notice that the 3 is included in the Range so we use bracket [ in the Interval Notation. Since there is no upper bound for the Range we denote that with the Infinity Symbol which is always followed by the Open Interval symbol “)”. Think of Infinity as NOT being a concrete endpoint.

Example2: If the Range is y≤5 then the corresponding Interval Notation is (-oo , 5] .

Again, the 5 is included in the Range so we use the bracket ] in the Interval Notation.

We are given the Standard Form ** y=3x²- 6x-2 ** .

Since ANY x value can be plugged into this equation (we have no fractions, radicals nor logarithms) we can conclude that the Domain is ‘all real numbers’. In Interval Notation: ** (-∞ , ∞) **

To find the Range we first compute the x-coordinate of the vertex **h = – b /(2a) = -(-6)/(2*3) = 1 ** .

Next, compute the y-coordinate of the vertex by plugging h=1 into the given equation: **k= 3*(1)²-6(1)-2=-5 ** .

Therefore, the vertex is ** (h,k)=(1,-5) ** .

The Range is simply all real numbers greater or equal to -5 or simply y>=-5.

Using Interval Notation: ** [-5 , ∞) **

Explanation: This parabola opens to the top since the leading coefficient 3 is greater than 0. This implies that the vertex is a minimum and therefore the parabola takes on any value greater than 5. Since the Range contains all possible y- values the Range is ** [-5 , ∞) **

Easy, wasn’t it?

Tip: When using the above Range of a Parabola Calculator for **3x²-6x-2**

we must enter the 3 coefficients a,b,c as **a=3, b=-6** and **c=-2**.

Get it now? Try the above Range of a Parabola Calculator again if needed.

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]]>The post Domain and Range Calculator appeared first on Mikes Calculators with Steps.

]]>1) The Domain is defined as the set of all possible x-values that can be plugged into a function.

2) The Range of a function is defined as the set of all resulting y values.

1) The Domain is defined as the set of x-values that can be plugged into a function. Here, we can only plug in x-values greater or equal to 3 into the square root function avoiding the content of a square root to be negative.

Thus, domain is ** x>=3 ** .

Using Interval Notation we write: ** [3,∞) **

2) The Range of a function is defined as the set of all resulting y values. Here, the lowest y coordinate is y=0 achieved when x=3 is plugged in. The larger the x value plugged in the larger the y coordinate we obtain.

Thus, the range is ** y>=0 ** .

Using Interval Notation we write: ** [0,∞) **

Just enter your Function and press the blue “ARROW” button. The Domain and Range will be displayed above the arrow.

1) The Domain are the x-values going left (from the smallest x-value) to right (to the largest x-value).

2) The Range are the y-values going from lowest (from the smallest y-value) to highest (to the largest y-value).

1) The Domain is all real numbers. Any number can be plugged into y=6.

2) The Range is just y=6. The lowest and highest y are both 6.

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]]>The post What is the Mean in Math? appeared first on Mikes Calculators with Steps.

]]>
Enter your Numbers (separated by commas) & Press the Button.

The **Mean** in Mathematics is just another word for **Average**.

Mathematician denote the Mean using the symbol **̄x̄**.

The Mean is found by adding up the given Numbers divided by the Number of Numbers given.

As a Formula: **̄x̄** = Sum of given Numbers / Number of Numbers = ** (x1+x2+x3+..+xn)/(n) **

**Example:** We are given 2,4,9. Then, ** ̄x̄** = (2+4+9)/3 = 15/3 = 5

The Mean is one of 3 common ways to describe the center of a set of numbers besides the Median and the Mode.

For Instance, if 3 boys weigh 100, 110 and 150 pounds, then on Average (aka their Mean Weight) they weigh 360/3=120 Pounds. The 120 pounds can be seen as a representation of the weight of the 3 boys.

Notice that the Mean uses each boy’s weight. So if only boy is extra light or extra heavy it will have a significant impact on the Mean. On the contrary, the Median (described below) is designed to not get affected by unusual weights.

The Median is the Center in a sorted list of Numbers. In case of an odd number of numbers there will be a single center number. In case of an even number of numbers in the list the Median equals the average of the 2 center numbers.

**1. Example:** We are given 4,9,2. First we have to sort the list to get 2,4,9 . The Median is 2 because it is in the Center of this sorted list. We have an odd (3) numbers in our list.

**2. Example:** We are given 6,4,9,2. First we have to sort the list to get 2,4,6,9 . This list has an even number of numbers. Thus, the Median is 5 as the average of 4 and 6.

For Instance, if 3 boys weigh 100, 110 and 150 pounds, then their Median Weight is 110 Pounds.

The 110 pounds can be seen as a representation of the weight of the 3 boys.

Notice that the Median does not get affected by unusual weights.

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]]>The post Sample Standard Deviation appeared first on Mikes Calculators with Steps.

]]>The Formula for the Standard Deviation of Sample** **is:

**Sample Standard Deviation** gives the average distance of your numbers to the mean of those numbers.

Example 1: A Standard Deviation of 0 means that the given set of numbers are the same since they don’t differ from their mean.

Example 2: A Standard Deviation of 1 means that the given set of numbers differ – on average – by 1 from their mean.

Bowling Example: A consistent bowler that bowls 110 and 90 games has a **lower **Standard Deviation than a bowler who bowls 50 and 150. While they each have a mean of 100 the 2. bowler scores varied much more from 100 than the first bowler.

Their Difference lies in the Denominators of their Formulas (for technical reasons):

When computing the Sample Standard Deviation we divide by n-1.

When computing the Population Standard Deviation we divide by n instead. Additionally, we must use the population’s mean, denoted as the greek letter µ .

This is the formula for the Population Standard Deviation:

The 1 Standard Deviation rule refers to the **Empirical Rule** of Normal Distributions (aka Bell Curves). See image.

About 68% of the Data fall within 1 Standard Deviation of the Mean.

About 95% of the Data fall within 2 Standard Deviations of the Mean.

About 99.7% of the Data fall within 3 Standard Deviations of the Mean.

**Example:** About 95% of the US Population have an IQ between 80 and 120.

Reason: Mean IQ=100 and Standard Deviation=10. Thus, 95% Americans fall within 2 standard deviations, 2*10 = 20 of 100.

Note: This means that about 2.5% have an IQ higher than 120.

The post Sample Standard Deviation appeared first on Mikes Calculators with Steps.

]]>The post Mean Median Mode Range Calculator appeared first on Mikes Calculators with Steps.

]]>
Enter your Numbers (separated by commas) & Press the Button.

**Mean** = Average = **x̄ **= Sum of all Numbers / Number of Numbers in List.

**Median **= Center Number of Ordered List

**Mode **= The most frequent Number in List

**Range**=Largest – Smallest Number in List

** Variance of Population **:

where **μ** = Population Mean

**Standard Deviation of Population** :

** Variance of Sample** :

**Standard Deviation of Sample **:

Let’s do an **Example with 7 numbers** (see right image)

a) To find the **Mean **we add up the 7 integers to get 80 and divide by 7 to get a Mean of 80/7 = 11.4 . Note: **Mean **is also called **Average**.

b) To find the **Median **we simply identify the center number to get a Median = 6. In case of 2 center numbers we will average them.

c) To find the **Mode **we simply identify the most common number to get a Mode = 1. Note: We may have 2 or more modes.

d) To find the **Range **we simply subtract the Minimum from the Maximum to get a **Range **= 42 – 1 =41.

e) **Outliers **are numbers that are way off.

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]]>The post Compute Discriminant – to discriminate between Real and Complex Solutions of a Quadratic Equation. appeared first on Mikes Calculators with Steps.

]]>2x

= b

= (-12)

= 144 – 128 = 16

Since 16>0 2x

The Discriminant is the red part of the famous Quadratic Equation Formula below:

The Discriminant D= b^{2}-4*a*c is the part of the above Quadratic Equation. It is the part inside the square root.

The Discriminant ‘discriminates’ or ‘distinguishes’ 3 different types of solutions to the Quadratic Equation.

1) If the Discriminant D is greater than 0 then we can take the square root and we will have 2 real solutions.

2) If the Discriminant D is equal to 0 then we can take the square root of 0 and we will have 1 real solutions.

3) If the Discriminant D is less than 0 then we can take the square root of a negative number and we will have 2 complex solutions.

In below’s example we have a Discriminant D=49. Since it is a positive number we know that our Quadratic Equation 2x^{2}+5x-3=0 has 2 real (non-complex) solutions. **What you take from this is that a Discriminant tells you the type of solution of any Quadratic Equation WITHOUT given you the actual solutions. **Those solutions can be found using our handy Quadratic Equation Solver at: https://mikescalculators.com/solve-quadratic-equation/

What is the Discriminant of 2x^{2}+5x-3?

The coefficients are a=2, b=5 and c=-3.

We plug those into the formula for Discriminant D= b^{2}-4*a*c

to get D=5^{2}-4*2*(-3)

which simplifies to

25 – 8*(-3) = 25 + 24 = 49

implying the Discriminant is D=49.

Using the above Discriminant Calculator to solve 2x^{2}+5x-3=0 we must enter the coefficients a=2, b=5 and c=-3.

With steps we see the Discriminant is D=49 .

Get it now? Try the above Discriminant Calculator a few more times or watch the video below.

The post Compute Discriminant – to discriminate between Real and Complex Solutions of a Quadratic Equation. appeared first on Mikes Calculators with Steps.

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