Explain what 1,000 times a hundred billion 2 hundred thirty-two million plus twenty trillion, thirty billion, forty million, two thousand, 4 hundred and eight is and write the answer in standard form, expanded form, and in any other form possible. Formulate a quadratic formula, exponential formula, and linear formula that has the same answer as well.
Please show your work and describe your answers and how you got it.
To solve the given expression, we'll break it down step by step:
1. 1,000 times a hundred billion (= 100,000,000,000) is:
1,000 * 100,000,000,000 = 100,000,000,000,000.
2. Adding 232 million (= 232,000,000) to the previous result gives us:
100,000,000,000,000 + 232,000,000 = 100,000,000,232,000,000.
3. Adding twenty trillion (= 20,000,000,000,000) to the previous result gives us:
100,000,000,232,000,000 + 20,000,000,000,000 = 120,000,000,232,000,000.
4. Adding thirty billion (= 30,000,000,000) to the previous result gives us:
120,000,000,232,000,000 + 30,000,000,000 = 120,030,000,232,000,000.
5. Adding forty million (= 40,000,000) to the previous result gives us:
120,030,000,232,000,000 + 40,000,000 = 120,030,000,272,000,000.
6. Adding two thousand four hundred and eight (= 2,408) to the previous result gives us:
120,030,000,272,000,000 + 2,408 = 120,030,000,272,002,408.
Now, let's represent the answer in different forms:
Standard form: 120,030,000,272,002,408.
Expanded form: 100,000,000,000,000 + 20,000,000,000,000 + 200,000,000 + 32,000,000 + 40,000 + 2,000 + 408.
Quadratic formula: There is no quadratic formula that can be formulated to fit this expression since quadratic formulas require an equation involving variables.
Exponential formula: Same as the quadratic formula, there is no exponential formula that can represent this expression.
Linear formula: The expression represents a single number and is not a linear equation, so a linear formula is not applicable.
In summary, the answer to the given expression is 120,030,000,272,002,408. It can be expressed in standard form, expanded form, and there are no quadratic, exponential, or linear formulas that can represent it since it is not an equation.
Can you create a linear, quadratic, exponential formulas using this answer and create your own problem and answer it?
Certainly! Let's create formulas for each type using the answer of 120,030,000,272,002,408.
1. Linear Formula:
A linear formula can be represented as y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept. In this case, since we have a single value, it'll be a constant linear equation:
y = 120,030,000,272,002,408.
2. Quadratic Formula:
Quadratic formulas involve equations with a second degree (or quadratic) term. However, since we have a single value rather than an equation, it's not possible to create a quadratic formula using this answer.
3. Exponential Formula:
An exponential formula can be represented as y = ab^x, where y is the dependent variable, x is the independent variable, a is the initial value, and b is the growth or decay factor. Similarly to the quadratic formula, we can't create an exponential formula with only a single value.
Now, let's create a problem and answer it using the linear formula:
Problem: You have a linear formula y = 120,030,000,272,002,408. Calculate the value of y when x = 5.
Solution:
Substitute x = 5 into the linear formula:
y = 120,030,000,272,002,408.
Therefore, when x = 5, y = 120,030,000,272,002,408.
Write 120,030,000,272,002,408 in word form.
120,030,000,272,002,408 in word form is "one hundred twenty trillion, thirty billion, two hundred seventy-two million, two thousand, four hundred eight."
To find the answer to the given expression, we will break it down step by step:
1. First, let's calculate 1,000 times a hundred billion (100,000,000,000) 2 hundred thirty-two million (232,000,000). We can do this by multiplying the two numbers:
1,000 * 100,000,000,000 * 232,000,000 = 2,320,000,000,000,000,000,000
2. Next, we will add twenty trillion (20,000,000,000,000), thirty billion (30,000,000,000), forty million (40,000,000), two thousand (2,000), four hundred (400), and eight (8) to the previous result:
2,320,000,000,000,000,000,000 + 20,000,000,000,000 + 30,000,000,000 + 40,000,000 + 2,000 + 400 + 8 = 2,340,030,040,000,000,000,408
So, the answer to the given expression in standard form is 2,340,030,040,000,000,000,408.
Now, let's represent this answer in expanded form:
2,340,030,040,000,000,000,408 can be expanded as:
(2 * 10^21) + (3 * 10^17) + (4 * 10^14) + (3 * 10^12) + (4 * 10^9) + (408)
Quadratic Formula:
To formulate a quadratic formula with the same answer, we need to convert the answer to zero. Let's consider the equation:
x^2 + bx + c = 0
Using the answer, we can generate the equation:
x^2 + (2,340,030,040,000,000,000,408)x + 2,340,030,040,000,000,000,408 = 0
Exponential Formula:
An exponential formula consists of a base and an exponent. Let's consider the exponential formula with base 10:
10^x = 2,340,030,040,000,000,000,408
Linear Formula:
A linear formula has the form y = mx + b. Let's consider the linear equation:
y = (2,340,030,040,000,000,000,408)x + 0
Where x and y are variables.
That's how we can represent the answer to the given expression in different forms and create formulas that yield the same result.