Container X has 2 cups of water with 6 teaspoons of sugar. Container Y has 4 cups of water with 8 teaspoons of sugar. In which c
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Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
- Left to Right<u> </u>
<u>Algebra I</u>
- Reading a Cartesian plane
- Coordinates (x, y)
- Slope Formula:
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Find points from graph.</em>
Point (-5, 0)
Point (-9, -8)
<u>Step 2: Find slope </u><em><u>m</u></em>
Simply plug in the 2 coordinates into the slope formula to find slope<em> m</em>
- Substitute in points [Slope Formula]:
- [Fraction] Subtract/Add:
- [Fraction] Divide:
Another triple integral. We're integrating over the interior of the sphere
Let's do the outer integral over z. z stays within the sphere so it goes from -2 to 2.
For the middle integral we have
x is the inner integral so at this point we conservatively say its zero. That means y goes from and
Similarly the inner integral x goes between
So we rewrite the integral
Let's work on the inner one,
There's no z in the integrand, so we treat it as a constant.
So the middle integral is
I gotta go so I'll stop here, sorry.
Applying the division rule of exponents, 6^10/6^6 can be rewritten in the form of b^n as: 6^10/6^6 = 6^4.
<h3>What is the Division Rule of Exponents?</h3>The division rule of exponents state that if we have a numerator and a denominator with the same base, the quotient will be the base, while we subtract the exponent value of the denominator from the exponent value of the numerator.
For example, if we have, a³/a², the division rule of exponents states that:
a^(3 - 2) = a^1 = a.
Given the expression, 6^10/6^6, we can rewrite the expression in the form of b^n by applying the division rule of exponents as shown below:
6^10/6^6 = 6^(10 - 6)
6^10/6^6 = 6^4
In conclusion, applying the division rule of exponents, 6^10/6^6 can be rewritten in the form of b^n as: 6^10/6^6 = 6^4.
Learn more about the division rule of exponents on:
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Answer:
Summary:
Standard form allow us to quickly find the y-intercept.
Vertex form allow us to quickly locate the vertex.
And factored form allows us to quickly determine the roots/zeros.
Step-by-step explanation:
The three forms of quadratics are the standard form, vertex form, and the factored form. Each of them reveals a specific part about the quadratic.
Standard Form:
The standard form of a quadratic is:
There are only two details that can be conveyed by a quadratic in standard form immediately: (1) the leading coefficient a, and (2) the y-intercept.
The leading coefficient a will tell us if the parabola curves upwards or downwards.
And the constant c will give us the y-intercept.
Vertex Form:
The vertex form of a quadratic is:
There are also two details that can be conveyed by a quadratic in vertex form: (1) the vertex, and (2) the leading coefficient.
The leading coefficient is given by a. Again, this tells us the orientation of the parabola.
And the vertex is given by (h, k).
Hence, in my opinion, vertex form is the best form of a quadratic since it immediately reveals the vertex, the most important aspect of a quadratic.
Factored Form:
The factored form of a quadratic is:
Where p and q are the zeros/roots/solutions of the quadratic.
Again, factored form gives us two details about the quadratic: (1) the leading coefficient, and (2) the zeros.
The zeros tells us when the parabola crosses the x-axis, which can assist in graphing.
Summary:
Therefore, each form of a quadratic equation has its own benefits.
Standard form allow us to find the y-intercept.
Vertex form allow us to quickly locate the vertex.
And factored form allows us to quickly determine the roots/zeros.
Hence, depending on the question, each form can be useful in its own way.