Write the equation for the following relation. Include all of your work in your final answer. Submit your solution.
1 answer:
Answer:
Step-by-step explanation:
The given relation is Q = {(x, y): (2, 8), (3, 27), (4, 64), (5, 125), . . .}
We can quickly recognize a pattern to write the equation of the given relation.
We can observe the following pattern among the x and y coordintaes.
We can see that the base of the powers on the right are the x-values of the relation and the values on the left are the y-values.
Hence, for any ordered pair (x,y), the equation is
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Answer:
x=5
Step-by-step explanation:
First, let's understand logarithms.
When there is no base given, like in this problem's right side of the equation, the base is automatically 10.
So, let's re-write that.
Now, let's test a few of the numbers out. For brevity, I already know it's 3. Let's show you why.
Problem 13
If we want to multiply (x^3-3x^2+2x) with (x^3-2x^2+x), then we can set up a diagram shown below. The terms are along the outside. The stuff inside is the result of multiplying each pair of outer terms.
- Example: x^3 times x^3 = x^6 in the top left corner
- Another example: 2x times x = 2x^2 in the bottom right corner.
This is known as the box method to keep track of all the terms multiplied.
Once the table is filled out, we add up each term inside the boxes. Combine like terms if possible. Notice that I color-coded the like terms (eg: the x^3 terms are in green boxes).
The final answer is x^6 - 5x^5 + 9x^4 - 7x^3 + 2x^2
