Can someone match these in order correctly for me? Please do it in text not in images I can't see those as those are blocked for
me!
1 answer:
Answers:
- 2^3 = 8
- 3^2 = 9
- 3^3 = 27
- 4^3 = 64
- 5^2 = 25
- 8^2 = 64
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Explanation:
The notation 5^2 is the same as writing
The second number is the exponent and it tells us how many copies of the base to multiply together. In the example 5^2, we have two copies of 5 multiplied to get 5^2 = 5*5 = 25
As another example, 4^3 = 4*4*4 = 64. We have three copies of 4 multiplied due to the exponent 3. You can use a calculator for this, but I recommend doing this by hand to get practice.
Note how 4^3 = 64 and 8^2 = 64. So 64 is used twice (which is why we have two tiles labeled "64").
The tiles labeled 9, 12, 10, and 16 are never used since they don't have any matching exponential expression.
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Answer:
The equation for circle of radius centered at the point
is:
Step-by-step explanation:
To derive this equation, we need the formula for the distance between two points in the plane. If the point is given by its cartesian coordinates, we can use the Pythagorean theorem to find what the distance between the points is.
Lets say we have two points, one given by cartesian coordinates P:(x,y) and the other given by cartesian coordiantes C:(h,k)
(see diagram)
We can see that
and by the pythagorean theorem we have:
Where is the distance between the points
Now, combining the last three equations we find:
We know that the definition of a circle is the locus of points that are at a distance r from a point called the center of the circle. if we take C:(h,k) as the center of the circle, and , the last equation becomes:
And that is the result we wanted.
