What are the coordinates of the image of vertex R after a reflection across the y-axis?
2 answers:
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Answer:
Step-by-step explanation:
The identities you need here are:
and
You also need to know that
x = rcosθ and
y = rsinθ
to get this done.
We have
r = 6 sin θ
Let's first multiply both sides by r (you'll always begin these this way; you'll see why in a second):
r² = 6r sin θ
Now let's replace r² with what it's equal to:
x² + y² = 6r sin θ
Now let's replace r sin θ with what it's equal to:
x² + y² = 6y
That looks like the beginnings of a circle. Let's get everything on one side because I have a feeling we will be completing the square on this:
Complete the square on the y-terms by taking half its linear term, squaring it and adding it to both sides.
The y linear term is 6. Half of 6 is 3, and 3 squared is 9, so we add 9 in on both sides:
In the process of completing the square, we created within that set of parenthesis a perfect square binomial:
And there's your circle! Third choice down is the one you want.
Fun, huh?
Answer:
<em>A. (C+D)^2 is the largest expression</em>
Step-by-step explanation:
<u>Squaring Properties </u>
The square of a number N is shown as N^2 and is the product of N by itself, i.e.
If N is positive and less than one, its square is less than N, i.e.
If N is greater than one, its square is greater than N
We have the following information: C and D represent two different school populations, C > D, and C and D must be positive. We can safely assume C and D are also greater or equal than 1. Let's evaluate the following expressions to find out which is the largest
A. (C+D)^2
Expanding
Is the sum of three positive quantities. This is the largest of all as we'll prove later
B. 2(C+D)
The extreme case is when C=2 and D=1 (recall C>D). It results:
2(C+D)=2(3)=6
The first expression will be
(3)^2=9
Any other combination of C and D will result smaller than the first option
C.
By comparing this with the first option, we see there are two equal terms, but A. has one additional term 2CD that makes it greater than C.
D.
The expression can be written as
(C+D)(C-D)
Comparing with A.
The subtracting factor (C-D) makes this product smaller than A which has two adding factors.
Thus A. is the largest expression
Check the picture below.
so the volume of the smaller cube will just be (1/3)³.
how many of those cubes will take to fill up the larger cube?
namely
how many times does (1/3)³ go into 44?
