I believe the answer is 3 minutes
At the 3 minute mark, Maxine will be half way done and Sammie will still have 6 minutes left to mow the grass
<h3>Answer: 6pi radians</h3>
(this is equivalent to 1080 degrees)
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Explanation:
f(x) = sin(x/3)
is the same as
f(x) = 1*sin( (1/3)(x-0) )+0
and that is in the form
f(x) = A*sin( B(x-C) )+D
The letters A,B,C,D are explained below
A = helps find the amplitude
B = 2pi/T, where T is the period
C = determines phase shift (aka left/right shifting)
D = determines vertical shift = midline
All we care about is the value of B as that is the only thing that is connected to the period T
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Compare f(x) = 1*sin( (1/3)(x-0) )+0 with f(x) = A*sin( B(x-C) )+D and we see that B = 1/3, so,
B = 2pi/T
1/3 = 2pi/T
1*T = 3*2pi ... cross multiply
T = 6pi
The period is 6pi radians. This is equivalent to 1080 degrees. To convert from radians to degrees, you multiply by (180/pi).
First of all, the identity property of multiplication (which is what this is I'm assuming) is that the number 1 multiplied by any other number is that number itself. (An example would be 2 multiplied by 1, which would be two) So in this problem, this rule applies too, since 2/3 multiplied by 1 would be 2/3!
Hope this helped :)
<h3>
Answer:</h3>
Any 1 of the following transformations will work. There are others that are also possible.
- translation up 4 units, followed by rotation CCW by 90°.
- rotation CCW by 90°, followed by translation left 4 units.
- rotation CCW 90° about the center (-2, -2).
<h3>
Step-by-step explanation:</h3>
The order of vertices ABC is clockwise, as is the order of vertices A'B'C'. Thus, if reflection is involved, there are two (or some other even number of) reflections.
The orientation of line CA is to the east. The orientation of line C'A' is to the north, so the figure has been rotated 90° CCW. In general, such rotation can be accomplished by a single transformation about a suitably chosen center. Here, we're told there is <em>a sequence of transformations</em> involved, so a single rotation is probably not of interest.
If we rotate the figure 90° CCW, we find it ends up 4 units east of the final position. So, one possible transformation is 90° CCW + translation left 4 units.
If we rotate the final figure 90° CW, we find it ends up 4 units north of the starting position. So, another possible transformation is translation up 4 units + rotation 90° CCW.
Of course, rotation 90° CCW in either case is the same as rotation 270° CW.
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We have described transformations that will work. What we don't know is what is in your drop-down menu lists. There are many other transformations that will also work, so guessing the one you have available is difficult.
I think you meant to add more to your question (posting the specific problem).
In general, one special right triangle is the <span>45°-45°-90° triangle, in which both legs are congruent and the hypotenuse = √2 * the length of the leg. if you happen to not have the length of the leg, the formula for finding the leg is: leg = hypotenuse / √2
Another special right triangle is the </span><span>30°-60°-90° triangle. With this kind of triangle the length of the hypotenuse is twice the length of the shorter leg. The length of the longer leg is √3 times the length of the shorter leg.
hypotenuse = 2 * shorter leg
longer leg = √3 * shorter leg</span>
