We are to show that the given parametric curve is a circle.
The trajectory of a circle with a radius r will satisfy the following relationship:

(with (x_c,y_c) being the center point)
We are given the x and y in a parametric form which can be further rewritten (using properties of sin/cos):

Squaring and adding both gives:

The last expression shows that the given parametric curve is a circle with the center (0,0) and radius A.
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If a teacher had 48 red pens and the ratio of red to blue pens she owns is 6:1, she will have a total of 56 pens
Let the number of red pens be R and the number of blue pens be B.
R = 48
R / B = 6 / 1
48 / B = 6 / 1
B = 48 / 6
B = 8
Total number of pens = Number of red pens + Number of blue pens
Total number of pens = R + B
Total number of pens = 48 + 8
Total number of pens = 56 pens
Therefore, she has a total of 56 pens
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Answer:
speed of each marble after collision will be 1.728 m/sec
Explanation:
We have given mass of the marble 
Velocity of marble 
Its collides with other marble of mass 25 gram
So mass of other marble 
Second marble is at so 
We have to find the velocity of second marble
From momentum conservation we know that
, here v is common velocity of both marble after collision
So 
v = 1.428 m /sec
So speed of each marble after collision will be 1.728 m/sec