If you have a stack of pennies without counting them how do you know if there is an even or odd number of them

Mathematics

1 answer:

zavuch27 [327]3 years ago

5 0

If I have a stack of pennies. And I have to tell that without counting whether there are even number of pennies or odd.

Even numbers are the numbers which are divisible by 2 and odd numbers are the numbers which are not divisible by 2.

Then I will put the given pennies in 2 rows and then I will match them to form a pair of 2 pennies. After matching, if there is 1 penny left over, then there is an odd number of pennies and if all the pennies have a match,then there is an even number of pennies.

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A particular curve is represented parametrically by x=cost, y=−sint, t∈[0,2π]. (a) As t increases on [0,2π], in which direction

cestrela7 [59]

Answer:

a) clockwise sense

b) x² + y² = 1

c) y ∈ [0,1]

Step-by-step explanation:

a) x = cos (t) y = -sin (t)

for t ∈ [ 0 , 2π ]

for t = 0 point P is x = cos (0) = 1 y = -sin (0) y = 0

The point is on the x axis

Now let´s see what happens for t = π/4

x = cos (π/4) x = √2/2 and y = - sin (π/4) y = - √2/2

Note π/4 is 45°

The coordinates of the new point P ´(t = π/4) are in the fourth quadrant

that means the point is moving clockwise sense.

b) x = cos(t)

y = -sin(t)

Squaring on both sides of each equation we get:

x² = cos²t

y² = sin²(t)

Adding side by side

x² + y² = cos²t + sin²t

x² + y² = 1

Values for y are y ( 0 , 1)

8 0

3 years ago

which of the three sets could not be the lengths of the sides of a triangle {6,10,12} {5,7,10} {4,4,9} {2,3,3}

Phoenix [80]

So for this, we will be applying the Triangle Inequality Theorem, which states that the sum of 2 sides must be greater than the third side for it to be a triangle. If any inequality turns out to be false, then the set cannot be a triangle.

$A+B>C\\A+C>B\\B+C>A$