The table with greater proportionality is table 3.
<h3>What is constant proportionality?</h3>
The constant of proportionality is the ratio between two directly proportional quantities.
As, the constant proportionality is
k= y/x
For table 1,
k = 1/1 = 2/2 =1
For table 2,
k = 6/1= 12/2 = 2
For table 3,
k = 5/1 = 10/2 = 5
For table 4,
k = 4/1 = 8/2 = 4
Hence, table 3 is with greater proportionality.
Learn more about this constant of proportionality here:
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Parallel sides mean that they are always the same distance from each other and will never touch. Knowing that, let's think of the shapes.
Rectangle: Yes, opposite sides are parallel. The two opposite sides of a rectangle will never touch.
Rhombus: Think of it as a diamond. You can still view it as a rectangle that has the top shifted over a bit. Therefore, yes, opposite sides are parallel because they will never touch.
Square: Is basically the same as the rectangle. Therefore, the answer is yes, opposite sides of squares are parallel.
Parallelogram: The definition of a parallelogram, like in its name, is a four-sided figure with opposite sides parallel. Therefore, yes, parallelograms have opposites sides that are parallel.
Therefore, the answer is all four of them.
Answer:
see explanation
Step-by-step explanation:
(4)
consider the left side
factor the numerator
cosx - cos³x = cosx(1 - cos²x)
cancel sinx on numerator/denominator
= cosxsinx =right side ⇒ verified
(5)
Consider the left side
expand the factors
(1 + cotΘ)² + (1 - cotΘ)²
= 1 + 2cotΘ + cot²Θ + 1 - 2cotΘ + cot²Θ
= 2 + 2cot²Θ
= 2(1 + cot²Θ) ← 1 + cot²Θ = cosec²Θ
= 2cosec²Θ = right side ⇒ verified
(6)
Consider the left side
the denominator simplifies to
cosxtanx = cosx × = sinx
= sinx( + )
= +
= tanx + 1 = right side ⇒ verified
The order of rotational symmetry is the number of times the shape maps onto itself during a rotation of 360°, for example:
- a rectangle has order of rotational symmetry of 2; 180° and 360° rotations will map it onto itself.
- for a regular hexagon has order of rotational symmetry of 6
- for a regular square has order of rotational symmetry of 4
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