Answer:
10cos(5x)sin(10x) = 5[sin (15x) + sin (5x)]
Step-by-step explanation:
In this question, we are tasked with writing the product as a sum.
To do this, we shall be using the sum to product formula below;
cosαsinβ = 1/2[ sin(α + β) - sin(α - β)]
From the question, we can say α= 5x and β= 10x
Plugging these values into the equation, we have
10cos(5x)sin(10x) = (10) × 1/2[sin (5x + 10x) - sin(5x - 10x)]
= 5[sin (15x) - sin (-5x)]
We apply odd identity i.e sin(-x) = -sinx
Thus applying same to sin(-5x)
sin(-5x) = -sin(5x)
Thus;
5[sin (15x) - sin (-5x)] = 5[sin (15x) -(-sin(5x))]
= 5[sin (15x) + sin (5x)]
Hence, 10cos(5x)sin(10x) = 5[sin (15x) + sin (5x)]
160 is the first because 1 inches 20 but it says 2 inches so at 40+40+40+40
and the 2nd part is yes he is correct because he converted the inches into feet so i think he is also correct
For a regular tessellation, the shapes can be duplicated infinitely to fill a plane such that there is no gap. The only shapes that can form regular tessellations are equilateral traingle(all sides are equal. This means that it can be turned to any side and it would remain the same), square and regular hexagon. Looking at the given options, we have
Shape Tessellate?
Octagon No
Hexagon Yes
Pentagon No
Square Yes
Triangle No(unless it is specified that it is an equilateral triangle)
The answer is -3x^2+10xy+8y^2
Answer: The required expected value is $3.46.
Step-by-step explanation:
Since we have given that
Number of value of 4 or less are
2,3,4
So, there are 12 in numbers.
So, probability would be
Since Aces are considered as the highest card in the deck.
So, remaining probability would be
Amount paid or value of 4 or less = $165
Amount not paid for other case = $45
So, the expected value would be
Hence, the required expected value is $3.46.
