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)]
Dive correct answers by total questions:
160/200 = 0.80
Multiply by 100 to get percent:
0.80 x 100 = 80%
Answer:
Part 22) The area is
and the perimeter is 
Part 24) The area is
and the perimeter is
Part 26) The area is equal to 
Step-by-step explanation:
Part 22) Find the perimeter and area
step 1
The area of a rectangle is equal to

we have


Remember that
When multiply exponents with the same base, adds the exponents and maintain the base
substitute in the formula


step 2
The perimeter of a rectangle is equal to

we have

substitute in the formula


Part 24) Find the perimeter and area
step 1
The area of triangle is equal to

where


Remember that
When multiply exponents with the same base, adds the exponents and maintain the base
substitute the given values


step 2
Find the perimeter
I will assume that is an equilateral triangle (has three equal length sides)
The perimeter of an equilateral triangle is

where

substitute


Part 26) Find the area
The area of a circle is equal to

where

Remember the property

substitute in the formula the given value


Answer:
2 and 13/60
Step-by-step explanation:
First, we must create a common denominator in the fractions. For the given denominators, it would be 60, so 3/4 would be 45/60 and 8/15 would be 32/60. From here, we can just subtract and get 2 and 13/60.
Hope this helps!