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)]
Answer:
27
Step-by-step explanation:
The equation is a onestep equation, so in order to find the variable, follow these steps:
d - 4 = 23
In order to isolate the variable or get the variable by itself, you need to get rid of the constants around it or the numbers without a variable. In order to do that for this equation, you'll need to do the inverse of subtracting 4, which would be adding four to both sides.
Adding 4 to positive 23 will give you the answer of 27;
d = 27
Therefore, the variable d equals 27
Hope this helps!
Answer:
its the first graph in the first one and the same thing with the second graph in the number 2 pleaes brailnliest
Step-by-step explanation:
Answer:
Step-by-step explanation:
∵ The quadratic equation form is :
y = [1/2(b - k)] (x - a)² + (b + k)/2
Where (a , b) is the focus and directrix y = k
∵ The focus is (4 , -3) and directix is y = -6
∵ 
∴ 
∴
another way:
Assume that (x , y) is the general point on the parabola
∵ The distance between the directrix and (x , y) = the distance between the focus and (x , y)
By using the distance rule:
∵ (y - -6)² = (x - 4)² + (y - -3)² ⇒ (y + 6)² = (x - 4)² + (y + 3)
∴ y² + 12y + 36 = (x - 4)² + y² + 6y + 9
∴ 12y - 6y = (x - 4)² + 9 - 36
∴ 6y = (x - 4)² - 27 ⇒ ÷ 6
∴ y = 1/6 (x - 4)² - 9/2
Answer:
If Lawrence has 24 beads and divided them into 4 groups you want to see how many he put into each group first
To do this we are going to take 24/4=6
Each group has 6 in it
If he gave one group to his sister, than he gave 6 beads to his sister
Now we want to take 6 away from 24 to find out how many he has left
24-6=18
He now has 18 beads
Hope this helps ;)
