Arcsin x + arcsin 2x = π/3
arcsin 2x = π/3 - arcsin x
sin[arcsin 2x] = sin[π/3 - arcsin x] (remember the left side is like sin(a-b)
2x = sinπ/3 cos(arcsin x)-cosπ/3 sin(arc sinx)
2x = √3/2 . cos(arcsin x) - (1/2)x)
but cos(arcsin x) = √(1-x²)===>2x = √3/2 .√(1-x²) - (1/2)x)
Reduce to same denominator:
(4x) = √3 .√(1-x²) - (x)===>5x = √3 .√(1-x²)
Square both sides==> 25x²=3(1-x²)
28 x² = 3 & x² = 3/28 & x =√(3/28)
120 is the answer to your question
Answer: 3.5 h
Step-by-step explanation:
<u>1. Data:</u>
a) s = 740 miles / h
b) d = 2,567 miles
c) t = ?
<u>2. Equation:</u>
<u>3. Solution:</u>
- Solve the equation for t:
s = d / t ⇒ t = d / s
t = 2,567 miles / (740 miles/h) ≈ 3.47 h ≈ 3.5 h
The function is L = 10m + 50
Here, we want to find out which of the functions is required to determine the number of lunches L prepared after m minutes
In the question, we already had 50 lunches prepared
We also know that he prepares 10 lunches in one minute
So after A-lunch begins, the number of lunches prepared will be 10 * m = 10m
Adding this to the 50 on ground, then we have the total L lunches
Mathematically, that would be;
L = 10m + 50
350(1+0.75)t (add the numbers)
350*1.75t (Calculate the product)
612.5 t
