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)
Answer:
4/6
Step-by-step explanation:
you multiply until both numbers have the same denominator so 1/7 times 6/6 equals 6/42 and multiply 4/6 times 7/7 it would be 28/42 so the answer would be that 4/6 is greater.
Answer:
x = 4, y = 4 or you can say (4, 4)
The algebraic expression is: x% * 100
<h3>How to translate the expression?</h3>
The statement is given as:
How much x% of sugar syrup can you make if you have 100 grams of sugar?
The amount of sugar is given as:
100 grams
So, the algebraic expression is:
x% * 100
Read more about algebraic expression at:
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Answer:
$172,984.44
Step-by-step explanation:
We can use the formula
to compute the final amount
Here P is the principal amount, the original deposit = $25,000
r is the annual interest rate = 6.5% = 0.065 in decimal
n is the number of times the compounding takes place. Here it is quarterly so it is 4 times a year
t is the number of time periods ie 30 years
A is the accrued amount ie principal + interest
Computing different components,
Therefore
