Answer:
3610
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
The first integral has a well-known beta function representation, so the second one should too. The beta function itself is defined as
and satisfies the identity
Later on, we'll also use the so-called reflection formula for the gamma function; for non-integer z,
as well as the identity
Replace in both integrals, so that
Now replace :
So, the original integral (which I condense here to a double integral) is
Problem 10
The two functions <u>are inverses</u> of each other. Why? Because we can think of f(x) = (x-7)/(-2) as y = (x-7)/(-2).
Swap x and y to get x = (y-7)/(-2). Solving for y leads to y = -2x+7 showing that g(x) = -2x+7 is the inverse of f(x) = (x-7)/(-2). This process can be done in reverse to get the same result.
===================================================
Problem 11
y = a(6)^(t/2)
y = a( 6^(1/2) )^t
y = a(2.4494897)^t
y = a( b )^t
where b = 6^(1/2) = 2.4494897 approximately
Set b equal to 1+r and solve for r
1+r = 2.4494897
r = 2.4494897-1
r = 1.4494897
This rounds to about r = 1.45
The r value is the decimal form of the percentage, which means we move the decimal point over two spots to the right to get 145% approximately
Answers:
The equation is roughly y = a(1 + 1.4494897)^t
The growth rate is approximately 145%
===================================================
Problem 12
You have the correct answer. Nice work.
===================================================
Problem 13
You are very close to the correct answer. However, you're missing the base of the log.
The answer should be . So you'll need to write in a small "49" under the log.
The general rule is that exponential equations in the form are equivalent to the log version of . For each equation, b is the base. The idea of logs is to isolate the exponent.
Answer:
10 and 18
Step-by-step explanation:
a + 2b = 46
A + 2(b+8) = 46
b + 2b + 16 = 46
3b+ 16 = 46
3b = 30
b = 10
That’s the first number.
b is 10 so a is 10+8 = 18 because it’s 8 more then the other number.
b + 2a = 46
(10) + 2(18) = 46
10 + 36 = 46
46 = 46