Let <em>a</em> be the first term in the sequence. If <em>r</em> is the ratio between consecutive terms, then the second term is <em>ar</em>, the third term is <em>ar </em>^2, the fourth is <em>ar</em> ^3, and so on, up to the <em>n</em>-th term <em>ar</em> ^(<em>n</em> - 1).
So the third, fourth, and fifth terms are such that
<em>ar</em> ^2 = 18
<em>ar</em> ^3 = 27
<em>ar</em> ^4 = 81/2
Solve for <em>a</em> and <em>r</em> :
(<em>ar</em> ^3) / (<em>ar</em> ^2) = 27/18 => <em>r</em> = 3/2
<em>ar</em> ^2 = <em>a</em> (3/2)^2 = 9/4 <em>a</em> = 18 => <em>a</em> = 8
Then the <em>n</em>-th term in the sequence is
<em>ar</em> ^(<em>n</em> - 1) = 9 (3/2)^(<em>n</em> - 1)
You can rewrite this by first rewriting 9 = 3^2, then
9 (3/2)^(<em>n</em> - 1) = 3^2 * 3^(<em>n</em> - 1) / 2^(<em>n</em> - 1) = 3^(<em>n</em> + 1)/2^(<em>n</em> - 1)
Answer:
56 cm
Step-by-step explanation:
By using a^2 + b^2 = c^2, you can determine that the slanted line of the trapezoid is ~11.6, which rounds to 12 cm.
12 + 14 + 24 + 6 = 56
Answer: 1/16
Step-by-step explanation: It's important to understand that the two spins are called independent events because the outcome of the first spin does not affect the outcome of the second spin.
To find the probability of independent events, we first find the probability of each event, then we multiply the probabilities together.
Since there is one 4 on the spinner and four possible outcomes, each of which is equally likely, the probability of spinning a 4 is 1/4.
This mens that 1/4 is the probability of
getting a 4 on the second spin too.
Now we multiply.
1/4 x 1/4 gives us 1/16.
So the probability of spinning a 4 twice is 1/16.
It means Mu. It came from ancient greek alphabet and <span>µ is commonly used by scientists in different academic fields. It's not used in common speech.</span>
Answer:
Step-by-step explanation:
This equation is more intimidating than the problem you have to solve.
You know that the sine of everything is always between -1 and +1. So for the entire expression to be >= 0, the a*tan(pi/8) bit has to be 1 at least. Given this, we can forget about the sin(...) term of the equation for the remainder of solving it.
You already figured out that tan(pi/8) is sqrt(2)-1.
So what we're saying is a * (sqrt(2) - 1) has to be 1 at least.
If we solve a(sqrt(2)-1) >= 1 for a we get:
a = 1/(sqrt(2)-1)
