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3 years ago

What is the 3rd term in the sequence?

Mathematics

1 answer:

makvit [3.9K]3 years ago

4 0

Answer:

Step-by-step explanation:

To find the third term substitute n = 3 into the n th term formula

a(3) = $\frac{3}{2}$ $(-2)^{3-1}$

= $\frac{3}{2}$ $(-2)^{2}$

= $\frac{3}{2}$ × 4 = 6

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Point Y is in the interior of ∠XWZ. Given that (ray) WX and (ray) WZ are opposite rays and m∠XWY = 4(m∠YWZ), what is m∠YWZ?

yuradex [85]

Answer:

m∠YWZ = 36°

Step-by-step explanation:

* Lets explain how to solve the problem

- Point Y is in the interior of ∠XWZ

- Rays WX and WZ sre opposite rays

- That means rays WX and WZ formed a straight angle

- m∠XWY = 4(m∠YWZ)

- We need to find the m∠YWZ

* Lets solve the problem

∵ Rays WX and WZ are opposite rays

∴ ∠XWZ is a straight angle

∵ The measure of the straight angle is 180°

∴ m∠XWZ = 180°

- Point Y is in the interior of ∠XWZ

∴ m∠XWZ = m∠XWY + m∠YWZ

∵ m∠XWY = 180°

∴ m∠XWY + m∠YWZ = 180° ⇒ (1)

∵ m∠XWY = 4(m∠YWZ) ⇒ (2)

- Substitute equation (2) in equation (1)

- That means replace m∠XWY by 4(m∠YWZ)

∴ 4(m∠YWZ) + m∠YWZ = 180

∴ 5(m∠YWZ) = 180

- Divide both sides by 5

∴ m∠YWZ = 36°

6 0

4 years ago

Plz help me with this

Agata [3.3K]

Answer:

It's the first option.

Step-by-step explanation:

y = cos x transformed to cos (x - π/2) moves the graph π/2 units to the right.

Multiplying by 3 to give 3 cos(x - π/2) stretches the graph 3 units parallel to the y-axis and adding 3 to this moves the graph up 3 units.

So the required equation is y = 3(cos x - π/2) + 3.

3 0

3 years ago

F(x) = lnx/x

My name is Ann [436]

$f(x) = \frac{lnx}{x}$

(a) $f'(x) = \frac{d}{dx}[\frac{lnx}{x}]$
Using the quotient rule:
$f'(x) = \frac{\frac{1}{x} \cdot x - lnx}{x^{2}}$
$f'(x) = \frac{1 - lnx}{x^{2}}$

For maximum, f'(x) = 0;
$\frac{1 - lnx}{x} = 0$
$lnx = 1, x = e$

(b) <em>Deduce:
</em> $e^{x} \geq x^{e}, x > 0$
<em>
Soln:</em> Since x = e is the greatest value, then f(e) ≥ f(x) > f(0)
$\frac{ln(e)}{e} \geq \frac{lnx}{x}$
$\frac{1}{e} \geq \frac{lnx}{x}$ , since ln(e) is simply equal to 1

Now, since x > 0, then we don't have to worry about flipping the signs when multiplying by x.
$\frac{x}{e} \geq lnx$
$x \geq elnx$
$x \geq ln(x^{e})$

Taking the exponential to both sides will cancel with the natural logarithmic function in the right hand side to produce:
$e^{x} \geq e^{ln(x^{e}})$
$e^{x} \geq x^{e}$ , as required.

3 0

3 years ago

Eights rooks are placed randomly on a chess board. What is the probability that none of the rooks can capture any of the other r

erastova [34]

Answer:

The probability is $\frac{56!}{64!}$

Step-by-step explanation:

We can divide the amount of favourable cases by the total amount of cases.

The total amount of cases is the total amount of ways to put 8 rooks on a chessboard. Since a chessboard has 64 squares, this number is the combinatorial number of 64 with 8, $64 \choose 8 .$

For a favourable case, you need one rook on each column, and for each column the correspondent rook should be in a diferent row than the rest of the rooks. A favourable case can be represented by a bijective function $f : A \rightarrow A ,$ with A = {1,2,3,4,5,6,7,8}. f(i) = j represents that the rook located in the column i is located in the row j.

Thus, the total of favourable cases is equal to the total amount of bijective functions between a set of 8 elements. This amount is 8!, because we have 8 possibilities for the first column, 7 for the second one, 6 on the third one, and so on.

We can conclude that the probability for 8 rooks not being able to capture themselves is

$\frac{8!}{64 \choose 8} = \frac{8!}{\frac{64!}{8!56!}} = \frac{56!}{64!}$