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4 years ago

Determine the explicit form of the function that describes the sequence below.

Mathematics

1 answer:

docker41 [41]4 years ago

3 0

Answer:

Step-by-step explanation:

This is a geometric sequence with n th term

$a_{n}$ = a $(r)^{n-1}$

Where a is the first term and r is the common ratio

r = $\frac{24}{16}$ = $\frac{36}{24}$ = $\frac{54}{36}$ = $\frac{3}{2}$ , hence

f(n) = 16 $(\frac{3}{2}) ^{(n-1)}$ → C

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Pythagorean theorem!! pls help me

zhuklara [117]

The unknown side is part of the 90 degree angle, so it is not the hypotenuse.

Using the Pythagorean theorem:

x = sqrt(14^2 - 10^2)

x = sqrt(196-100)

x = sqrt(96)

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7 0

3 years ago

While Brendan is vacationing with his family at the cabin, they take a motorboat on the river. The motorboat travels

taurus [48]

Part 1: The speed of the boat traveling downstream is $(18+w)$ miles per hr.

The speed of the boat traveling upstream is $(18-w)$ miles per hr.

Part 2: The speed of the current is 4 miles per hour.

Explanation:

Part (1): The motorboat travels 18 miles per hour in still.

Let w represents the speed of the current.

When the boat travels downstream, the speed of the current will get added to the speed of the boat.

Thus, the expression can be written as $(18+w)$ miles per hr

Hence, the speed of the boat traveling downstream is $(18+w)$ miles per hr.

When the boat travels upstream, the speed of the current will get subtracted to the speed of the boat.

Thus, the expression can be written as $(18-w)$ miles per hr.

Hence, the speed of the boat traveling upstream is $(18-w)$ miles per hr.

Part (2): The boat travels 49 miles upstream in the same time it takes to travel 77 miles downstream.

The distance formula is given by $distance $=$ speed $\times$ time$

Substituting, we have,

$49=(18-w)t\\49=18t-wt$ ---------------(1)

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Solving using elimination method,

$49=18 t-w t\\77=18 t+w t\\-------\\126=36t$

Dividing both sides by 36, we have,

$t=3.5$

Substituting $t=3.5$ in $49=18 t-w t$ , we get,

$49=18(3.5)-w (3.5)\\$

$49=63-3.5w\\$

$-14=-3.5w\\$

$4=w$

Thus, the speed of the current is $w=4$ miles per hour.

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4 years ago

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Maksim231197 [3]

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3 years ago

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lilavasa [31]

Answer:

See proof below

Step-by-step explanation

cot^2(x) - csc^2(x) = -1

In trigonometry identity

cot^2x = cos²x/sin²x

Csc²x = 1/sin²x

Substitute into the original expression

cos²x/sin²x - 1/sin²x

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Recall that sin²x+cos²x = 1

Sin²x = 1-cos²x

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Substitute ** into *

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3 years ago

What is the rvalue of the following data to three decimal places?

Elina [12.6K]

Answer:

Step-by-step explanation:

because I know and took the test

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3 years ago