Find the value of each variable in simplest radical form

Mathematics

1 answer:

kipiarov [429]4 years ago

6 0

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Which number comes next in this series? 1/64, 1/32, 1/16, 1/8, 1/4, 1/2, ?

alexgriva [62]

This is a geometric sequence, with the first term: 1/64

The common ratio is found through the ratio of the first two terms and the second and third term.
$\frac{\frac{1}{32}}{\frac{1}{64}} = \frac{\frac{1}{16}}{\frac{1}{32}}$
$\frac{1}{32} \cdot 64 = \frac{1}{16} \cdot 32$

Since there is a common difference of 2, we can generalise this sequence to find the nth term:
$T_n = ar^{n-1}$
a is the first term, r is the common ratio, and n is the nth term in the sequence.

$T_n = \frac{1}{64} \cdot 2^{n-1}$
Substituting n = 7, we get:
$T_7 = \frac{1}{64} \cdot 2^{7 - 1}$
$T_7 = \frac{1}{64} \cdot 64$
$T_7 = \frac{64}{64} = 1$

Thus, the next term in the sequence is 1.

6 0

3 years ago

As you are walking down a path, you see a sign telling the path has a 2% grade (ie., a rise of 2 metres for a horizontal change

Leni [432]

Answer:

Option (A)

Step-by-step explanation:

It has been given in this question that sign telling path has a 2% grade.

2% grade means a rise of 2 meters for a horizontal change of 100 m (As given in the figure attached).

All the trigonometric ratios for the angle θ between the path and the horizontal are,

Sinθ = $\frac{\text{Opposite side}}{\text{Hypotenuse}}$