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3 years ago

10.6 written as a decimal and a fraction or a mixed number in simplest form

1 answer:

6 0

$10.6 \times \frac{10}{10} = \frac{106}{100} = \frac{53 \times 2}{50\times 2} \\\\ = \frac{53}{50} = \boxed{\bf{1 \frac{3}{50}}}$

and 10.6 is already written as a decimal.

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Determine whether the series is convergent or divergent by expressing sn as a telescoping sum (as in Example 8). [infinity] 6 n2

vekshin1

Answer:

Step-by-step explanation:

given

$\sum\limits^\infty_{n=3}\frac{6}{n^2-1}=\sum\limits^\infty_{n=3}\frac{6}{(n-1)(n+1)}\\\\=\sum\limits^\infty_{n=3}\frac{6}{2}(\frac{1}{n-1}-\frac{1}{n+1})\\\\=\frac{6}{2}\sum\limits^\infty_{n=3}(\frac{1}{n-1}-\frac{1}{n+1})\\\\=3[(\frac{1}{2}-\frac{1}{4})+(\frac{1}{3}-\frac{1}{5})+(\frac{1}{4}-\frac{1}{6})+(\frac{1}{5}-\frac{1}{7})+...]\\\\=3[\frac{1}{2}+\frac{1}{3}]=3[\frac{3+2}{6}]=3[\frac{5}{6}]\\\\=\frac{15}{6}=\frac{5}{3}$

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3 years ago

Help me solve for the right triangle

AleksAgata [21]

Answers:

B = 50

a = 10.9

c = 17.0

================================================

Explanation:

This is a right triangle, so the acute angles are complementary, meaning they add to 90

B+40 = 90

B+40-40 = 90-40

B = 50

Also, because this is a right triangle, we can use trig ratios to compute the missing sides

tan(angle) = opposite/adjacent

tan(40) = a/13

a = 13*tan(40)

a = 10.908

a = 10.9

cos(angle) = adjacent/hypotenuse

cos(40) = 13/c

c*cos(40) = 13

c = 13/cos(40)

c = 17.0

note: make sure your calculator is in degree mode

7 0

3 years ago

Two integers, a and b, have a greatest common factor of 1. If a =12 and b is greater than 35 but no more than 40, what is the va

yarga [219]

Answer: 37

Step-by-step explanation:

a=12

35 < b < 40

$\wedge\ means\ GCF\\a\ \wedge\ b= 1\\12\ \wedge\ 37= 1\\12\ \wedge\ 38= 2\\12\ \wedge\ 39= 3\\$

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2 years ago

Complete this sentence: in a triangle, the angle with the smallest measure is always opposite the

Marta_Voda [28]

Answer:

Complete this sentence: in a triangle, the angle with the smallest measure is always opposite the <u><em>shortest side</em></u>.

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3 years ago

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