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3 years ago

3 / m + 4 - 4 / m = 6 (i) Show that this equation can be written as 6m^2 + 25m+16= 0

Mathematics

2 answers:

dem82 [27]3 years ago

8 0

Answer: Proved Below

Step-by-step explanation: Hence, Proved that is equivalent to

Evgen [1.6K]3 years ago

6 0

Answer:

Proved Below

Step-by-step explanation:

$\sf \frac{3}{m+4} - \frac{4}{m} = 6\\LCM = m(m+4)\\Multiplying \ both \ sides \ by\ m(m+4)\\3m - 4(m+4) = 6m(m+4)\\3m-4m-16 = 6m^2+24m\\-m-16 = 6m^2+24m\\Adding\ m\ to\ both\ sides\\-16 = 6m^2+24m+m\\-16 = 6m^2+25m\\Adding \ 16 \ to \ both \ sides\\0 = 6m^2+25m+16\\OR\\6m^2+25m+16 = 0$

Hence, Proved that $\sf \frac{3}{m+4} - \frac{4}{m} = 6$ is equivalent to $\sf 6m^2+25m+16 = 0$ .

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Dr. Mitchell owns a veterinarian clinic. For a week, he collected data during examinations on the kind of animal a boy or girl h

san4es73 [151]

Answer: A) A boy is 19% more likely than a girl to own a dog than a cat or other animal.

Step-by-step explanation:

Here are the options:

A) A boy is 19% more likely than a girl to own a dog than a cat or other animal.

B) A boy is 33% more likely than a girl to own a dog than a cat or other animal.

C) A boy is 50% more likely than a girl to own a dog than a cat or other animal.

D) A boy is 52% more likely than a girl to own a dog than a cat or other animal.

Boy with a dog = 27

Total animals owned by boys = 27+15+10 = 52

Probability of owning a dog = 27/52 = 0.5192

Girl with dogs = 18

Total animals owned by girls = 18+25+12 = 55

Probability of owning a dog = 18/55 = 0.3273

Therefore, 0.5192 - 0.3273 = 0.1919 = 19.19%

Therefore, A) A boy is 19% more likely than a girl to own a dog than a cat or other animal.

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3 years ago

Find the sum of the convergent series. (round your answer to four decimal places. ) [infinity] (sin(9))n n = 1

Alexus [3.1K]

The sum of the convergent series $\sum_{n=1}^{\infty}~(sin(1))^n$ is 5.31

For given question,

We have been given a series $\sum_{n=1}^{\infty}~(sin(1))^n$

$\sum_{n=1}^{\infty}~(sin(1))^n=sin(1)+(sin(1))^2+...+(sin(1))^n$

We need to find the sum of given convergent series.

Given series is a geometric series with ratio r = sin(1)

The first term of the given geometric series is $a_1=sin(1)$

So, the sum is,

= $\frac{a_1}{1-r}$

= sin(1) / [1 - sin(1)]

This means, the series converges to sin(1) / [1 - sin(1)]

$\sum_{n=1}^{\infty}~(sin(1))^n$

= $\frac{sin(1)}{1-sin(1)}$

= $\frac{0.8415}{1-0.8415}$

= $\frac{0.8415}{0.1585}$

= 5.31

Therefore, the sum of the convergent series $\sum_{n=1}^{\infty}~(sin(1))^n$ is 5.31

Learn more about the convergent series here:

brainly.com/question/15415793

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11 months ago