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2 years ago

Prove: The difference of the reciprocals

Mathematics

1 answer:

murzikaleks [220]2 years ago

7 0

Step-by-step explanation:

let two successive integers n, n+1

difference of the reciprocals:

$\frac{1}{n}-\frac{1}{n+1} \\=\frac{(n+1)-n}{(n)(n+1)}\\=\frac{1}{(n)(n+1)}\\=\frac{1}{(n)}\frac{1}{(n+1)}\\$

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Someone please help me answer this!!

Liula [17]

Answer:

100 in is the answer.

Step-by-step explanation:

a = 60 in

b = 80 in

c = ?

According to the Pythagorean theorem,

a² + b² = c²

60² + 80² = c²

3600 + 6400 = c²

c² = 10000

c = 100 in

∴ the distance between the opposite corners of the bed is 100 in

7 0

2 years ago

A person runs 1/8 mile in 1/64 hour.<br> The person's speed is (BLANK) miles per hour.

snow_tiger [21]

Answer: The person's speed is 8 miles per hour.

Step-by-step explanation:

To solve we want to convert the $\frac{1}{8}$ and $\frac{1}{64}$ proportionally for the number of miles per hour. We know that multiplying a fraction by its reciprocal will equal 1. So let's do that for the value of the hour.

$\frac{1}{64}$ × $\frac{64}{1} =\frac{64}{64} =1$

Since we multiplied that to the number of hours we must also do that for the number of miles.

$\frac{1}{8}$ × $\frac{64}{1} =\frac{64}{8} =8$

7 0

1 year ago

What is the next term in the sequence below?

andreyandreev [35.5K]

Answer: Option a.

Step-by-step explanation:

1. The sequence shown in the problem is a Geometric sequence, because it has a common ratio. This means that when you multiply one of those numbers by the common ratio, you obtain the next number.

2. Then, you can calculate the common ratio as following:

$r=\frac{108}{-324}=-\frac{1}{3}$

3. Therefor, the next term is:

$(12)(-\frac{1}{3})=-4$

7 0

2 years ago

Read 2 more answers

A survey of

Zina [86]

Answer:

0.0208<p<0.0592

Step-by-step explanation:

-Given the sample size is 400 and the desired proportion is 16.

-The confidence interval can be determined as follows:

$CI=\hat p\pm z\sqrt{\frac{\hat p(1-\hat p}{n}}\\\\\hat p=x/n=16/400=0.04$

#We the use this proportion to find the CI at 95%:

$CI=0.04\pm 1.96\times \sqrt{\frac{0.04(1-0.04)}{400}}\\\\=0.04\pm 0.0192\\\\=[0.0208,0.0592]$

Hence, the 95% confidence interval is 0.0208<p<0.0592

7 0

3 years ago

Determine whether the relationship between the circumfrance of a circle and its diameter is a direct variation. If so, identify

kipiarov [429]

Answer:

The relationship between the circumference of a circle and its diameter represent a direct variation and the constant of proportionality is equal to the constant $\pi$

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y=kx$

where K is the constant of proportionality

In this problem we know that

The circumference of a circle is equal to

$C=\pi D$

therefore

the relationship between the circumference of a circle and its diameter is a direct variation and the constant of proportionality is equal to the constant $\pi$

3 0

3 years ago