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3 years ago

Find the common difference of the arithmetic sequence shown.

Mathematics

2 answers:

konstantin123 [22]3 years ago

7 0

Answer:

Option B is correct.

The common difference of the arithmetic sequence is, $\frac{1}{8}$

Step-by-step explanation:

Common difference(d) states that take any pair of successive numbers, and subtract the first from the second.

Given the arithmetic sequence:

1/4 , 3/8, 1/2...

⇒ $(a_1)$ = 1/4, $a_2 = \frac{3}{8}$ , $a_3 = \frac{1}{2}$ and so on..

By definition of common difference

$a_2 -a_1 = \frac{3}{8}-\frac{1}{4} = \frac{3-2}{8} = \frac{1}{8}$

$a_3 -a_2= \frac{1}{2}-\frac{3}{8} = \frac{4-3}{8} = \frac{1}{8}$ and so on..

⇒ $d = a_2-a_1 = a_3-a_2=.....= \frac{1}{8}$

Therefore, the common difference of the arithmetic sequence is, $\frac{1}{8}$

Natalija [7]3 years ago

6 0

Answer:

1/8

Step-by-step explanation:

To find the common difference, subtract the first term (1/4) from the second term (3/8); it's 1/8. Notice that if you subtract 3/8 from 1/2 as a check, you obtain 1/8 again.

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2 years ago

The surface area of a given cone is 1,885.7143 square inches. What is the slang height?

kap26 [50]

Answer:

If $r >> h$ , the slang height of the cone is approximately 23.521 inches.

Step-by-step explanation:

The surface area of a cone (A) is given by this formula:

$A = \pi \cdot r^{2} + 2\pi\cdot s$

Where:

$r$ - Base radius of the cone, measured in inches.

$s$ - Slant height, measured in inches.

In addition, the slant height is calculated by means of the Pythagorean Theorem:

$s = \sqrt{r^{2}+h^{2}}$

Where $h$ is the altitude of the cone, measured in inches. If $r >> h$ , then:

$s \approx r$

And:

$A = \pi\cdot r^{2} +2\pi\cdot r$

Given that $A = 1885.7143\,in^{2}$ , the following second-order polynomial is obtained:

$\pi \cdot r^{2} + 2\pi \cdot r -1885.7143\,in^{2} = 0$

Roots can be found by the Quadratic Formula:

$r_{1,2} = \frac{-2\pi \pm \sqrt{4\pi^{2}-4\pi\cdot (-1885.7143)}}{2\pi}$

$r_{1,2} \approx -1\,in \pm 24.521\,in$

$r_{1} \approx 23.521\,in \,\wedge\,r_{2}\approx -25.521\,in$

As radius is a positive unit, the first root is the only solution that is physically reasonable. Hence, the slang height of the cone is approximately 23.521 inches.

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2 years ago

What is 4 and 1/2 times 2 ????

strojnjashka [21]

4 1/2 times 2 equals to 9.

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answer is 9

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2 years ago

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