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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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Figure lmno is a parrellelogram The sum of measures of angles l and m is

snow_tiger [21]

Answer:

l+m = 180°{being co-interior angle}

Step-by-step explanation:

7 0

3 years ago

When an amount of heat Q (in kcal) is added to a unit mass (kg) of a

lisov135 [29]

Answer:

The change in temperature per minute for the sample, dT/dt is 71. $\overline {6}$ °C/min

Step-by-step explanation:

The given parameters of the question are;

The specific heat capacity for glass, dQ/dT = 0.18 (kcal/°C)

The heat transfer rate for 1 kg of glass at 20.0 °C, dQ/dt = 12.9 kcal/min

Given that both dQ/dT and dQ/dt are known, we have;

$\dfrac{dQ}{dT} = 0.18 \, (kcal/ ^{\circ} C)$

$\dfrac{dQ}{dt} = 12.9 \, (kcal/ min)$

Therefore, we get;

$\dfrac{\dfrac{dQ}{dt} }{\dfrac{dQ}{dT} } = {\dfrac{dQ}{dt} } \times \dfrac{dT}{dQ} = \dfrac{dT}{dt}$

$\dfrac{dT}{dt} = \dfrac{\dfrac{dQ}{dt} }{\dfrac{dQ}{dT} } = \dfrac{12.9 \, kcal / min }{0.18 \, kcal/ ^{\circ} C } = 71.\overline 6 \, ^{\circ } C/min$

For the sample, we have the change in temperature per minute, dT/dt, presented as follows;

$\dfrac{dT}{dt} = 71.\overline 6 \, ^{\circ } C/min$

8 0

3 years ago

A soccer ball has an interior diameter of 22 cm. How many cubic centimeters of air does a soccer ball

Delvig [45]

Answer:

Volume of soccer ball = 5,572.45 Cm³ (Approx)

Step-by-step explanation:

Given:

Diameter of soccer ball = 22 Cm

Radius of soccer ball = 22 Cm / 2 = 11 Cm

Find:

Volume of soccer ball = ?

Computation:

$Volume\ of\ soccer\ ball = \frac{4}{3} \pi r^3\\\\ Volume\ of\ soccer\ ball = \frac{4}{3} \times\frac{22}{7} \times 11^3\\\\ Volume\ of\ soccer\ ball = 5,572.45332$