Mathematics, 11.08.2019 03:10 Rinjo

Is this correct? the writing in red is all my work. it's about sigma notation.

Answers: 2

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Answer from: matt16913

Step-by-step explanation:

OK. It's an arithmetic sequence:

$a_1=20,\ a_2=18.5,\ a_3=17,\ ...\\\\a_1=20,\ d=-1.5$

The explicit formula of an arithmetic sequence:

a_n=a_1+(n-1)d

Substitute:

a_n=20+(n-1)(-1.5)=20-1.5n+1.5=21.5-1.5n

The sigma notation of the sum of the first ten terms:

$\sum\limits_{n=1}^{10}(21.5-1.5n)$

What are your mistakes:

$\sum\limits_{n=20}^{6.5}\to\boxed{n=20},\ \boxed{6.5}$

The first ten terms, not from 20th to 29th (you wrote 6.5?)

$\sum\limits_{n=1}^{10} - \text{the sum for n = 1 to n = 10}$

Answer from: kaylastronaut

$\boxed{\displaystyle \sum_{k=1}^{10}(21.5 - 1.5n)}$

Step-by-step explanation:

If you have an arithmetic sequence

a₁ + a₂ + a₃ + … + aₙ

the general sigma notation for the sum of the first n terms is

$\displaystyle \sum_{k=1}^{n} a_{k}\\k \text{ is the index or counter}\\n \text{ is the number of the last term}\\a_{k} \text{ is the general formula for each term}$

k = 1 means that you start at the first term and keep incrementing until k = n.

The formula for the nth term of an arithmetic sequence is

aₙ = a₁ + (n - 1)d

In your sequence,

a₁ = 20 and d= -1.5, so

aₙ = 20 - 1.5(n - 1) =20 - 1.5n + 1.5 = 21.5 - 1.5n

Thus, the sigma notation for your sequence is

$\boxed{\displaystyle \sum_{k=1}^{10}(21.5 - 1.5n)}$

Answer from: Quest

Aline graph should be used

Answer from: Quest

"it's not the heat, it's the humidity". that's a partly valid phrase you may have heard in the summer, but it's actually both. the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature. this has important considerations for the human body's comfort. when the body gets too hot, it begins to perspire or sweat to cool itself off. if the perspiration is not able to evaporate, the body cannot regulate its temperature. evaporation is a cooling process. when perspiration is evaporated off the body, it effectively reduces the body's temperature. when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases. in other words, the human body feels warmer in humid conditions. the opposite is true when the relative humidity decreases because the rate of perspiration increases. the body actually feels cooler in arid conditions. there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation:

75% of the temperatures are below what value? how do you know? 75% of the temperatures are above w

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Is this correct? the writing in red is all my work. it's about sigma notation.
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