Mathematics, 04.10.2021 14:00 Joseph17Peralta

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Answer from: Quest

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2

Answer from: Quest

x= -3 and $x=\frac{-3+/-3i\sqrt{3} }{2}$

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

$(x^3-a^3)=$ $(x-a)(x^2+ax+a^2)$

where a is the cube root of $a^3$ .

here this is 27 and the cube root of 27 is 3. so we write using the form:

$(x-3)(x^2+(3)x+3^2)\\(x-3)(x^2+3x+9)$ .

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

$x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}$

where a = 1, b=3, and c=9

$x=\frac{-3+/-\sqrt{3^2-4(1)(9)} }{2(1)} \\x=\frac{-3+/-\sqrt{9-36)} }{2} \\x=\frac{-3+/-\sqrt{-27)} }{2}\\x=\frac{-3+/-3i\sqrt{3} }{2}$

this cubic has two complex roots.

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

Answer from: Quest

i got 10.28 but that rounds up to 10.3

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