Entropy can be thought of as a measure of a system's disorder: a lower degree of disorder implies lower entropy, and vice versa. for example, a highly ordered ice crystal has a relatively low entropy, whereas the same amount of water in a much less ordered state, such as water vapor, has a much higher entropy. entropy is usually denoted by s, and has units of energy divided by temperature (j/k). for an isothermal process (the temperature of the system remains constant as it exchanges heat with its surroundings), the change in a system's entropy is given by δs=qt, where q is the amount of heat involved in the process and t is the absolute temperature of the system. the heat q is positive if thermal energy is absorbed by the system from its surroundings, and is negative if thermal energy is transferred from the system to its surroundings.

x = 7

step-by-step explanation:

equating the expression for area to the given area

2x² - 7x - 4 = 45 ( subtract 45 from both sides )

2x² - 7x - 49 = 0 ← in standard form

to factor consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × - 49 = - 98 and sum = - 7

the factors are - 14 and + 7

use these factors to split the middle term

2x² - 14x + 7x - 49 = 0 ( factor the first/second and third/fourth terms )

2x(x - 7) + 7(x - 7) = 0 ← factor out (x - 7)

(x - 7)(2x + 7) = 0

equate each factor to zero and solve for x

x - 7 = 0 ⇒ x = 7

2x + 7 = 0 ⇒ 2x = - 7 ⇒ x = -

thus the positive value for x is x = 7

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