Mathematics, 17.07.2019 06:28 ksawyer745

Arectangle has one side on the xx-axis and two vertices on the curve y=74+x2. y=74+x2. find the vertices of the rectangle with maximum area.

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Given that a rectangle has one side on the x-axis and two vertices on the curve $y= \frac{7}{4+x^2}$

We find the vertices of the rectangle with maximum area as follows:

Because of the symmetry of the given curve, the base of the retangle is 2x and the height of the rectangle is y.

Thus, the area of the required rectangle is 2xy where $y= \frac{7}{4+x^2}$

Thus, $Area=\frac{14x}{4+x^2}$

For maximum area, we find value of x for which the derivative of the function for the area is equal to zero.

The derivative of the function for the area is given by:

$(Area)'= \frac{14(4-x^2)}{(4+x^2)^2} =0 \\ \\ \Rightarrow4-x^2=0 \\ \\ \Rightarrow x^2=4 \\ \\ \Rightarrow x=\sqrt{4}=2$

Thus, the area is maximum when x = -2 and x = 2

When x = -2,

$y= \frac{7}{4+(-2)^2}= \frac{7}{4+4} = \frac{7}{8}$

Similarly, when x = 2,

$y= \frac{7}{4+(2)^2}= \frac{7}{4+4} = \frac{7}{8}$

Therefore, the required vertices are: $(-2,0),\ \left(-2, \frac{7}{8} \right), \ \left(2, \frac{7}{8}\right), \ (2, 0)$

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

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step-by-step explanation:

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Arectangle has one side on the xx-axis and two vertices on the curve y=74+x2. y=74+x2. find the vert...