Mathematics, 21.06.2020 20:57 igsgymnast

Find the area of a triangle bounded by the y-axis, the line f(x)=9−2/3x, and the line perpendicular to f(x) that passes through the origin. Area =

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Answer from: quanyacoles124

The area of the triangle is 18.70 sq.units.

Step-by-step explanation:

It is provided that a triangle is bounded by the y-axis, the line $f(x)=y=9-\frac{2}{3}x$ .

The slope of the line is: $m_{1}=-\frac{2}{3}$

A perpendicular line passes through the origin to the line f (x).

The slope of this perpendicular line is: $m_{2}=-\frac{1}{m_{1}}=\frac{3}{2}$

The equation of perpendicular line passing through origin is:

$y=\frac{3}{2}x$

Compute the intersecting point between the lines as follows:

$y=9-\frac{2}{3}x\\\\\frac{3}{2}x=9-\frac{2}{3}x\\\\\frac{3}{2}x+\frac{2}{3}x=9\\\\\frac{13}{6}x=9\\\\x=\frac{54}{13}$

The value of y is:

$y=\frac{3}{2}x=\frac{3}{2}\times\frac{54}{13}=\frac{81}{13}$

The intersecting point is $(\frac{54}{13},\ \frac{81}{13})$ .

The y-intercept of the line f (x) is, 9, i.e. the point is (0, 9).

So, the triangle is bounded by the points:

(0, 0), (0, 9) and $(\frac{54}{13},\ \frac{81}{13})$

Consider the diagram attached.

Compute the area of the triangle as follows:

$\text{Area}=\frac{1}{2}\times 9\times \frac{54}{13}=18.69231\approx 18.70$

Thus, the area of the triangle is 18.70 sq.units.

Find the area of a triangle bounded by the y-axis, the line f(x)=9−2/3x, and the line perpendicular

Answer from: Quest

answer: 230 miles ( vote ! )

step-by-step explanation:

180.39 minus 17.99 equals 162.4

then divide 162.4 by .80 to get 230

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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