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olchik [2.2K]
4 years ago
7

For the given interval, is the function increasing or decreasing? ​

Mathematics
1 answer:
Greeley [361]4 years ago
7 0

Answer:

increasing

Step-by-step explanation:

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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
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Answer:

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 <em>y</em> 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 <em>y</em>-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.

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I don't know the answer but if your questions are on a textbook, you can download the app Slader on your phone. You can scan the barcode on the textbook, and it gives you the answers and explains it.

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To figure out a special number, Tammi’s mother was supposed to double her age and then add 4. Instead, Tammi’s mother added 4 to
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