You have the side lengths 3 in., 6 in., and 10 in. Can these side lengths form a triangle

Mathematics

2 answers:

OverLord2011 [107]3 years ago

6 0

No they cannot because 3 is way to short

Tasya [4]3 years ago

6 0

These side lengths cannot form a triangle.
To form a triangle the two shorter sides have to be greater than the biggest side.
3 + 6 = 9
9 < 10
This makes it impossible to form a triangle with these lengths

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The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of 4 cm/s. When the length is

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Answer:

The area of the rectangle is increasing at a rate of 168 square centimeters per second.

Step-by-step explanation:

Geometrically speaking, the area of a rectangle ( $A$ ), in square centimeters, is described by following expression:

$A = w\cdot l$ (1)

Where:

$w$ - Width, in centimeters.

$h$ - Height, in centimeters.

By Differential Calculus, we find an expression for the rate of change of the area of the rectangle ( $\dot A$ ), in square centimeters per second:

$\dot A = \dot w\cdot l + w\cdot \dot l$ (2)

Where:

$\dot w$ - Rate of change of the width of the rectangle, in centimeters per second.

$\dot l$ - Rate of change of the length of the rectangle, in centimeters per second.

If we know that $w = 12\,cm$ , $l = 15\,cm$ , $\dot w = 4\,\frac{cm}{s}$ and $\dot l = 9\,\frac{cm}{s}$ , then the rate of change of the area of the rectangle is: