5. Using the counting principle, determine the number of outcomes for a three-color spinner that is spun four times in a row.

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Ответ:

orlando19882000

16.05.2023

Mathematics

2.114 cm.sec

Step-by-step explanation:

Given that an isosceles right triangle with legs of length s has area A.

At the instant when s 32 2 centimeters, the area of the triangle is increasing at rate of 12 square centimeters per second.

For a right triangle with legs = s each , area

= $A= \frac{s^2}{2}$

Differentiate with respect to t

We get

$\frac{dA}{dt}= \frac{1}{2}(2s) \frac{ds}{dt} \\ \frac{ds}{dt}= \frac{1}{s} \frac{dA}{dt}$

When dA/dt = 12 and A =32.2 we get

$\frac{ds}{dt}= \frac{1}{s}* 12\\12*\sqrt{\frac{1}{2A} }\\= 1.49534$

Hypotenuse

$h^2 = 2s^2\\h = \sqrt{2} s\\\frac{dh}{dt}=\sqrt{2} \frac{ds}{dt} \\=\sqrt{2}*1.49534\\=2.114$

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