Mathematics, 24.06.2019 21:00 hannabeth91

Acircle has radius of 18 cm. find the area of the smaller of the two regions determined by a chord with length of 18 square root of 2 cm. (hint: look for right triangles using pythagorean theorem converse) plz

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Answer from: errr5529

$81 ( \pi - 2)\text { square cm}$

Step-by-step explanation:

Let O be the radius of the circle and AB be the chord of length 18√2 cm.

Since, the radius of the circle is 18 cm,

Therefore, OA = OB = 18 cm,

Let, N be the mid point of the chord then,

AN = NB = 9√2 cm

In triangle AON,

Since, $\angle ANO = 90^{\circ}$ ( by the property of circle)

$\angle AON = sin^{-1} (\frac{9\sqrt{2} }{18} )$

$\angle AON = sin^{-1} (\frac{\sqrt{2} }{2} )$

$\angle AON = sin^{-1} (\frac{1}{\sqrt{2} } )$

$\angle AON = 45^{\circ}$

Similarly, in triangle BON,

$\angle BON = 45^{\circ}$

⇒ $\angle AOB = \angle AON +\angle BON = 45^{\circ}+45^{\circ} = 90^{\circ}$

Therefore, the area of sector AOB = $\frac{90^{\circ}}{360^{\circ}} \pi (18)^2$

= $\frac{1}{4} \pi (18)^2$

= $81\pi \text{ square cm}$

Area of triangle AOB = $\frac{1}{2} \times ON\times AB$

= $\frac{1}{2} \times \sqrt{OA^2-AN^2}\times AB$

= $\frac{1}{2} \times \sqrt{324-162}\times 18\sqrt{2}$

= $\frac{1}{2} \times \sqrt{162}\times 18\sqrt{2}$

= $\frac{1}{2} \times \sqrt{2}\times \sqrt{81}\times 18\sqrt{2}$

= $162\text{ square cm}$

Therefore, the area of smaller region by the chord AB = Area of sector AOB - Area of triangle AOB = $81\pi - 162$

= $81 ( \pi - 2)\text { square cm}$

Acircle has radius of 18 cm. find the area of the smaller of the two regions determined by a chord w

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

all group life insurance is term insurance. actually it is annual renewable term and it is rated on the average age and claims experience of the entire group, which is called "experience rating." remember, this type of insurance has a 31-day grace period and is convertible to whole life upon leaving employment. a contributory group plan requires that both the employer and the employees pay part of the premium. at least 75% of those eligible must participate, so the group is sure to get most of the healthy employees as well as those that are sick.

step-by-step explanation:

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