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Ask QuestionPosted by Ankit Kumar 6 years, 2 months ago
- 3 answers
Yogita Ingle 6 years, 2 months ago
Using mid point formula ,
that is , coordinates of mid point of a line segment with end points (x1 , y1) and (x2 , y2) are
=> ( (x1 + x2 )/ 2 , (y1 + y2)/2 )
therefore , using above formula ,
=> mid point of (-5,7) and (-1,3) is
=> x- coordinate = [-1+(-5)]/2 = = -6/2 = -3
and y coordinate = (7+3)/2 = 5
=> coordinates are (-3 , 5 )
Posted by Aryan Singh 6 years, 2 months ago
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Yogita Ingle 6 years, 2 months ago
Area of shaded region = area of semicircle of diameter BC - {area of quadrant of radius AB /AC - area of ∆ABC }
So, area of semicircle of diameter BC = 1/2 πr²
= 1/2 × 22/7 × 7√2 × 7√2 [ ∵ BC is hypotenuse of right angle ∆ABC , here AB = BC = 14 so, BC = 14√2 = 2 × radius ⇒ radius = 7√2 ]
= 11 × 7 × 2 = 154 cm²
area of quadrant of radius AB/AC = 1/4 πr²
= 1/4 × 22/7 × 14 × 14
= 22 × 7 = 154 cm²
area of ∆ABC = 1/2 height × base
= 1/2 × 14 × 14 = 98 cm²
Now, area of shaded region = 154cm² - { 154cm² - 98cm²} = 98cm²
Hence, area of shaded region = 98 cm²
Posted by Ujjwal Kumar Pathak 6 years, 2 months ago
- 2 answers
Yogita Ingle 6 years, 2 months ago
The volume of hemisphere ={tex} \dfrac{4851}{2} cm^{2}{/tex}
To find, the curved surface area(CSA) of a hemisphere = ?
We know that,
The volume of a hemisphere {tex}=\dfrac{2}{3} \pi r^{3}{/tex}
{tex}⇒\dfrac{2}{3} \times \dfrac{22}{7} r^{3}=\dfrac{4851}{2} cm^{2}{/tex}
{tex}⇒ r^3=(4851\times 7 \times 3)/(2 \times 2 \times 22){/tex}
{tex}⇒ r^3=\dfrac{101871}{88}{/tex}
{tex}⇒ r^3 = 1157.625{/tex}
{tex}⇒ r^3 = \dfrac{1157625}{100}{/tex}
{tex}⇒ r^3 = (\dfrac{105}{10})^{3} =10.5^{2}{/tex}
⇒ r = 10.5 cm
{tex}∴ The curved surface area(CSA) of a hemisphere =2\pi r^{2}{/tex}
{tex}= 2 \times \dfrac{22}{7} \times 10.5 \times 10.5{/tex}
{tex}= 2 \times 22 \times 1.5 \times 10.5cm^{2}{/tex}
{tex}= 44 \times 15.75cm^{2}{/tex}
{tex}=693cm^2{/tex}
Hence, the curved surface area(CSA) of a hemisphere ={tex}693cm^2.{/tex}
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Cos^2 - sin^2 => (21/29)^2 - (20/29)^2 => 441/841 - 400/841 => 41/841..
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Yogita Ingle 6 years, 2 months ago
cos2 θ + sin2 θ = 1
⇒ cos2 77° + sin2 77° = 1
⇒ cos 2 77° = 1 – sin2 77°
⇒ cos 77° = √(1 – sin2 77°)
And Given that sin 77° = x
⇒ cos 77° = √(1 – x2 )
Tan77° = x/ √(1 – x2 )
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Aman Narwal 6 years, 2 months ago
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