CBSE > Class 10 > Mathematics | CBSE Board | Homework Help

Given: In {tex}\triangle{/tex}ABC,

To prove: BC² = AB² + AC² - AB.AC
Construction: Draw CE {tex}\perp{/tex} AB
Proof: In {tex}\triangle{/tex}BEC
BC² = CE² + BE² ..(i)
In {tex}\triangle{/tex}ACE, AC² = CE²+ AE²
CE² = AC² - AE² ..(ii)
from (i) and (ii)
BC²= AC² - AE² + (AB - AE)² ({tex}\because{/tex} BE = AB - AE)
BC² = AC² + AB² - 2AB.AE - 2AB{tex}\frac{1}{2}{/tex}AC
Since side opposite to 30° angel is half hypoteneuse.
In {tex}\triangle{/tex}ACE, AE = {tex}\frac{1}{2}{/tex}AC
BC² = AB² + AC² - AB.AC

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CBSE > Class 10 > Mathematics

3 answers

Anushka Jugran? 6 years, 11 months ago

Learn all the identities.. And practice well

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CBSE > Class 10 > Mathematics

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Its provided in this app

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Or u cn get frm this app also

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Its available on google

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CBSE > Class 10 > Mathematics

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CBSE > Class 10 > Mathematics

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CBSE > Class 10 > Mathematics

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Water flosser the rate of 10 M per minute from a cylindrical pipe 5 mm in diameter how long would it take to fill a conical vessel was diameter and surface area is 40 cm and depth 24 cm

Posted by H B 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Anshika & Aliens???? 6 years, 11 months ago

Radius of the pipe = 5/2 mm = 5/2 x 1/10 cm = 1/4 cm Speed of water = 10 m/min = 1000 cm/min Volume of water that flows in 1 minute = Π r2 h = 22/7 x 1/4 x 1/4 x 1000 = 1375/7 cm3 Radius of conical vessel = 40/2 = 20 cm; Depth = 24 cm Therefore, Capacity of the vessel = 1/3 x Π r2 h = 1/3 x 22/7 x 20 x 20 x 24 = 70400/7 cm3 Therefore, Time required to fill the vessel = capacity of the vessel / volume of water flowing per minute = 70400/7 / 1375/7 = 70400/7 x 7/1375 = 256/5 minutes = 51 min 12 sec

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Water flows @ 10m per minute from a cylindrical pipe v m m in diameter how long would it take to fill a conical vessel was diameter at the surface is 40 cm and depth 24 cm

Posted by H B 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Radius of the pipe is {tex}\begin{array}{l}\frac52\mathrm{mm}\;=\;\frac52\times\frac1{10}\;\mathrm{cm}\\\end{array}{/tex}

= {tex}\begin{array}{l}\;\frac14\;\mathrm{cm}\\\end{array}{/tex}

Speed of water = {tex}\begin{array}{l}\;\frac{10\;\mathrm m}\min\;=\;\frac{1000\;\mathrm{cm}}\min\\\end{array}{/tex}

⇒ v = {tex} \frac { 10 } { 60 }{/tex} m/s = {tex} \frac { 1 } { 6 }{/tex} m/s

∴ Volume of flowing water = Volume of cone

⇒ Area of base × height (dist.) = {tex} \frac { 1 } { 3 } \pi R ^ { 2 } H{/tex}

⇒ A × vt = {tex} \frac { 1 } { 3 } \pi R ^ { 2 } H{/tex} [as distance=speed ×time]

⇒ πr².vt= {tex} \frac { 1 } { 3 }{/tex}πR²H

⇒ r².vt= {tex} \frac { 1 } { 3 }{/tex}R²H

⇒ {tex} \frac { 1 } { 400 } \times \frac { 1 } { 400 } \times \frac { 1 } { 6 } t = \frac { 1 } { 3 } \times 0.2 \times 0.2 \times 0.24{/tex}

⇒ {tex}t = \frac { 2 \times 2 \times 24 \times 400 \times 400 } { 3 \times 10000 }{/tex}

⇒ t = 4 × 24 × 4 × 4 × 2 sec

{tex} = \frac { 4 \times 24 \times 4 \times 4 \times 2 } { 60 } \mathrm { min } = \frac { 512 } { 10 }{/tex} = 51.2 min

= 51 min + 0.2 min = 51 min + 0.2 × 60sec

⇒ t = 51 min and 12 sec.

Hence, conical tank will fill in 51 min and 12 sec.

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CBSE > Class 10 > Mathematics

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CBSE > Class 10 > Mathematics

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CBSE > Class 10 > Mathematics

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Rita Gokani 6 years, 11 months ago

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CBSE > Class 10 > Mathematics

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CBSE > Class 10 > Mathematics

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CBSE > Class 10 > Mathematics

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CBSE > Class 10 > Mathematics

1 answers

Surendrapal Singh Singh Gaur 6 years, 11 months ago

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CBSE > Class 10 > Mathematics

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Posted by Chirag Sankhyan 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Ram Kushwah 6 years, 11 months ago

{tex}\begin{array}{l}Let\;the\;number\;is\;x\\so\;x(4-\sqrt3)=39\\x=\frac{39}{(4-\sqrt3)}=\frac{39(4+\sqrt3)}{(4-\sqrt3)(4+\sqrt{3)}}=\frac{39(4+\sqrt3)}{16-3}\\=\frac{39(4+\sqrt3)}{13}=3(4+\sqrt3)\\\end{array}{/tex}

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Posted by Gaurav Kumar 6 years, 11 months ago

CBSE > Class 10 > Mathematics

4 answers

Maths Lover **** √Π÷= 6 years, 11 months ago

Given that, Radius of cone=radius of hemisphere(r)=1cm Height of the cone=1cm Now, Volume of the solid=volume of cone+volume of hemisphere =1/3Πr^2h+2/3Πr^3 =1/3Π×1×1×1+2/3Π1×1×1 =1/3Π+2/3Π =Π{1/3+2/3} =Π{1+2/3} =Π{3/3} =Π×1 =Πcm^3

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Bhavya Choubey 6 years, 11 months ago

No actually my ans is wrong .The correct ans is π cm3 .Honey u r right

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Bhavya Choubey 6 years, 11 months ago

2√2/3 π....may be

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. . 5 years, 8 months ago

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