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Preeti Dabral 4 years, 3 months ago
Given √2 = 1.414.
To find : value of √6 - √3 upto three places of decimal .
Solution :
We have , √6 - √3
= √2 × √3 - √3
= √3(√2 - 1)
= 1.732 (1.414 - 1)
[√3 = 1.732]
= 1.732 × 0.414
= 0.707
√6 - √3 = 0.707 Hence the value of √6 - √3 upto three places of decimal is 0.707. Among the given options option (B) 0.707 is correct.
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Preeti Dabral 4 years, 3 months ago
Given
Let ,
where , k is any constant
So ,
and
and
Now , Multiply eq (1) & eq (2) ,
Since , bases are equal , so exponents must be equal .
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Sia ? 4 years, 3 months ago
In {tex}\triangle{/tex}ABC,
BP bisects {tex}\angle{/tex}ABC
{tex}\therefore{/tex} {tex}\angle{/tex}ABP = {tex}\angle{/tex}PBC = {tex}\frac{1}{2}{/tex}{tex}\angle{/tex}B ={tex}\frac{1}{2}{/tex}(2{tex}\angle{/tex}C) = {tex}\angle{/tex}C . . . . (1)
In PBC,
{tex}\therefore{/tex} {tex}\angle{/tex}PBC = {tex}\angle{/tex}PCB (= ∠C)
{tex}\therefore{/tex} PB = PC . . . [Sides opposite to equal angles] . . .(2)
In {tex}\triangle{/tex}APB and {tex}\triangle{/tex}DPC,
AB = CD . . . [Given]
PB = PC . . .[From (2)]
{tex}\angle{/tex}ABP = {tex}\angle{/tex}DCP (= {tex}\angle{/tex}C)
{tex}\therefore{/tex} {tex}\triangle{/tex}APB = {tex}\triangle{/tex}DPC . . . . [By SAS property]
{tex}\therefore{/tex} {tex}\angle{/tex}BAP = CDP (= {tex}\angle{/tex}A) . . .[c.p.c.t.] . . . (3)
and AP = DP . . . [c.p.c.t.] . . . .(4)
In {tex}\triangle{/tex}APD,
As AP = DC . . . [From (4)]
{tex}\therefore{/tex} {tex}\angle{/tex}PDA = {tex}\angle{/tex}PAD = {tex}\frac{A}{2}{/tex}
{tex}\therefore{/tex} {tex}\angle{/tex}DPA = {tex}\pi-\left(\frac{A}{2}+\frac{A}{2}\right)=\pi-A{/tex} . . . . (5)
From {tex}\angle{/tex}DPC
{tex}\angle{/tex}DPC = {tex}\pi{/tex} – (A + C)
{tex}\therefore{/tex} {tex}\angle{/tex}DPA = {tex}\pi{/tex} – {tex}\angle{/tex}DPC = {tex}\pi{/tex} – [{tex}\pi{/tex} – (A + C)] = A + C . . .(6)
From (5) and (6)
{tex}\pi{/tex} – A = A + C {tex}\therefore{/tex} 2A + C = {tex}\pi{/tex} . . . (7)
Again
A + B + C = {tex}\pi{/tex} . . .[Sum of three angles of a triangle = {tex}\pi{/tex}]
{tex}\therefore{/tex} A + 2C + C = {tex}\pi{/tex} . . .[As B = 2C]
{tex}\therefore{/tex} A + 3C = {tex}\pi{/tex} . . . (8)
Multiplying (7) by 3, we get
6A + 3C = 3{tex}\pi{/tex}
5A = 2{tex}\pi{/tex} . . .[By subtracting (8) from (9)]
{tex}\therefore{/tex} {tex}A=\frac{2 \pi}{5}=\frac{2}{5} \times 180^{\circ}=72^{\circ}{/tex}
{tex}\therefore{/tex} {tex}\angle{/tex}BAC = 72o
Posted by Navraj Kaur 4 years, 3 months ago
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Sia ? 4 years, 3 months ago
l = 22.5 m, b = 10 cm, h = 7.5 cm.
∴ Total surface area of brick = 2(lb + bh + hl)
= 2(22.5 × 10 + 10 × 7.5 + 7.5 × 22.5)
= 2(225 + 75 + 168.75)
= 2(468.75) = 937.5 cm2 = .09375 m2
The no.of brick that can be painted out ={tex}{9.375}\over.09375{/tex}
= 100 Brick.
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Raksha P G 4 years, 3 months ago
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