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Meghna Thapar 5 years, 7 months ago
A sphere is a geometrical figure that is perfectly round, 3-dimensional and circular - like a ball. Geometrically, a sphere is defined as the set of all points equidistant from a single point in space. A sphere is a solid figure that is round and has the shape of a ball. For example, a glass peble, a basketball etc are spherical shape. Another example of a sphere is the earth we are standing on! When we look at a globe, we see that the earth is three-dimensional and has the shape of a ball.
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Yogita Ingle 5 years, 7 months ago
Remainder theorem: If a polynomial P(x) is divided by (x-c), then the remainder is equal to P(c).
The given polynomial are
{tex}p(t)=4t^3-st^2+7{/tex}
{tex}q(t)=t^2+st+8{/tex}
Using remainder theorem the remainder of {tex}\frac{p(t)}{t-1} {/tex}is p(1) and the remainder of{tex} \frac{q(t)}{t-1}{/tex} is q(1).
Substitute t=1 in the given functions.
{tex}p(1)=4(1)^3-s(1)^2+7\Rightarrow 4-s+7=11-s{/tex}
{tex}q(1)=(1)^2+s(1)+8=1+s+8=9+s{/tex}
It is given that if p(t) and q(t) divided by (t-1), then the remainder is same.
p(1)=q(1)
Substitute these values.
11-s=9+s
Add s on both sides.
11=9+s+s
11=9+2s
Subtract 9 from both sides.
11-9=2s
2=2s
Divide both sides by 2.
1=s
Therefore, the value of s is 1.
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Yogita Ingle 5 years, 7 months ago
Let common multiple is x
then side of triangle are x, 3x and 2x
As per given condition
x + 3x + 2x = 30
6x = 30
x = 30/6 = 5
So, the smallest side of triangle is 5 cm.
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Yogita Ingle 5 years, 7 months ago
15√6 + √216
= 15√6 + √36× 6
= 15√6 + 6√ 6
= (15+ 6)√ 6
= 21√ 6
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