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3 A+2 5---------- B 2--------A=7B=6

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The nth term of a GP series is Tn = arn-1, where a = first term and r = common ratio = Tn/Tn-1) . The sum of infinite terms of a GP series S∞= a/(1-r) where 0< r<1. If a is the first term, r is the common ratio of a finite G.P. consisting of m terms, then the nth term from the end will be = arm-n

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the answer of the question is 33cm

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Given: the right circular cone has a diameter of 14 cm and height = 4 cm=>diameter of the right circular cone=(14 / 2 )cm=7 cm.

This right circular cone is melted and moulded into a hollow hemisphere ,the hollow hemisphere has an external diameter of 10 cm.

=>radius=5 cm

Let the inner radius of the melted or the resulting hemisphere be 'r' cm.

∴Volume of the cone=Volume of the hollow hemisphere

=>π×7²×4/3=2π(5³-r³)/3=>r=4.14 cm

∴Its internal diameter=8.28 cm

And its total curved surface area={(2×π×7²)+(2×π×4.14²)}=415.35 cm²

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11/3=3.67

17/5=3.4

19/6=3.17

3/8=0.375

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We know

P(E) + P(E') = 1

P(E') = 1 - 3/7 = 4/7

P(E) = 0.67

P(E) + P(not E) = 1

P(not E) = 1 - 0.67 = 0.33

x²+1+2x=2x-6x²=-7x=7i

3/4 × 8/24 = 1/4 8/24 × 3/4 = 1/4 so (3/4 × 8/24) = (8/24 × 3/4)

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Let the cost (in Rs.) of 1 bat and 1 ball be x and y respectively.Hence, from the given information the pair of equations will be3x + 6y = 3900; 1x + 2y = 1300which can also be written as:3x + 6y – 3900 = 0; x + 2y – 1300 = 0Note that what we got here is a dependent pair as a1/a2= b1/b2= c1/c2Hence this does not have a unique solution and instead has infinitely many solutions.Let us understand this geometrically.

For 3x + 6y – 3900 = 0

x

700

300

Y

300

500

Forx + 2y – 1300 = 0

X

800

500

Y

250

400

The points are plotted and joined to get lines forming the following graph:From the graph it is clear that the lines are coincident and hence each point on them represents a solution of the pair. Hence the pair has infinitely many solutions.

In short, the multiplicative identity is the number1, because for any other number x,1*x = x. So, the reason that any number to the zeropowerisoneis because any number to the zeropower is just the product of no numbers at all, which is the multiplicative identity,1.

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Euler's Formula states that if we add the number of faces and vertices together and then subtract the number of edges, we will get 2 as our answer. The formula is written as F + V - E = 2

For F = 20, V = 12E = F + V - 2E = 20 + 12 - 2E = 32 - 2E = 30

Value of E = 30

x = 5

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a(m^2 + 49 - 14m)=a(m^2 -7m -7m + 49)=a(m-7)(m-7)

Given : In triangle ABC , AD is perpendicular to BC and AD² = BD.DC

To prove : BAC = 90°

Proof : in right triangles ∆ADB and ∆ADCSo, Pythagoras theorem should be apply , Then we have , AB² = AD² + BD² ----------(1)AC²= AD²+ DC² ---------(2)

AB² + AC² = 2AD² + BD²+ DC²= 2BD . CD + BD² + CD² [ ∵ given AD² = BD.CD ] = (BD + CD )² = BC²Thus in triangle ABC we have , AB² + AC²= BC²

hence triangle ABC is a right triangle right angled at A

∠ BAC = 90°

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For roots to be Real and Equal B^2-4AC = 0 Thus , We get m=12 or m=20