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Two plane mirrors m and n, perpendicular to each other. CA is incident ray and BD is reflected ray.To Prove : CA || DBConstruction : OQ and OB are perpendiculars to m and n respectivelyProof :

Given:- ratio of sum of n terms of two AP’s = (7n+1):(4n+27).

Let’s consider the ratio these two AP’s mth terms as am : a’m →(2)

Recall the nth term of AP formula, an = a + (n – 1)d

Hence equation (2) becomes,

am : a’m = a + (m – 1)d : a’ + (m – 1)d’

On multiplying by 2, we get

am : a’m = [2a + 2(m – 1)d] : [2a’ + 2(m – 1)d’]= [2a + {(2m – 1) – 1}d] : [2a’ + {(2m – 1) – 1}d’]= S2m – 1 : S’2m – 1= [7(2m – 1) + 1] : [4(2m – 1) +27] [from (1)]= [14m – 7 +1] : [8m – 4 + 27]= [14m – 6] : [8m + 23]

Thus the ratio of mth terms of two AP’s is [14m – 6] : [8m + 23].

∴Ratio of their 10ᵗʰ terms=(140-6):(80-23)=134:57

A Pentagon has 5 angles and 5 sides.The total angle inside any polygon can be calculated with

(n - 2) × 180°

Where n is the number of sides. In this case it's 5.

So,

n - 2 = 5 - 2 = 3

And,

3 × 180° = 540°

So the total angle is 540 degree. Since the ratio of each angle is given,

Angle 1 = (4 × 540) ÷ 4 + 5 + 6 + 7 + 5

2160 ÷ 27 = 80°

Similarly,

Angle 2 is 100°

Angle 3 is 120°

Angle 4 is 140°

Angle 5 is 100°

plzz explain in class 8 type

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Area of metal plate=32cm×12cmarea of square =4^2 cm^2=16cm ^2area of metal plate =n×area of square32×12 cm^2=n×16 cm^2n=32×12 /16n=2424 square

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Arithmetic mean = 8+5+6+x+2+7 /6 =5 28+x=30x=2

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The fractions are (2/9), (2/3), (8/21).To compare the fractions, we make the denominator equal. LCM of 9,3,21 is 63.(2/9) = (14/63).(2/3) = (42/63).(8/21) = (24/63).Here, we can see that (14/63) < ( 24/63) < (42/63)So, (2/9) < ( 8/21) < ( 2/3).

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8*3+1/3 ÷525/3÷525/3* 1/5=5/3

Let the first term be X. Since these 4 numbers are in proportion, X*25= 90*5 [ product of extremes = product of means] => X = (90*5)/25=> X = 18.

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no answer is like 18 5. 3 6.

Ans :- Post 1991, the liberalization has opened more for CORPORATE AND MNCs to rule the economy with huge price variation. More than 2.5 crores of employments were destroyed . But it was more because of the advanced technology and automation.

A mixed economy had it been continued with infusion of technology and liberal market economy to allow more funds flow, things would have been different. People who are the real customers would have taken care of productions and consumption which are rolling stone of an economy. Now consumption is coming down and productions are not be absorbed in the absence of diminishing purchasing powers.

part 1 of soln

Let f(x) = y

y = 2x + 3/4

4y - 3 = 2x

x = (4y - 3)/2

Therefore, f^-1(y) = (4y - 3)/2

hence e^-1

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5m*2m*5m*2m=1003rd is the correct option plzz mark me as best

Perimeter of rectangular plot=2(l+b)=2(120+90) m=420 m

Therefore, length of wire needed to surround the plot 4 times= 4×perimeter of plot=4×420 m=1680 m

2-x^2 = 0x^2 = 2x = +-√2

The number of terms is N =(25-1)/2 + 1= 13The sum of terms, which is the arithmetic progression with difference 2, is:S =(1 + 25) ×13÷ 2 = 13× 13The average is:A = S / N =13× 13 / 13 = 13

So, to calculate the average of arithmetic progressionwas needed to calculate the number of terms N, the average arithmetic progression is the average of first and last term:A = (1 + 25) / 2 = 13

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answer 25

1st

2nd

Let a be the first term and d be the common difference of the given AP.Sum of the first n terms is given bySn = n/2 {2a + (n - 1)d}Putting n = 10, we getS₁₀ = 10/2 {2a + (10 - 1)d}210 = 5 (2a + 9d)2a + 9d = 210/52a + 9d = 42 ...............(1)Sum of the last 15 terms is 2565⇒ Sum of the first 50 terms - sum of the first 35 terms = 2565S₅₀ - S₃₅ = 2565⇒ 50/2 {2a + (50 - 1)d} - 35/2 {2a + (35 - 1)d} = 256525 (2a + 49d) - 35/2 (2a + 34d) = 2565⇒ 5 (2a + 49d) - 7/2 (2a + 34d) = 513⇒ 10a + 245d - 7a + 119d = 513⇒ 3a + 126d = 513⇒ a + 42d = 171 ........(2)Multiply the equation (2) with 2, we get2a + 84d = 342 .........(3)Subtracting (1) from (3) 2a + 84d = 342 2a + 9d = 42- - -_______________ 75d = 300_______________d= 4Now, substituting the value of d in equation (1)2a + 9d = 422a + 9*4 = 422a = 42 - 362a = 6a = 3So, the required AP is 3, 7, 11, 15, 19, 23, 27, 31, 35, 39 ........

thanks sushma