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2.

4.

option d) Apiss mellifera is the correct answer.

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Given: PR > PQ

Apply Pythagoras theorem in triangle APQ,

AP² = AQ² - PQ² ... (1)

Apply Pythagoras theorem in triangle APR,

AP² = AR² - PR² ... (2)

From equation (1) and (2),

AR² - PR² = AQ² - PQ²

Given PR > PQ, So,

AR² - PQ² > AQ² - PQ²

AR² > AQ²

AR > AQ

Hence Proved

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We know that, the lengths of tangents drawn from an external point to a circle are equal.∴ TP = TQIn ΔTPQ,TP = TQ⇒ ∠TQP = ∠TPQ ...(1) (In a triangle, equal sides have equal angles opposite to them)∠TQP + ∠TPQ + ∠PTQ = 180º (Angle sum property)∴ 2 ∠TPQ + ∠PTQ = 180º (Using(1))⇒ ∠PTQ = 180º – 2 ∠TPQ ...(1)We know that, a tangent to a circle is perpendicular to the radius through the point of contact.OP ⊥ PT,∴ ∠OPT = 90º⇒ ∠OPQ + ∠TPQ = 90º⇒ ∠OPQ = 90º – ∠TPQ⇒ 2∠OPQ = 2(90º – ∠TPQ) = 180º – 2 ∠TPQ ...(2)From (1) and (2), we get∠PTQ = 2∠OPQ

Let AB be a chord of a circle with center O and let AP and BP be the tangents at A and B.Let the tangent meet at P.Join OP Suppose OP meets AB at C.To prove : ∠PAC = ∠PBCProof : In ΔPAC and ΔPBCPA = PB [Tangents from an external point to a circle are equal]∠APC = ∠BPC [PA and PB are equally inclined to OP]PC = PC [Common]ΔPAC ≅ ΔPBC [SAS Congruence]∠PAC = ∠PBC [C.P.C.T]

GivenTA and TB are tangent to a circle with centre O from point TConsider, ΔOAT and ΔOBTHere, OA = OB [Radii of circle]OT = OT [Common side]TA = TB [Tangents from an external point to a circle are equal in length]∴ ΔOAT ≅ΔOBT [By SSS congruence criterion]Recall that exterior angle of a triangle is equal to sum of interior opposite angles.Hence in ΔAPT, ∠APO = ∠a + ∠bIn ΔAPO, OA = OP [Radii of circle]∠OAP = ∠OPA = ∠a + ∠b ... (1) [Angles opposite to equal sides are equal]From the figure, ∠OAP=90°- ∠b ... (2) [Since radius is perpendicular to tangent]From equations (1) and (2), we get∠a + ∠b = 90° - ∠b⇒ ∠a = 90° - 2∠b … (3)In ΔOAT, ÐOAT + ÐAOT + ÐATO = 180° [Angle sum property of triangle]90° + ∠a + ∠b+∠c+=180°∠a+∠b+∠c=90°90°- 2∠b + ∠b + ∠c=90°- ∠b + ∠c=0∠b = ∠cHence, AP bisects ∠TAB

As mod is always positiveso answer will be√2

if ⁿCₓ = ⁿCᵤ then, x + u = n ]

Here, ⁿC₈ = ⁿC₂ so, according to results , n = 8 + 2 = 10 hence, n = 10

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Formula of n th term in AP = a+(n-1)d

Where, a is the first term n is the term number d is the common ratio

Now when n = 7So, a+(7-1)d=a+6d

When n = 3 So, a+(3-1)d=a+2d

Since we are given that the ratio of 7th to 3rd term of an AP is 12:5 ⇒(a + 6d)/(a + 2d) = 12/5⇒5a+30d=12a+24d⇒6d = 7a⇒a=6d/7

Now 13th term =a+(13-1)d =a+12d =

4th term =a+(4-1)d =a+3d =

Now ratio of 13th and 4th term= (a+ 12d)/(a + 3d)= (6d/7 + 12d) / (6d/7 + 3d)= (90d/7) / (27d/7)= 90/27= 10/3

Thus the ratio of the 13th and 4th term is 10:3

in triangle 🔺 ADP, A+D+P=180THUS, A=180-(85+40) A=180-125 A=55

In the ΔABY: ∠Y + ∠A /2 + ∠B = 180°In the ΔDCX: ∠D +∠C /2 + X = 180°

Add them to get: (∠A +∠C)/2 +∠B +∠D +∠X +∠Y = 360° we know∠A + ∠B +∠C + ∠D = 360°

From these two equations , we get: angle X+ ∠Y = (∠A+∠C) /2

please specify the question in english

Draw a rough diagram of a solid showing the combination of a cone and cylinder,whose base radii are same.

thanx.... 😊 It was really helpful... ☺

Vol. of cylinder = πr^2h= 22/7*(4.5/2)^2*10= 22/7*5.0625*10= 159.107143 cm^3vol.of plate = π*r^2*h= 22/7*(1.5/2)^2*0.2= 22/7*0.5625*0.2=0.35357143 cm^3No.of plates = vol.of cylinder/vol.of plates= 159.107143/0.35357143= 450 plates.

nhi samajh mai aaya

a)If x²=16 then x=±4b)If x²=0.0004 then x=±0.02c)If x²=1(7/9) that is x=16/9 then x=±(4/3).Hence all the values of X are rational.

1) x^2-2x+5It is of form Ax^2+Bx+c where A= 1, B=-2, C=5B^2-4AC= (-2)^2-(4*5)=4-20=-16the value is negative , hence it has no zeroes2) x^2+6x+10It is of form Ax^2+Bx+c where A= 1, B=6, C=10B^-4AC= 6^2-(4*1*10)=36-40=-4the value is negative , hence it has no zeroesLike if you find it useful

For 1 year both simple interest and compound interest are same.So the difference will be 0

10000 is the right answer

10000 is the correct answer

10000 is the right answer

10,000 is the correct answer

10000...................

∠1 = ∠4 ( vertically opposite angle)∠1 = ∠5 ( corresponding angles)∠4 = ∠5 ( alternative angles)

Similarly∠2 = ∠3 ( vertically opposite angle)∠2 = ∠6 ( corresponding angles)∠3 = ∠6 ( alternative angles)

1000 add 90000 we will get 91000

the answer of this question is 1000+90000=91000

91000 is the correct answer

91000 is the correct answer

91000 is the correct answer of the given question

1000+90000=91,000 very easy to do it

When we 1000+90000 we get 91000