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sin30 = 1/2 and tan45 = 15sin30 + 3tan45= 5*(1/2) + 3(1)= 5/2 + 3= 5.5

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let radius of both be r and height of cone be hnow csa of a hemisphere=CSA of cone2πr^2=2πrhr=hr/h=1/11:1

Given; PS is bisector of angle QPR PT is perpendicular to QR

To Prove; angle TPS = 1/2 (angle Q - angle R)

Solutio; We know that angle QPS = 1/2 angle P(1) angle Q + angle QPT = 90 degreeangle QPT = 90 degree -angle Q (2) On putting equations (1) and (2)

angle TPS = angle QPS - angle QPT= 1/2 angle P - ( 90 - angle Q )= 1/2 angle P - 90 + angle Q = 1/2 angle P - 1/2 (angle Q + angle P + angle R) + angle Q= 1/2 angle P - 1/2 angle Q - 1/2 angle P - 1/2 angle R + angle Q = -1/2 angle Q - 1/2 angle R + angle Q (+ve and -ve 1/2 angle P got cancled )

by takig LCM in angle Q we get

-1/2 angle Q + 2/2 angle Q - 1/2 angle R

(-1/2 + 2/2) angle Q - 1/2 angle R

= 1/2 angle Q - 1/2 angle R

angle TPS = 1/2 ( angle Q -1/2 angle R ) (Hence proved)

Given: PR > PQ & PS bisects ∠QPR

To prove: ∠PSR > ∠PSQ

Proof: ∠PQR > ∠PRQ — (i) (PR > PQ as angle opposite to larger side is larger.)

∠QPS = ∠RPS — (ii) (PS bisects ∠QPR)

∠PSR = ∠PQR +∠QPS — (iii) (exterior angle of a triangle equals to the sum of opposite interior angles)

∠PSQ = ∠PRQ + ∠RPS — (iv) (exterior angle of a triangle equals to the sum of opposite interior angles)

Adding (i) and (ii)∠PQR + ∠QPS > ∠PRQ + ∠RPS

⇒ ∠PSR > ∠PSQ [from (i), (ii), (iii) and (iv)]

Let√2 be a rational number

Therefore,√2= p/q [ p and q are in their least terms i.e., HCF of (p,q)=1 and q≠ 0

On squaring both sides, we get p²= 2q² ...(1)Clearly, 2 is a factor of 2q²⇒ 2 is a factor of p² [since, 2q²=p²]⇒ 2 is a factor of p

Let p =2 m for all m ( where m is a positive integer)

Squaring both sides, we get p²= 4 m² ...(2)From (1) and (2), we get 2q² = 4m² ⇒ q²= 2m²Clearly, 2 is a factor of 2m²⇒ 2 is a factor of q² [since, q² = 2m²]⇒ 2 is a factor of q

Thus, we see that both p and q have common factor 2 which is a contradiction that H.C.F. of (p,q)= 1

Therefore, Our supposition is wrong

Hence√2 is not a rational number i.e., irrational number.

Please post the question accurately.

it is correcy

cc is b skywalk you have any other person is yes is there any chance

Given,OR is perpendicular to line PQTo prove,∠ROS = 1/2(∠QOS – ∠POS)A/q,∠POR = ∠ROQ = 90° (Perpendicular)∠QOS = ∠ROQ + ∠ROS = 90° + ∠ROS --- (i)∠POS = ∠POR - ∠ROS = 90° - ∠ROS --- (ii)Subtracting (ii) from (i)∠QOS - ∠POS = 90° + ∠ROS - (90° - ∠ROS)⇒ ∠QOS - ∠POS = 90° + ∠ROS - 90° + ∠ROS⇒ ∠QOS - ∠POS = 2∠ROS⇒ ∠ROS = 1/2(∠QOS – ∠POS)Hence, Proved.

maybe 120 degree ........

Given : For cone -1. Height of the cone = 4cm 2. diameter of the cone = 6cm 3.radius of the cone = = 3cm Slant height of the cone l = √r²+h² ⇒ l = √3²+4² ⇒ l = √9+16 ⇒ l = 5 Lateral surface area of the cone = πrl ⇒ 3.14 × 3 × 5 ⇒ 3.14 × 15 ⇒ 47,10 cm²

For Hemisphere - 1. Diameter of the hemisphere = 6cm 2. Radius of hemisphere = 3cm

Lateral surface area of hemisphere = 2πr² ⇒ 2 × 3.14 × 3²⇒ 2 × 3.14 × 9 ⇒ 18 × 3.14 ⇒ 56.52 cm²

The surface are of toy = lateral surface area of cone + lateral surface area of hemisphere ⇒ 47.10 + 56.52 ⇒ 103.62cm³

∴ The total surface area of toy = 103.62cm³

For equal zerosD= 0= b^2= 4acb= 1a= kc= kso4k^2= 1k^2= 1/4k= +-1/2

put x=24k-14+8=04k-6=0k=3/2

thanks jaan

Value of k will bek(2*2)-14(2)+8=04k-28+8=04k= 20k=5

thanks i am very thankful to u

winner got 63% so looser must get 37% so difference is 26% which is 9620 so total votes = (100×9620)/26 = 37000

According to the question,55% of votes - 45 % of votes = 8756Let the total number of votes be x.Then, 55 % of x - 45 % of x = 8756=> (11/20 - 9/20) * x = 8756=> 2x/20 = 8756=> x/ 10 = 8756=> x = 87560

little bit confouse

pls give full question