Question

guys here

7 and 8 number question plzz help me

Answer 1

(7)

Given points are A(-3,5) and B(4,-9), P(2,-5).

Let the ratio be k:1

Here, m₁ = k and m₂ = 1.

         x = 2,y = -5.

         x₁ = -3 and y₁ = 5, x₂ = 4,y₂ = -9.

Using section formula:

x = (m₁x₂ + m₂x₁)/m₁ + m₂

⇒ 2 = [k(4) + -3]/k + 1

⇒ 2(k + 1) = 4k - 3

⇒ 2k + 2 = 4k - 3

⇒ 2k - 4k = -3 - 2

⇒ 2k = 5

⇒ k = 5/2

Therefore, the ratio is 5:2.

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(8)

Given, radius of spheres = 6 cm, 8cm, 10cm.

We know that volume of sphere = (4/3)πr^3.

Given that three spheres are melted to form a sphere.

⇒ (4/3)πr₁³ + (4/3)πr₂³+(4/3)πr₃³ = (4/3)R₃

⇒ r₁³ + r₂³ + r₃³ = (R)³

⇒ (6)³ + (8)³ + (10)³ = (R)³

⇒ 1728 = R³

⇒ (12)³ = R³

⇒ R = 12.

Therefore, radius of the sphere so formed is 12 cm.

Hope this helps!