Question

$\sf{Question 1→\sf \large\left \{ {{ \: \: \: \: \: \: \: \: {x}^{ \sqrt{y} } + {y}^{ \sqrt{x} } = \dfrac{49}{48} } \: \: \: \atop { \large\sqrt{x} + \sqrt{y} = \dfrac{7}{2} }} \right\} Find\ x\ and\ y }$

Sare Brainly Wale MATLAbi Hai​

Answer 1

Answer:

It is the same as solving

a^2b+b^2a=49/48 with the constraints a,b≥0

and a+b=7/2,

hence it boils down to finding the solutions of

g(a)=a^7−a+(7/2−a)^2a=49/48

over the interval [0,7/2].

g(a)≥2 if a≥1/3

and over [0,1/3] the function g(a) is increasing,

hence there is a unique solution in a right neighbourhood of the origin. By applying few steps of Newton's method with starting point 1/100 we get a≈0.00824505

hence x≈0.00006798.

Answer 2

Step-by-step explanation:

Given,

In ΔABC,

∠A is an obtuse angle

sin A = 3/5,

=> cos A = -4/5

(°.° A is obtuse, it lies in 2nd quadrant )

and,

sin B = 5/13,

=> cos B = 12/13

To find: sin C

We know that, in a triangle

∠A+∠B+∠C = 180

=> ∠A + ∠B = 180- ∠C

=> sin ( ∠A + ∠B ) = sin ( 180- ∠C )

=> sinA cosB + cosA sinB = sinC

=> sinC = (3/5)(12/13) + (-4/5)(5/13)

=> sin C = 36/65 - 20/65

=> sin C = 16/65