Explanation

Given: sinθ = 8/17

cosθ = √(1 − (8/17)²)

= √(1 − 64/289)

= √(225/289)

= 15/17

Last verified on 15-05-2026

Explanation

Given:

a² + b² = 65

a = 1

Put value of a:

1² + b² = 65

1 + b² = 65

Subtract 1 from both sides:

b² = 64

Take square root:

b = 8 (positive value)

So, b = 8.

Last verified on 15-05-2026

Explanation

The decomposition is:

(8x + 6)/[x(x + 2)] = A/x + B/(x + 2)

Multiply both sides by x(x + 2) so the denominators cancel out:

8x + 6 = A(x + 2) + Bx

Now find A and B:

Put x = 0. That makes the Bx term zero, so 6 = 2A. That gives A = 3.  

Put x = -2. That makes the A(x + 2) term zero, so -10 = -2B. That gives B = 5.

So it equals 3/x + 5/(x + 2).

Last verified on 15-05-2026

Explanation

Given y = 18 when x = 3:

18 = k(3²)

18 = 9k

k = 2

Now for x = 5:

y = 2(5²)

y = 2 × 25

y = 50

Last verified on 15-05-2026

Explanation

Find f(3):

f(3) = 3² − 2(3)

= 9 − 6

= 3

Find f(1):

f(1) = 1² − 2(1)

= 1 − 2

= −1

Now add:

f(3) + f(1) = 3 + (−1) = 2

Last verified on 15-05-2026