The numeratorof a fraction is 5 more than its denominator if 3 is added to both

If x is denominator, numerator is x + 5

If 3 is added to both the numerator and denominator, then

x + 5+3 / x +3 = 4/3

3(x+8) = 4(x+3)

3x + 24 = 4x +12

3x-4x = 12-24

x = 12

x = 12+5 = 17

So, (x+5+3)/x+3

= 20/15 = 4/3

dα/dt  =  - 0,25  rad/sec

Step-by-step explanation:

The vertical wall, the ground from the vertical wall up to the ladder, and the ladder shape a right triangle. angle α  will be the angle between the ladder and the ground, then:

cos α  = distance between the wall and the down end of the ladder (x)  /  length of the ladder

cos α   =  x/ L

- sin α * dα/dt   =  dx/dt * L /L²

- sin α * dα/dt   =  dx/dt /L

When   the down end of the ladder is 8 ft apart from the wall

cos  α   =  8 / 10   =  0,8  then    cos² α  +  sin²α  = 1

sin² α  =  1 - cos²α        sin²α =  1 - (0.8)²    sin²α  = 0.36

sin α  = 0.6

dα/dt  =  ?

dx/ dt  =  3/2

L  = 10 ft

x  =  8 ft

By substitution

- 0.6*dα / dt   = (3/2) / 10

dα/dt  =  -  1.5 / 6

dα/dt  =  - 0,25  rad/sec

(-) means the angle is decreasing