So I'm hoping you mean 6, or else the probability is 0. So the possible ways of getting a sum of 6 is 1&5, 2&4, 3&3, 4&2, 5&1. There are 36 different ways of rolling the dice, so divide the 5 possible ways by 36. Then, we need to add the possibility of getting at least one 6 in the roll. It doesn't matter what the other die is, so for each die, the probability is 1/6, and for both, the probability is 2/6. Add this to the probability of getting a sum of 6, and you get your answer.
Step-by-step explanation:
a)
dy/dx = 4x √(1 − y²)
Separate the variables:
dy / √(1 − y²) = 4x dx
Integrate:
sin⁻¹ y = 2x² + C
Solve for y:
y = sin(2x² + C)
b)
Plug in initial value.
4 = sin(0 + C)
Sine cannot be greater than 1, so there is no solution.
ok the first one
and this is the second one
