Each die has 6 possible outcomes (the numbers from 1 to 6).
If we roll two dices, the total number of outcomes is 6 * 6 = 36.
From these outcomes, the ones that have a sum of 4 are:
(1, 3), (2, 2) and (3, 1).
So, if we have 3 wanted outcomes from a total of 36, the probability is:
Therefore the correct option is the second one.
log₉(<em>x</em> - 7) + log₉(<em>x</em> - 7) = 1
2 log₉(<em>x</em> - 7) = 1
log₉(<em>x</em> - 7) = 1/2
Take the base-9 antilogarithm of both sides; in other words, make both sides powers of 9:
can also be written as √9 = 3, and
, so the equation reduces to
<em>x</em> - 7 = 3
Solve for <em>x</em> :
<em>x</em> = 10
The positions when the particle reverses direction are:
The acceleraton of the paticle when reverses direction is:
Why?
To solve the problem, we need to remember that if we derivate the position function, we will get the velocity function, and if we derivate the velocity function, we will get the acceleration function. So, we will need to derivate two times.
Also, when the particle reverses its direction, the velocity is equal to 0.
We are given the following function:
So,
- Derivating to get the velocity function, we have:
Now, making the function equal to 0, to find the times when the particle reversed its direction, we have:
We know that the particle reversed its direction two times.
- Derivating the velocity function to find the acceleration function, we have:
Now, substituting the times to calculate the accelerations, we have:
Now, substitutitng the times to calculate the positions, we have:
Have a nice day!
Answer:
<em> (a). ∠UXV, ∠XVY ; (b). UV = 8 m .</em>
Step-by-step explanation:
