To solve for the number of ushers needed based on the number of spectators, we can use the concept of direct proportionality.
We know that the number of ushers \( U \) is directly proportional to the number of spectators \( S \). This can be expressed with the equation:
\[ U = kS \]
where \( k \) is the constant of proportionality.
Given that when \( S = 510 \), \( U = 17 \), we can find \( k \):
\[ 17 = k \times 510 \] \[ k = \frac{17}{510} = \frac{1}{30} \]
Now we can use this value of \( k \) to find out how many ushers are needed for \( 1,050 \) spectators:
\[ U = \frac{1}{30} \times 1050 \] \[ U = \frac{1050}{30} = 35 \]
Thus, the number of ushers needed if there are \( 1,050 \) spectators is 35 ushers.