3 lines are shown. A line with points P, R, N intersects a line with points O, R, M at point R. A line extends from point R to p

Answer: Fourteen students are not enrolled in any foreign languages.

Step-by-step explanation: Begin with the total student count and subtract the number enrolled in each language class. This yields 19 for French, 12 for Spanish, and 7 for those taking both. Summing these numbers gives 38. Next, repeat this process, subtracting each category from 30 to find how many students are not participating in either language. You would end up with 11 for French, 18 for Spanish, and 23 for both. Adding these values results in 52. Finally, subtract 38 from 52 to arrive at the final result of 14.

Answer:

Step-by-step explanation:

Step 1:-

We have c1(t) = e^ t i + (sin(t))j + t³k

and c2(t) = e^−t i + (cos(t))j − 6t³k.

By adding c1(t) and c2(t):

c1(t)+c2(t) = e^ t i + (sin(t))j + t³k + e^−t i + (cos(t))j − 6t³k

Now, employing the derivative formula:

Next, differentiate with respect to 't'

By factoring out i, j, and k terms, we arrive at:

Answer:

The sequence decreases by 5

thus the subsequent numbers are

-13,-18,-23,-28