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:
d) Both blocks experienced equivalent energy loss due to friction
Explanation:
As stated in the question, two tractors are pulling two identical stone blocks the same distance across similar surfacesAdditionally, block A moves at double the speed of block B when completing the race
This implies both blocks suffer from comparable friction loss
Moreover, we understand that
Energy loss from friction is 
Thus, the friction loss should be identical for both blocks
therefore, option d is the accurate choice
Answer:
The area calculates to 83.905 cm^3
Step-by-step explanation:
The overall ratio is 9 + 7 + 6 = 22
Thus, the side lengths are computed as follows;
9/22 * 44 = 18 cm
7/22 * 44 = 14 cm
6/22 * 44 = 12 cm
Heron’s formula allows us to determine the area of the triangle
First, we calculate s
s = (a + b + c)/2 = (18+14+12)/2 = 44/2 = 22
Heron’s formula can be expressed as;
A = √s(s-a)(s-b)(s-c)
where a, b, and c are 18, 14, and 12 respectively
Plugging in the values, we obtain;
A = √22(22-18)(22-14)(22-12)
A = √(22 * 4 * 8 * 10)
A = √(7,040)
A = 83.905 cm^3