We can formulate the trajectory of the parabola using the vertex form equation: y = a (x – h)^2 + k. The coordinates for the vertex are at h and k, representing the peak height, thus h = 250 and k = 120. Consequently, the equation becomes y = a (x – 250)^2 + 120. At the starting point where x = 0 and y = 0, we find a: 0 = a (0 – 250)^2 + 120, which simplifies to 0 = a (62,500) + 120, leading to a = -0.00192. The complete equation is y = -0.00192 (x – 250)^2 + 120. To determine y when x = 400, we substitute: y = -0.00192 (400 - 250)^2 + 120, yielding y = 76.8 ft. Hence, the ball clears the tree by 76.8 ft – 60 ft = 16.8 ft.
For Mia's calculations, she should use y first because y signifies 22, while x indicates 4 dollars earned weekly.
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:
Robyn's model is logical, while Mark's is illogical.
Step-by-step explanation:
This question doesn't require calculations. What we need to do is analyze each model logically.
Mark's
Mark's representation indicates 20 instead of 2, which signifies that 200 is ten times greater than 20, making it nonsensical.
Robyn's
Robyn's representation displays 2, suggesting that 200 is 100 times greater than 2, which is not only accurate but also reasonable since 100 * 2 equals 200.