(a) Differentiate each of the components to get r'(t). The rule is
.. d/dt (a*e^(bt)) = a*b*e^(bt)
The answer you have shown is the correct one.
(b) See the figure. The red curve is the position r(t) for 0 ≤ t ≤ 2. The dashed orange line is the tangent line, whose equation is
.. L(t) = r(0) +r'(0)*t = (2 +2t)i +(3 -3t)j
Answer:
Step-by-step explanation:
h=-5t²+135
when t=3 s
h=-5(3)²+135=-45+135=90 m
Answer:

Step-by-step explanation:
Given
Points: (1, 9) and (9, 3)
Ratio = 2/3
Required
Determine the coordinate of the center
Represent the ratio as ratio

The new coordinate can be calculated using

Where



Substitute these values in the equation above



Hence;
<em>The coordinates of the new center is </em>
<em></em>
Answer:
26x³ - 12x² + 5x + 7
Step-by-step explanation:
- (2x³ - 3x + 11) - (3x² + 1) x (4 - 8x)
- 2x³ - 3x+11 - (12x² - 24x³ + 4 - 8x)
- 2x³ - 3x + 11 - 12x² + 24x³ - 4 + 8x
- 26x³ + 5x + 7 - 12x²
= 26x³ - 12x² + 5x + 7