<span>The maxima of a differential equation can be obtained by
getting the 1st derivate dx/dy and equating it to 0.</span>
<span>Given the equation h = - 2 t^2 + 12 t , taking the 1st derivative
result in:</span>
dh = - 4 t dt + 12 dt
<span>dh / dt = 0 = - 4 t + 12 calculating
for t:</span>
t = -12 / - 4
t = 3
s
Therefore the maximum height obtained is calculated by
plugging in the value of t in the given equation.
h = -2 (3)^2 + 12 (3)
h =
18 m
This problem can also be solved graphically by plotting t
(x-axis) against h (y-axis). Then assigning values to t and calculate for h and
plot it in the graph to see the point in which the peak is obtained. Therefore
the answer to this is:
<span>The ball reaches a maximum height of 18
meters. The maximum of h(t) can be found both graphically or algebraically, and
lies at (3,18). The x-coordinate, 3, is the time in seconds it takes the ball
to reach maximum height, and the y-coordinate, 18, is the max height in meters.</span>
[tex]\begin{gathered} \text{The inequality is,} \\ 5
Answer:
y = - 0.9167 - 0.75x
Step-by-step explanation:
Given the data:
(−1, 0), (1, −2), (3, −3)
X : - 1, 1, 3
Y : 0, - 2, - 3
The regression model is written in the form:
y = C + mx
Where ;
C = intercept ; m = slope / gradient
Using the regression model calculator on the data values given above :
Slope (m) = - 0.75
Intercept (c) = - 0.9167
Hence,
y = - 0.9167 - 0.75x
c
Answer:
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