Which equation does the graph below represent?
1 answer:
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Answer: vector equation r = (7+3t)i + (4+2t)j + (5 - 5t)k
parametric equations: x = 7 + 3t; y = 4 + 2t; z = 5 - 5t
Step-by-step explanation: The vector equation is a line of the form:
r = + t.v
where
is the position vector;
v is the vector;
For point (7,4,5):
= 7i + 4j + 5k
Then, the equation is:
r = 7i + 4j + 5k + t(3i + 2j - k)
<u><em>r = (7 + 3t)</em></u><u><em>i</em></u><u><em> + (4 + 2t)</em></u><u><em>j </em></u><u><em>+ (5 - 5t)</em></u><u><em>k</em></u>
The parametric equations of the line are of the form:
x = + at
y = + bt
z = + ct
So, the parametric equations are:
<em><u>x = 7 + 3t</u></em>
<em><u>y = 4 + 2t</u></em>
<em><u>z = 5 - 5t</u></em>
You divide 8,096 by 21 and you should get the answer of 385.52381
Part A
To find the ticket price when the price is $16
Let us substitute the value of t = 16
p = -10 x (16 x16) + 500 x 16 + 60
p = -2560 + 8000 + 60
p =$ 5500
Part B
To get the maximum profit, we will have to differentiate P with respect to t
The maximum profit will be obtained when the derivative is zero
-20t + 500 = 0
20t = 500
t = 500/20
t = 25
This means that the ticket price has to be $25 so as to obtain the maximum price
Part C
The maximum profit will be obtained by substituting t = 25 into the original equation