angela fully charged her laptop, then unplugged it and tracked the battery level at certain times under constant use. the table
below shows her findings. find an equation for the line of best fit, then estimate the battery level after two hours of constant use unplugged. What’s the equation we use ? Solution ? Someone please help fast
1 answer:
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Answer: = 1087.5
Step-by-step explanation: To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedon is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.
An equation of a plane is found with a point and a normal vector. <u>Normal</u> <u>vector</u> is a perpendicular vector on the plane.
Given the points, determine the vectors:
P = (5,0,0); Q = (0,9,0); R = (0,0,4)
vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)
vector QR = (0,9,0) - (0,0,4) = (0,9,-4)
Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:
n = PQ × QR =
n = 36i + 0j + 45k - (0k + 0i - 20j)
n = 36i + 20j + 45k
Equation of a plane is generally given by:
Then, replacing with point P and normal vector n:
The equation is: 36x + 20y + 45z - 180 = 0
Second, in evaluating the triple integral, set limits:
In terms of z:
When z = 0:
When z=0 and y=0:
x = 5
Then, triple integral is:
Calculating:
= 1087.5
<u>The volume of the tetrahedon is 1087.5 cubic units.</u>
