Which table shows a function that is decreasing only over the interval (–1, 1)? A 2-column table with 5 rows. The first column i
2 answers:
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Answer:
(a)r=15-b
11.9 Inches
(b)See attached
Step-by-step explanation:
Length of the candle =15 inch
Let b represent the burned length of the candle (in inches)
Let r represent the remaining length of the candle (in inches).
Therefore:
(a) r+b=15
r=15-b
When b=3,1 Inches
Remaining Length, r=15-3.1=11.9 Inches
(b)The graph showing te relationship between r and b is shown below.
r is plotted on the y-axis while b is plotted on the x-axis as labelled.
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>
