According to Egyptian artifacts, how early was the concept of the square root known? 1850 BCE 1700 BCE 400 CE 830 CE
2 answers:
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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>
The number of pages in the book is 180
<u>Explanation:</u>
The first thing we should do is to convert these fractions to percentage
3/4 of the remainder on thursday:
Thursday: (100 - (13.33 + 33.33 + 22.22) * (3/4) = 23.33%
he still has 14 pages left to read on friday
Friday: [100 - (13.33 + 33.33 + 22.22) ] - 23.33 = 7.77%
Which means that 14 pages represent 7.77% of the book.
Therefore the number of pages of the book is given by:
Therefore, number of pages in the book is 180