The denominator of a fraction is 10 more than its numerator.
1 answer:
The right answer is Option C : 5
Step-by-step explanation:
Let,
The numerator of fraction = x
The denominator of a fraction is 10 more than its numerator.
When 1/3 is added to this fraction,
the resulting fraction’s denominator is three times the denominator of the original fraction its numerator is 15 less than its denominator
Therefore, it becomes
Taking LCM on left side
Multiplying both sides by 3(x+10)
The numerator of original fraction is 5.
The right answer is Option C : 5
Keywords: fraction, addition
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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>
