What is the number six million, thirty thousand, expressed in scientific notation
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The roots of the equation , 2+3=m, are non real roots.
The quadratic formula's discriminant is represented by the square root symbol -4ac. If there are two solutions, one solution, or none at all, the discriminant informs us.
As of now, 2m²+3=m we need to find the kind of roots they have.
2m²+3=m
2m²-m+3=0
Here, we can derive the following values from the equation:
a = 2, b = -1, c = 3
An equation's discriminant is stated as:
D = b²-4ac
D = (-1)(-1) - 4(2)(3)
D = 1 - 24
D = -23
Discriminant can determine the kind of roots that the equation contains.
In this instance, the discriminant is below 0.
The equation's roots are complex conjugates when D < 0.
Hence the roots for the equation are non real roots.
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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>
