Find the height of the cone if the volume is 400pi in.^3 and the radius is 20 in
1 answer:
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Answer:
Step-by-step explanation:
A vector perpendicular to the plane ax+by+cz+d=0 is of the form .
So, a vector perpendicular to the plane x − y + 2z = 7 is .
The parametric equations of a line through the point and parallel to the vector
are as follows:
Put and
Therefore,
xy-plane:
Put z = 0 ⇒ t = -2 ⇒x = - 1 , y = 6
So, at point (-1,6,0)
yz-plane:
Put x = 0 ⇒ t = -1 ⇒ y = 5, z =2
So, at point (0,5,2)
xz-plane:
Put y = 0 ⇒ t = 4 ⇒ x = 5, z = 12
So, at point (5,0,12)
we will proceed to resolve each case to determine the solution
we have
we know that
If an ordered pair is the solution of the inequality, then it must satisfy the inequality.
<u>case a)</u>
Substitute the value of x and y in the inequality
------> is True
therefore
the ordered pair is a solution of the inequality
<u>case b)</u>
Substitute the value of x and y in the inequality
------> is False
therefore
the ordered pair is not a solution of the inequality
<u>case c)</u>
Substitute the value of x and y in the inequality
------> is True
therefore
the ordered pair is a solution of the inequality
<u>case d)</u>
Substitute the value of x and y in the inequality
------> is True
therefore
the ordered pair is a solution of the inequality
<u>case e)</u>
Substitute the value of x and y in the inequality
------> is False
therefore
the ordered pair is not a solution of the inequality
<u>Verify</u>
using a graphing tool
see the attached figure
the solution is the shaded area above the line
The points A,C, and D lies on the shaded area, therefore the ordered pairs A,C, and D are solution of the inequality
