An urn contains 5 are red balls and 6 blue balls. Suppose 5 are randomly selected without replacement. What is the probability t
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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>
an isosceles triangle is a triangle with two twin sides, and therefore two twin angles.
if one angle is 98°, well, we can't have another 98° angle because that makes 98+98 = 196°, and the sum of all interior angles in a triangle cannot be more than 180°.
so the other remaining angles must be the twin smaller angles, namely 180 - 98 = 82, and each twin takes half of that, namely 41°.
Check the picture below.
Answer:
Maximum (250,125) Answer
Step-by-step explanation:
This is more of a graphing problem than it is anything else.
Begin by graphing all 4 given equations.
When you do that, mark the intersection points of at least 2 lines. In this case it is exactly 2 lines for each intersecting point.
6x + 4y <= 2000 and 2x + 4y <= 1000 intersect at (250,125)
x=>0 and y=>0 intersect at (0,0)
6x + 4y <=2000 and x => 0 intersect at 333.333
2x + 4y <=1000 and y>=0 intersect at 0,250.
Any other intersection points fall outside the range of the givens. The shaded part we are interested in is sort of a very dark green/blue. It is the interior of the quadrilateral determined by the 4 vertices that are marked.
Now all you have to do is determine the maximum point using P=15x + 12y
For 0,0 P = 15*0 + 12,0 = 0
For 0,250 P = 15*0 + 12*250 = 3000
For 333.3333,0 P = 15*333.3333 + 12*0 = 5000 rounded.
For 250,125 P = 15*250 + 12*125 = 5250 Which is the maximum
Answer (250,125) produces the maximum value Answer
