Answer:
Exponential Decay -
A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.
Step-by-step explanation:
Hope this answered your question ^^
Find an equation of the plane that contains the points p(5,−1,1),q(9,1,5),and r(8,−6,0)p(5,−1,1),q(9,1,5),and r(8,−6,0).
topjm [15]
Given plane passes through:
p(5,-1,1), q(9,1,5), r(8,-6,0)
We need to find a plane that is parallel to the plane through all three points, we form the vectors of any two sides of the triangle pqr:
pq=p-q=<5-9,-1-1,1-5>=<-4,-2,-4>
pr=p-r=<5-8,-1-6,1-0>=<-3,5,1>
The vector product pq x pr gives a vector perpendicular to both pq and pr. This vector is the normal vector of a plane passing through all three points
pq x pr
=
i j k
-4 -2 -4
-3 5 1
=<-2+20,12+4,-20-6>
=<18,16,-26>
Since the length of the normal vector does not change the direction, we simplify the normal vector as
N = <9,8,-13>
The required plane must pass through all three points.
We know that the normal vector is perpendicular to the plane through the three points, so we just need to make sure the plane passes through one of the three points, say q(9,1,5).
The equation of the required plane is therefore
Π : 9(x-9)+8(y-1)-13(z-5)=0
expand and simplify, we get the equation
Π : 9x+8y-13z=24
Check to see that the plane passes through all three points:
at p: 9(5)+8(-1)-13(1)=45-8-13=24
at q: 9(9)+8(1)-13(5)=81+9-65=24
at r: 9(8)+8(-6)-13(0)=72-48-0=24
So plane passes through all three points, as required.
Answer:
The recipe calls for 19/12 or 1 7/9 cups.
Step-by-step:
In order to get this answer, we have to add all three fractions together. First, we have to find the LCM (Least Common Multiple) between the three denominators:
2: 2, 4, 6, 8, 10, 12
3: 3,6,9,12
4: 4,8,12
The LCM between these three denominators is 12.
4x3=12
2x6=12
3x4=12
You now multiply the numerator by the same number you multiplied by for the denominator in order to get 12:
3/4 becomes 9/12
1/2 becomes 6/12
1/3 becomes 4/12
We now add all the fractions together:
9/12+6/12+4/12= 19/12
We got 19/12 but the answer is an improper fraction so we turn it into a mixed number:
12x1=12 (7 remaining)
This is written as 1 7/12.
Hope this helps! :)
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