Complete question is;
Given n objects are arranged in a row. A subset of these objects is called unfriendly, if no two of its elements are consecutive. Show that the number of unfriendly subsets of a k-element set is ( n−k+1 )
( k )
Answer:
I've been able to prove that the number of unfriendly subsets of a k-element set is;
( n−k+1 )
( k )
Step-by-step explanation:
I've attached the proof that the number of unfriendly subsets of a k-element set is;
( n−k+1 )
( k )
The equation of a line is y=-1/4x-7, (option 1)
<h3>
What is the equation of a line? </h3>
A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis.
<h3>
How do you find the equation of a line?</h3>
Write the equation in the form y = mx + b to find the slope m and the y-intercept. This will allow you to graph the equation using the slope and y-intercept.
Given:-
Equation of the line is y=4x+8
The point through which the line passes (-8,4).
here the slope of the line is m1=4
To find the perpendicular line we know the formula
m1*m2=-1
By putting the value of m1 we get m2= -1/4
By using the one-point formula of the line we have
=>(y-y1)=m2*(x-x1)
By putting the values of y1 and x1 we get
(y1,x1)=(-8,4)
=>(y+8)=-0.25*(x-4)
y+0.25x+7=0
Hence the desired equation of the line is y=-1/4x-7
To find more about the straight line equations visit :
brainly.com/question/25969846
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Answer:
Step-by-step explanation:
Since, the surface area of a cylinder,
................(1)
Where,
r = radius,
h = height,
If 
( by middle term splitting )
By zero product property,
r = 3 or r = - 6 ( not possible )
Thus, radius, r = 3 meters,
Now, differentiating equation (1) with respect to t ( time ),
∵ h = constant, ⇒ dh/dt = 0,
We have, 
Now,
Volume of a cylinder,
Differentiating w. r. t. t,
Answer:
28
Step-by-step explanation:
8 - 8 / 8 + 7 *3
PEMDAS
8 - 1 * 7 - 3
8 - 1 + 21
28
