Answer:
Step-by-step explanation:
Let the time flown by the flying carpet be 
. Then, we have that 
.
We multiply both sides of the equation by to get 
.
We subtract 
from both sides to get 
.
We divide both sides of the equation by 
.
We know that the speed of the flying carpet in still wind is the average of the rates of the speed of the flying carpet with the wind and against the wind.
The speed with wind is 
mph.
The speed against wind is 
mph.
The speed in still wind is 
.
Therefore, the answer is 
and we're done!
Answer:
(-∞,7) U (7,∞)
Step-by-step explanation:
f(x)= x+2
g(x) = x-7
Here we have x-7 in the denominator
To find domain we set the denominator =0 and solve for x
x-7=0
Add 7 on both sides
x=7
x=7 makes the denominator 0 that is undefined
So we ignore 7 for x
Hence domain is
(-∞,7) U (7,∞)
Proving a relation for all natural numbers involves proving it for n = 1 and showing that it holds for n + 1 if it is assumed that it is true for any n.
The relation 2+4+6+...+2n = n^2+n has to be proved.
If n = 1, the right hand side is equal to 2*1 = 2 and the left hand side is equal to 1^1 + 1 = 1 + 1 = 2
Assume that the relation holds for any value of n.
2 + 4 + 6 + ... + 2n + 2(n+1) = n^2 + n + 2(n + 1)
= n^2 + n + 2n + 2
= n^2 + 2n + 1 + n + 1
= (n + 1)^2 + (n + 1)
This shows that the given relation is true for n = 1 and if it is assumed to be true for n it is also true for n + 1.
<span>By mathematical induction the relation is true for any value of n.</span>
Answer:
the area = 25
Step-by-step explanation:
a= side length x side length
a = 5 x 5
a = 25
Answer:
65.45
Step-by-step explanation:
you do 3.14*5^2*2.5/3
