Jonas jogged up the hill at an average rate of of a 1/12 mile per minute and then walked down the hill at an average rate of of
a 1/16 mile per minute. The round trip took him 42 minutes. What is the missing value in the table that represents the distance of the trip down the hill?
Table
Rate Time Distance
Up the Hill 1/12 x 1/12(x)
Down the Hill 1/16 42-x ?
Table
Rate Time Distance
Up the Hill 1/12 x 1/12(x)
Down the Hill 1/16 42-x ?
2 answers:
Refer to attached table
Answer -
(In miles)
EXPLANATION
We know that distance traveled is calculated by multiplying average speed by total time.
According to the table,
Uphill average speed =
(in miles per minute)
Uphill travel time = x (in minutes)
Total distance uphill =
(In miles)
The same way,
Downhill average speed =
(in miles per minute)
Downhill travel time = 42 - x
Total distance downhill = Speed * Time = (In miles)
Answer -
EXPLANATION
We know that distance traveled is calculated by multiplying average speed by total time.
According to the table,
Uphill average speed =
Uphill travel time = x (in minutes)
Total distance uphill =
The same way,
Downhill average speed =
Downhill travel time = 42 - x
Total distance downhill = Speed * Time =
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Answer with Step-by-step explanation:
1. We are given that an expression
We have to prove that this expression is always is even for every integer.
There are two cases
1.n is odd integer
2.n is even integer
1.n is an odd positive integer
n square is also odd integer and n is odd .The sum of two odd integers is always even.
When is negative odd integer then n square is positive odd integer and n is negative odd integer.We know that difference of two odd integers is always even integer.Therefore, given expression is always even .
2.When n is even positive integer
Then n square is always positive even integer and n is positive integer .The sum of two even integers is always even.Hence, given expression is always even when n is even positive integer.
When n is negative even integer
n square is always positive even integer and n is even negative integer .The difference of two even integers is always even integer.
Hence, the given expression is always even for every integer.
2.By mathematical induction
Suppose n=1 then n= substituting in the given expression
1+1=2 =Even integer
Hence, it is true for n=1
Suppose it is true for n=k
then is even integer
We shall prove that it is true for n=k+1
=
=
=Even +2(k+1)[/tex] because is even
=Sum is even because sum even numbers is also even
Hence, the given expression is always even for every integer n.