Answer:
Step-by-step explanation:
Not exactly sure what your question is - I am assuming that it is something like:
Show/prove that for any integer x, x^2 - x is even.
Suppose that x is an even integer. The product of an even integer and any other integer is always even (x = 2n, so x * y = 2 n * y which is even. Therefore x^2 is even. An even minus an even is even. (The definition of an even number is that it is divisible by 2 or has a factor of 2. So the difference of even numbers could be written as 2*( the difference of the two numbers divided by 2); therefore the difference is even)
Suppose that x is an odd integer. The product of 2 odd numbers is odd - each odd number can be written as the sum of an even number and 1; multiplying the even parts with each other and 1 will produce even; multiplying the 1's will produce 1, so the product can be written as the sum of an even number and 1 - which is an odd number. The difference between two odd numbers is even - the difference between the even parts is even (argument above), the difference between 1 and 1 is zero, so the result of the difference is even.
x^2 is therefore even if x is even and odd if x is odd; The difference x^2 - x is even by the arguments above.
Answer:
Someone ples answer this
Step-by-step explanation:
It’s so hard
Answer:
Option D. 9 mi/hr downstream, 6 mi/hr upstream
Step-by-step explanation:
<u><em>The complete question is</em></u>
Alicia can row 6 miles downstream in the same time it takes her to row 4 miles upstream. She rows downstream 3 miles/hour faster than she rows upstream. Find Alicia’s rowing rate each way
Define the variables
Let
x -----> Alicia's rowing rate downstream in miles per hour
y ----> Alicia's rowing rate upstream in miles per hour
we know that
The rate is equal to the distance divided by the time
so
The time is equal to the distance divided by the rate
we have
-----> equation A
----> equation B
equate equation A and equation B
<em>Find the value of x</em>
therefore
Alicia's rowing rate downstream is 9 mi/h
Alicia's rowing rate upstream is 6 mi/h
Answer:
12
Step-by-step explanation:
We know that 1/3 of a pizza is cheese meaning that 6 pizzas are made of cheese and there are only two leaving the rest pepperoni and 12 are left if we subtract the cheese pizzas minus the 18 pizzas we have 12 which are pepperoni.
The work done (in foot-pounds) in stretching the spring from its natural length to 0.7 feet beyond its natural length is 1.23 foot-pound
<h3>Data obtained from the question</h3>
From the question given above, the following data were obtained:
- Force (F) = 3 pounds
- Extension (e) = 0.6 feet
- Work done (Wd) =?
<h3>How to determine the spring constant</h3>
- Force (F) = 3 pounds
- Extension (e) = 0.6 feet
- Spring constant (K) =?
F = Ke
Divide both sides by e
K = F/ e
K = 3 / 0.6
K = 5 pound/foot
Thus, the spring constant of the spring is 5 pound/foot
<h3>How to determine the work done</h3>
- Spring constant (K) = 5 pound/foot
- Extention (e) = 0.7 feet
- Work done (Wd) =?
Wd = ½Ke²
Wd = ½ × 5 × 0.7²
Wd = 2.5 × 0.49
Wd = 1.23 foot-pound
Therefore, the work done in stretching the spring 0.7 feet is 1.23 foot-pound
Learn more about spring constant:
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