Find the length of the missing leg of a right triangle given a leg of length 8 and a hypotenuse of length 10.
2 answers:
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Lets say that the two unknown integers are 
and 
.
We know the following things about and :
And, we want to find
.
To solve this, we'll use the expansion of the squared of the sum of any two inegers; this is expressed as:
So, given what we know about the unknown integers, the previous can be written as:
We can easily solve for:
The answer is 168.
Another approach to solve the problem is, from the two starting equations, compute the values of and , which are 12 and 14, and directly compute their product; however, the approach described is more elegant.
We know the following things about
And, we want to find
To solve this, we'll use the expansion of the squared of the sum of any two inegers; this is expressed as:
So, given what we know about the unknown integers, the previous can be written as:
We can easily solve for
The answer is 168.
Another approach to solve the problem is, from the two starting equations, compute the values of
The chart has been completed in the picture attached.
Step-by-step explanation:
Step 1:
It is given that the number of bacteria doubles every 6 hours.
So if there are 1 million now, in 6 hours there would be double that i.e. 2 million and it will go on.
Step 2:
As the first column says the number of 6-hour periods, the second column is the actual number of hours.
So the second column is multiples of 6 so the second column is filled with;
0, 6, 12, 18, 24, 30, 36, 42 and 48.
Step 3:
The current population is calculated by multiplying the previous population by 2.
For 0 hours, the population = 3 million,
For 6 hours, the population = million,
For 12 hours, the population = million,
For 18 hours, the population = million,
For 24 hours, the population = million,
For 30 hours, the population = million,
For 36 hours, the population = million,
For 42 hours, the population = million, and
For 48 hours, the population = million.
So at the end of 48 hours, there will be approximately 768 million bacteria on the pinhead.
Answer:
Step-by-step explanation:
The zeros of the polynomial are all the values of x for which the function
In this case we know that the zeros are:
,
Now we can write the polynomial as a product of its factors
Note that the polynomial is of degree 3 because the greatest exponent of the variable x that results from multiplying the factors of f (x) is 3