<span>If you have a quadratic equation in the form <span>a<span>x2</span>+bx+c</span>
</span>Step 1) Determine the product of AC (the coefficients in a quadratic equation)Step 2) Determine what factors of <span><span>a⋅c</span> sum to b</span>Step 3) "ungroup" the middle term to become the sum of the factors found in step 2Step 4) group the pairs.
Answer:
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Step-by-step explanation:
First you need to find the area of the whole circle.

The radius is given as 10, so just insert 10 into the equation of the area of a circle equation.

Putting

after the 100 because that is what is commonly done.
Because the circle is then being split into 4 equal sections, we need to find 1/4 of the area of the whole circle to find the area of one of these sections.
Since the area of the whole circle is

then we just divide that by 4,
leaving us with 25

and that is our final answer
Answer:
Step-by-step explanation:
As the statement is ‘‘if and only if’’ we need to prove two implications
is surjective implies there exists a function
such that
.- If there exists a function
such that
, then
is surjective
Let us start by the first implication.
Our hypothesis is that the function
is surjective. From this we know that for every
there exist, at least, one
such that
.
Now, define the sets
. Notice that the set
is the pre-image of the element
. Also, from the fact that
is a function we deduce that
, and because
the sets
are no empty.
From each set
choose only one element
, and notice that
.
So, we can define the function
as
. It is no difficult to conclude that
. With this we have that
, and the prove is complete.
Now, let us prove the second implication.
We have that there exists a function
such that
.
Take an element
, then
. Now, write
and notice that
. Also, with this we have that
.
So, for every element
we have found that an element
(recall that
) such that
, which is equivalent to the fact that
is surjective. Therefore, the prove is complete.
The quantity of the liquid in Richard's tank after 20 minutes will be 120 gallons and in Jason's tank will be 240 gallons.
<h3>What are gallons?</h3>
A gallon is a British unit which is used for the measurement of liquids that is equal to eight pints. In Britain, it is equal to about 4.546 litres. In America, it is equal to about 3.785 litres.
It is given in the question that:-
Richard fills his pool at a rate of 6 gallons per minute.
Jason's pool already contains 200 gallons, and he fills it at a rate of 2 gallons per minute.
After 20 minutes the amount of liquid in the tank will be:-
For Richard = 6 gallons per minute. x 20 minutes= 120 gallons
For Jason= 2 gallons per minute x 20 =40 gallons
Jason has 200 gallons already in the tank
So it will become = 200+24=240 gallons.
Hence quantity of the liquid in Richard's tank after 20 minutes will be 120 gallons and in Jason's tank will be 240 gallons.
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