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To balance chemical equations we need to look at each element individually on both sides of the equation.
To start with we can add up the elements to see which are unbalanced.
CaCO3 + HCl -> CaCl2 + CO2 + H2O
There is one Calcium atom on the left and one Calcium atom on the right so this is balanced.
There is 1 Carbon atom on the left and 1 Carbon atom on the right so this is balanced.
There are 3 Oxygen atoms on the left and 3 Oxygen atoms on the right so this is balanced.
There is 1 hydrogen atom on the left but 2 on the right so this is unbalanced. Therefore we need to balance it by using 2 molecules of HCl:
CaCO3 + 2HCl -> CaCl2 + CO2 + H2O
Lastly we need to check that the chlorine is balanced, and it is as we can see there are now 2 on each side. Therefore this is now a balanced equation.
Whenever we balance an eqaution you have to change the number of molecules used represented by the big numbers before a molecule e.g 2HCl. You cannot change the subscript (small) numbers as this is the number of each element in a molecule, and you would end up making up your own molecule that doesn't make sense! For example you could not do H2Cl!
The easiest way to balance equations is by going through step by step and each time you make a change- check how it affects the rest of the equation.see more
The control of body temperature as well as other factors such as blood CO2 concentration, or blood glucose concetration is part of a biological mechanism called homeostasis.
Blood vessels have the ability to dilate and constrict to control body temperatre.
When body temperature is too low, the tiny blood vessels near the surface of the skin (capillaries) constrict (vasoconscriction). This decreases the blood flow near the surface of the skin so less heat is lost through radiation.
When body temperature is too high, the capillaries dilate (vasodilation), which increases blood flow near the surface of the skin and so more heat is lost through radiation.see more
To simplify this equation we need factorize both quadratic equations into brackets, so we can then cancel out terms on both the denominator and numerator.
For the first euqation: x2-9, there is no x value so when we split the quadratic equation into 2 brackets we know our values must add up to 0. As it is x2 we know that each bracket has an x.
(x )(x ), becuase there is a minus sign we can deduce that one of the brackets must have a negative sign. Therefore as 9 is a square number we can deduce that it is (x-3)(x+3).
For the second quadratic there is a 2x2 so we know that there must be a 2x and an x in each bracket, (2x )(x ). We must then think of 2 values that times together to make -3. We know that one of our values must be neative and one positive in order to make -3. (2 negatives or 2 positives would both make a positive). Values we may have are: -1,3 or 1,-3.
Therefore by methods of trial and error our second qudratic is: (2x-1)(x+3)
We can then put both factorised quadratics back into the original equation and cancel out an brackets that are the same:
We can see that (x+3) is common on both the numerator and denominator so it can be cancelled out. Therfore our simplified equation is: