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A very way to understand this very logically.
First know what is multiplication?
It is recurring addition.
So if we multiply 3 by (-2), that means:-
(-2)+(-2)+(-2)= -6
Now see the examples below:
4 X (-4) = -16
3 X (-4) = -12
2 X (-4) = -8
1 X (-4) = -4
0 X (-4) = 0
Have you noticed a trend. Notice carefully that as the numbers which are being multiplied by (-4) are decreasing 1 by 1 the product is increasing by (+4).
So for the numbers 4,3,2,1,0 the products are:-
-16
-16+4= -12
-12+4= -8
-8+4= -4
-4+4=0
So what will be in the next step when we do:
(-1) X (-4)=?
The series will continue 0+4 an will result to a positive 4
and it will go like this:
(-1) X (-4)= 4
(-2) X (-4)= 8
(-3) X (-4)= 12
+4 is added in each step. This was the best explanation to this according to me which was told to me by my teacher which he made himself.
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What is the answer to the problem X cubed plus six x squared plus three x plus one divided by x minus two?
Your answer will depend on the parameters of the instructions. If you're looking for the first derivative, simply use the product rule by changing the denominator to a negative exponent and bringing it up (take the negative square root of the quantity x-2 to the top). Then, follow the rules of calculus and algebra. Wow, that's a mess. Let's see... you get "the quantity x cubed plus 6x squared plus 3x plus 1 times the quantity -1(x-2) raised to the negative second plus the quantity x-2 raised to the negative first times the quantity 3x squared plus 12x plus 3." This is because of the Product Rule. Simplifying (by factoring out (x-2) raised to the negative second and combining like terms) gives us "(x-2) raised to the negative second times the quantity 2x cubed minus 24x minus 7." This can also be written as "2x cubed minus 24x minus 7 all over the quantity x-2 squared." f'(x)= 2x^3-24x-7 (x-2)^2
The product of two positive numbers is 363 Minimize the sum of the first and three times the second?
The first constraint implies x*y=363, while you are finding the minimum of x+3y. You can do this with multivariable calculus approaches, but I will assume the simplest method is desired and use single-variable calculus methods. Since xy=363, y=363/x Substitute this into x+3y, and you get: f(x)=x+3(363/x)=x+1089/x Since you have this function as a function of a single variable now, you can minimize it like any other single variable function. f'(x)=1-1089x-2 by setting f'(x)=0, the solutions x=33 and x=-33 are found. x=-33 is an extraneous solution, since you are required to have positive numbers. So, you must investigate x=33 and confirm it is a minimum. If x=33 is a minimum of f(x), then values less than x=33 will yield a negative value in f'(x), since the function f(x) must slope downward up until it reaches a minimum. Conversely, values greater than x=33 will yield positive values in f'(x). 1<33 f'(1)=-1088 -1088<0, so f'(1) is negative 40>33 f'(40)=511/1600 511/1600>0, so f'(40) is positive. In a final summating statement: Since the function f(x)=1-1089/x2 has a critical point at x=33 and since values less than x=33 result in negative values of f'(x) and values greater than x=33 result in positive values of f'(x), x=33 is a local minimum of f(x). To get your final final answer: x=33 y=363/x implies y=363/33=11 x=33,y=11
Find the product of two numbers that add up to 64?
There are many pairs of numbers that add of to 64. One is (1,63), and the product is 63. Another is (2,62), and the product is 124. There seems to be something missing from the question, perhaps some constraint on the product. Please restate the question.
What makes a product in math special?
A product in maths is found by multiplying numbers together. Not sure about the use of the word special?
What would be the product of zero and infinity?
There is no way to arrive at any mathematical result for the product of zero and infinity; it is a meaningless expression.
The product of any two integers is a positive integer?
No, if a negative integer is multiplied by a positive integer, the product is negative. However, if both of the integers are either positive or negative, the product is positive.
What can you say about the product of an integer and a positive integer?
-- The product is an integer. -- If the original two integers are both positive, then the product is positive. -- If the original two integers have different signs, then the product is negative.
What is the product of a positive integers and negative integer?
always a negative
What is the product of two negative integers?
The product of two negative integers is positive as for example -4 times -5 = 20
What is the product of an even number of negative integers?
A positive integer.
Are the sum of two negative integers positive?
No. Two negative integers added together will never equal a positive integer. It is the product of two negative integers that is positive.
What is the rule in dividing integers?
The rule in dividing integers is to divide the absolute values. Two positive integers or two negative integers equals positive product. If one integer is positive and the other is negative, the product is negative.
What is the product of 5 negative integers and 1 positive integer?
Negative 4
Is the product of a negative and positive integer a negative?
Yes. The product of a negative integer and a positive integer is a negative integer.
What is the rules for multiplication integers?
When multiplying integers, multiplying by the same sign will always produce a positive integer. Such as a negative times a negative equals a positive. If the signs are different then the product will be a negative.
Is the product of 4 negative integers positive or negative?
Positive. The product of even numbers of negative integers is always positive, whereas the product of odd nummbers of negative integers is always negative.
How do you multiply positive and negative integers?
The product of a positive and a negative number (integer or otherwise) is negative.For example, (4) x (-3) = -12.The product of a positive and a negative number (integer or otherwise) is negative.For example, (4) x (-3) = -12.The product of a positive and a negative number (integer or otherwise) is negative.For example, (4) x (-3) = -12.The product of a positive and a negative number (integer or otherwise) is negative.For example, (4) x (-3) = -12.
