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Calculus
The branch of mathematics that deals with the study of continuously changing quantities, with the use of limits and the differentiation and integration of functions of one or more variables, is called Calculus. Calculus analyzes aspects of change in processes or systems that can be modeled by functions. The English physicist, Isaac Newton, and the German mathematician, G. W. Leibniz, working independently, developed calculus during the 17th century.
25,068 Questions
What is X squared plus 6x minus 55?
Without knowing what "x" is, we cannot say what the answer will be. And without knowing the answer, we cannot solve for "x".
Set x at zero, for example. Zero squared is zero, plus 6 time zero which is zero, minus 55. Your answer is then -55.
Set x at one, for example. One squared is one, plus 6 times 1 which is six, minus 55. Your answer is then -48.
Etc.
Factor this trinomial x2 plus 2x-15 equals?
You need to factor the following trinomial:
x2 + 2x - 15
In other words, you want to find an expression in this form, which is equal to the trinomial:
(A + B)(C + D)
Finding the values for A, B, C, and D is mostly a trial-and-error process, but here are a few tips that are helpful for situations such as this:
- AC (A times C) equals the number of the highest order in the trinomial (in this case, x2)
- BD equals the number of the lowest order in the trinomial (in this case, -15)
- AD plus BC equals the remaining number in the trinomial (in this case, 2x)
Since A times C equals x2, we know that we have something like this:
(x + B)(x + D)
Now, we also know that -3 times 5 is -15, and -3 plus 5 is 2. So, we have found the following:
(x - 3)(x + 5)
You can use the FOIL pattern (multiply the First numbers, then the Outside, Inside, and Last numbers and add together) to check that this factorization is correct:
(x - 3)(x + 5)
= AC + AD + BC + BD
= x2 + 5x - 3x - 15
= x2 + 2x - 15
It looks like that's the right answer. So, the factorization of this trinomial is (x - 3)(x + 5).
How do you solve problems like -2 plus 5x equals 13?
This is how I learned:
-2 + 5x = 13
5x + -2 + 2 = 13 + 2
5x = 15
-- --
5 5
x = 3
Then check:
-2 + 5 x 3 = ?
-2 + 15 = ?
13 =13
This is because when you add and subtract integers, adding negative is subtracting.
Subtracting negatives is like adding, but the result is negative. So, when you take
-2 + 2 it equals 0.
Yes, a set can be infinitely large. For instance, the set of all odd integers is infinitely large.
Solve this equation 9h plus 2 - 79?
That's not an equation, and there's no solution required.
An equation has an 'equals' sign ( " = " ) somewhere in it.
That expression is just 9h - 77. Its numerical value depends on what 'h' is. Every time
'h' changes, the value of that expression changes. That's all there is to say about it.
Subtract 12x from each side: 3x - 5 = 7
Add 5 to each side: 3x = 12
Divide each side by 3: x = 4
What is the square root of 121-8 to the second power divided by 32 x 4?
(sqrt(121)-8)**2/(32*4)
(11-8)**2/(128)=9/128
(-11-8)**2/(128)=361/128
sqrt121-8**2/(32*4)
11-64/128=10.5
-11-64/128=-11.5
sqrt(121-8**2)/(32*4)
sqrt(57)/128
-sqrt(57)/128
(sqrt(121)-8)**2/32*4
(11-8)**2/32*4=9/8
(-11-8)**2/32*4=361/8
sqrt121-8**2/32*4
11-64/32*4=3
-11-64/32*4=-19
sqrt(121-8**2)/32*4
sqrt(57)/8
-sqrt(57)/8
How is being good at mathematics going to help you with physics chemistry and engineering?
Because the majority of economics, physics and engineering and general chemistry requires you to be able to calculate, not just learning concepts.
It is correct to write it any way you like.
However, when dealing with equations it is usual to give the dependent variable (usually y) first; if it is unknown which variable is the dependent one (or for any general expression), they are usually written in alphabetical order.
What is the inverse function of y equals -x-5?
This was on my test yesterday . . .it's really easy, just put a one over the -x-5.
