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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
This pendulum, which is 2.24m in length, would have a period of 7.36 seconds on the moon.
9x-45 equals 0 add what to both sides and multiply both sides by what?
Add 45 to each side, giving 9x = 45. Divide both sides by 9, giving x = 5
Can multiplication principle be used to solve equations like 7x equals 63?
Just divide both sides by 7...
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).
This is done by solving either of the equations for one of the two variables, and then plugging that solution in to the other equation in place of that variable. In this case both equations equal the same variable, y, so it is very easy to do:
Given:
y = 2x + 3
y = 3x + 1
Therefore:
2x + 3 = 3x + 1
∴ 3x - 2x = 3 - 1
∴ x = 2
And then you could plug that value of x back into one of the original equations to find the value of y:
y = 2x + 3
∴ y = 2(2) + 3
∴ y = 4 + 3
∴ y = 7
So you know that x is equal to two, and y is equal to seven. You can solve for either variable first. In this case, y is the simpler value to substitute, but x can be exchanged in exactly the same way:
y = 2x + 3
∴ y - 3 = 2x
∴ (y - 3)/2 = x
Now we substitute that equation for x in our other equation:
y = 3x + 1
∴ y = 3(y - 3)/ 2 + 1
∴ y = 3y/2 - 9/2 + 1
∴ y = (3y - 9 + 2) / 2
∴ 2y = 3y - 9 + 2
∴ -y = -7
∴ y = 7
and then solve for x:
y = 2x + 3
∴ 7 = 2x + 3
∴ 2x = 4
∴ x = 2
giving you the same results.
Its y equals 4x3 plus 4x2 a quadratic equation?
Interpreting this equation as y=4x3+4x2
This is not a quadratic equation. By definition, a quadratic equation is a polynomial equation of order two, meaning it is composed only of coefficients multiplied by x's raised to any exponential power of maximum 2. The most that any of the exponents in the equation can be is 2. Since this equation has a term of 4x3, it is not quadratic since this term has an exponent of 3. This means that the equation is of degree three. This equation is a cubic equation.
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.
Yes, a set can be infinitely large. For instance, the set of all odd integers is infinitely large.
What is X2-4x plus 9 when x equals -8?
If [ x = -8 ], then
x2 - 4x + 9
= (-8)2 - 4(-8) + 9
= 64 + 32 + 9
= 105
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.
The mean value theorem can be applied to all continuous functions (or expressions), and so it is applicable here.
There is no equation in te question and furthermore, no c (other than the first letter of cos in the expression so there are no values for c to satisfy anything!
