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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 does x equal if x square equals -3?
If you want to work with real numbers, there is no answer. the square of any number, whether positive or negative, is a positive number, so x2 cannot be -3.
If you accept complex numbers as a solution, the square root of minus 1 is called i (when squared, both i and -i give -1); the square root of -3 is equal to the square root of 3 times i, the square root of -4 is 2i, etc.
Complex numbers are frequently used in some areas of science (electricity, quantum mechanics, and others); in other areas, it just doesn't make sense to use them. Similarly, for some problems fractional solutions, or negative solutions, may be acceptable, for others, not.
How do you solve 5 to the power of x equals 15?
Using logarithms. In economics, we most commonly use the the base e, which is known as ln. For example
5^x = 15, apply ln[.] to both sides
ln[5^x] = ln[15]
and since logarithms have the property of turning exponents into coefficients
xln5 = ln15
x = ln15/ln5
x = 1.6826
How do you solve 3log5 125 - log2 8 equals x?
Your calculator won't usually have a function to calculate logs in base 5 or base 8 directly, but this can easily be solved. For example:
log5125 = log 125 / log 5 (taking both logs in base 10, or both logs in base e)
In this particular case, you can also solve the equation mentally - you don't even need a calculator! Just use the definition of a log: "To what power must I raise 5 to get 125?" The answer to this is, by definition, log5125. Similarly with log28.
In the expression 8 - x, "8" is the minuend and "x" is the subtrahend. When you subtract x from 8, you are finding the difference between the two values. The result will vary depending on the value of x.
Oh, dude, x times y equals the product of x and y. It's like when you have x groups of y things, and you're too lazy to count them all out individually, so you just multiply them together and call it a day. Math, man, it's wild.
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What is the value of x when y equals 0?
Well, isn't that a happy little question! When y equals 0, it means that the point is right on the x-axis. So, the value of x at that point is also 0. Just like painting, math can be a beautiful and peaceful experience when we take our time to understand it.
What is the remainder when 2 is synthetically divided into the polynomial -3x2 plus 7x minus 9?
Oh, what a happy little question! Let's gently divide 2 into the polynomial -3x^2 + 7x - 9. When we do that, we find that the remainder is -6x - 21. Just remember, there are no mistakes, only happy little accidents in math!
Well, honey, solving 3x + 4 is as easy as stealing candy from a baby. You just subtract 4 from both sides to isolate the 3x, then divide by 3 to get x. Voila! You've cracked the code and solved that little math puzzle.
6 x 2.25 equals 13.5. This calculation involves multiplying the whole number 6 by the decimal number 2.25. To find the product, you can multiply 6 by 225 (ignoring the decimal point) to get 1350, and then move the decimal point two places to the left to account for the two decimal places in 2.25, resulting in 13.5.
The graph of y = -x^2 + 3 crosses the x-axis when y = 0. To find the number of times it crosses the x-axis, we set -x^2 + 3 = 0 and solve for x. This equation has two solutions, so the graph crosses the x-axis twice. Therefore, the answer is C. Two.
This is a hard concept to understand, since infinity is not a definite number. It can keep carrying on forever, which makes it a surreal number.
However, 1 can be measured by infinity as well, due to the never ending amount of decimal places, for example, 1 x 10^-6 [0.000001], 1 x 10^-12 [0.000000000001] and so on.
So, since it is impossible to determine the boundary of infinity, for 1 and for infinity itself, it is most agreed that the result will still be infinity, for whatever sum or subtraction you do, excluding infinity - infinity (0).
What would be the value of y when x is 100?
To determine the value of y when x is 100, we need more information about the relationship between x and y. If we have an equation or function relating x and y, we can substitute x=100 into the equation to find the corresponding value of y. Without this information, it is impossible to determine the value of y when x is 100.
How do you simplify x times 3?
Well, honey, to simplify x times 3, you just multiply them together. So, the answer is 3x. It's as simple as that, darling.
Since we always say that x equals the number 1, because we can assume that the equation is 1 + 1. So the answer is 2.
What is 2 times the sum of x and y?
To find 2 times the sum of x and y, you first need to calculate the sum of x and y by adding the two variables together. Once you have the sum, you multiply it by 2 to get the final result. In mathematical terms, the expression for 2 times the sum of x and y can be written as 2(x + y).
Whats the area of 5cm and 3cm?
If the dimensions given are the length and the width, the area is determined by multiplying the length X width (5 X 3 = 15 sq cm).
This question cannot be answered without the whole equation:
If the equation is y = 2x, then y = 6 for x = 3.
If the equation is y = x + 2, then y = 5 for x = 3.
If the equation is y = 99/x, then y = 33 for x = 3.
If you can provide the complete equation, your question could be answered more precisely.
How do you solve a to the power of m times a to the power of n?
You don't solve it!!! It is a method of manipulation of indices.
a^(n) X a^(m) = a^(n+m)
Similarly,
a^(n) / a^(m) = a^(n-m)
[a^(n)]^(m) = a^(nm)
Which is the best way to solve the equation x2 n?
To solve the equation x^2 = n, you would take the square root of both sides to isolate x. This would give you x = ±√n, where the ± symbol indicates that there are two possible solutions, one positive and one negative. Therefore, the best way to solve this equation is to take the square root of n and include both the positive and negative roots as solutions.
There is no last digit of Pi, (π). It is an irrational number which means it goes on forever.
Pi (approx 3.1416) doesn't have a last digit because it is irrational (and coincidentally, transcendental).
That means, basically, the decimal form of pi extends infinitely past the decimal point and so you will never get to "the last digit of pi".
Why all functions are relations but not all relations are functions?
I'm pretty sure that no one has actually wrote a complete proof of this statement, but the concept centers around the fact that functions are relations where the codomain is dependent on the domain, but relations don't necessarily have to be. If that sounds vague, it's because no one has really came up with a precise answer yet.
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Actually, the definition of a function ensures that it is a relation. Given that, all you need to do is to find one relation that is not a function. A popular one is y = sqrt(x) for x ≥ 0. Since each value of x (other than 0), is mapped onto 2 distinct values of y the relation is not a function. However, it is easily made into function by limiting the codomain to non-negative reals or to non-positive reals.
Similarly, relations such as reciprocal or logarithm can be made into functions by defining the domain or codomain to get around the exceptions.
What is the mean between these 1.2 1.3 1.4 1.5?
To find the mean of a set of numbers, you add all the numbers together and then divide by the total number of values. In this case, the sum of 1.2, 1.3, 1.4, and 1.5 is 5.4. Dividing 5.4 by 4 (the total number of values) gives you a mean of 1.35.
