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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 the simplest form of 765 over 2023?
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What number must be added to x2 plus 5x to complete the square?
x2 + 5x + 6¼ = (x + 2½)2 and, hence, is a perfect square.
As the co-efficient of x2 (the first term) is 1, you can safely follow this rule:
Add the square of half the co-efficient in the second term, in order to complete the square.
In this case, you take half of 5 (which is 2½) and, then, square it. This gives you your 6¼.
What is a mathematical sentence?
A mathematical sentence usually refers to an equation.
x + y = 3 can be "translated" into this mathematical sentence: The sum of x and y is 3.
Can a logarithmic function have a base of zero?
No. No number can be generated by raising zero to a power.
Zero raised to any power is still zero.
What is Log3 3 plus log3 x plus 2 equals 3?
log33+log3x +2=3
log33+log3x=1
log3(3x)=1
3x=3
x=1
Other interpretation:
log33+log3(x+2)=3
log3(3(x+2))=3
3(x+2)=27
x+2=9
x=7
Problem: x+5x+4
Answer:6x+4
Explanation: You have 5 x's...you add the other x to the 5 x's and that makes 6 x's...then the +4 stays the same because you have nothing to combine it with. So therefore, your answer would be 6x+4.
Algebraic expressions are useful for translating problems into the language of mathematics. An algebraic expression for the problem "6 times the sum of 4 and y" would be: 6(4+y) = 24 + 6y.
That is fairly accurate. I like to use 1.5 times the width of the nut.
5y + 1 = 4y - 1 Subtract 4y from both sides of the equation. y + 1 = -1. Add 1 to both sides of the equation. y + 2 = 0 Subtract 2 from both sides of the equation. y = -2
How to Solve this problem x-2 divide x3-2x2 plus x-3?
That depends on what the problem is. The expresion alone is not a problem. It's just an expression.
Presumably, what you want to do here is to simplify it. We're given:
(x - 2) / (x3 - 2x2 + x - 3)
Let's start by tring to divide the numerator into the denominator using long division:
x2 + 1 (x - 2) x3 - 2x2 + x - 3 x3 - 2x2 0 + x - 3 x - 2 -1 R Since we get a non-zero remainder, we can see that x - 2 is not a factor of the denominator. And in fact, looking further into it, we will find that the denominator can not be factored, and so this problem can not be simplified.What is the answer to Log x plus 4 minus log6 equals 1?
log(x) + 4 - log(6) = 1
so
log(x) + 4 + log(1/6) = 1
Take exponents to the base 10 and remember that 10log(x) = x:
x * 104 * 1/6 = 10
x = 6/1000 or 0.006
Can you solve the equation 6 equals -10-p over 5?
If the equation is 6 = -10 - p/5 then multiply all terms by 5 :-
30 = -50 - p : p = -50 - 30 = -80
Can velocity of an object change when its acceleration is constant?
Certainly! By definition, the acceleration is the change, so it will change unless that amount is zero.
How long will it take to drive 70 miles at 75 miles per hour?
60 minutes = 1 hour
70 miles divided by 75 miles = 0.93 of an hour
0.93 x 60 = 56 minutes
What is the value of x in 2X plus 33 equals 4X plus 11?
2x + 33 = 4x + 11
-11 -11
2x + 22 = 4x
-2x -2x
22 = 4x
Divide each side by 4
x = 5.5
