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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 will be the output of differentiator if the input is sine wave?
a phase shifted sine wave of a different amplitude.
Which is heavier a cubic centimeter of gold or a cubic centimeter of lead?
The weight of lead 11.34 grams per cubic centimetre
The weight of gold is 19.3 grams per cubic centimetre(from new person) Okay, I agree, but learn how to spell centimetER.Forget about spelling because in Europe they do spell it centimetre, just like theater and theatre. The specific gravities of the two metals, meaning that gold is 19.32 times heavier than water and likewise lead is 11.34 times as heavy. A cc of gold does seem to be almost twice as heavy as a cc of lead, but according to their respective atomic weights, the opposite begs to differ in this seemingly odd paradox. You see, gold (Au) on the periodic chart, has an atomic mass of 196.9 whereas lead (Pb) is slightly heavier with an atomic weight of 207.2 You might ask, why the paradox? Simple really. For that given measure of volume such as a cc, there are almost twice amount of gold atoms packed into that space as there are lead atoms. This is due to the arrangement of their respective atoms, similar to how water molecules are more densely packed together in the liquid state as compared to the solid state of ice.
What is the value of x 4 x -2 equals 4?
x= 1.5
4x -2=4 <<< Original problem
+2 +2 <<< reverse operations (problem requires subtraction, so add to solve)
4x=6 <<< New problem
4x/4=6/4 <<<reverse operations (new problem requires multiplication, so divide to solve)
x=1.5 <<< answer
How do you solve f of x equals x squared plus 5x plus 1?
f(x) = x2 + 5x + 1
The roots of this equation are x = -0.2087 and x = -4.7913 (approx).
The solution 3x plus 4y equals 5?
With only the amount of information given in this one equation, it's not possible to calculate
the value of 'x' or 'y'.
One more equation is required in order to calculate both.
8x plus 23 plus 4x - 7x equals 68 show work?
8x + 23 + 4x - 7x = 64; Find X
To make this easier, add like terms:
(8x + 4x - 7x) + 26 = 64
Use the order of operations:
(12x - 7x) + 26 = 64
5x + 26 = 64
-26 -26
5x = 38
5 5
Finally:
x = 7(3/5)
Why is 1 over 3 equal to 2 over 6?
1/3 is equal to 2/6 as they are equivalent fractions.
Equivalent fractions are made by multiplying (or dividing) both the numerator and denominator by the same value:
1/3 = (1×2)/(3×2) = 2/6
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This is a result of the way fractions are multiplied together (multiply the numerators together and multiply the denominators together), and a fraction with the same numerator and denominator is the same as the number 1 (since a fraction is equivalent to the the numerator divided by the denominator when converted to a decimal) and multiplying a number by 1 is the same as leaving the number alone:
2/2 = 2 ÷ 2 = 1
1/3 = 1/3 × 1 = 1/3 × 2/2 = (1×2)/(3×2) = 2/6
What does x equal when 3x plus -1 equals 8?
x = 3
Solution:
3x + -1 = 8
3x = 8 + 1
3x = 9
x = 9/3
x = 3
Check:
3(3) + -1 = 8
9 + -1 = 8
8 = 8
What is the graph of 3x plus 2y equals 13?
3x + 2y = 13
Subtract 3x from each side:
2y = -3x + 13
Divide each side by 2:
y = (-3/2)x + (13/2)
The graph is a straight line, with a slope of (-3/2),
through the point (0, 13/2) .
