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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 has y-intercept 4 and x-intercept -1?
use the line equation y=mx+b
plug in the slope (rise over run) 4/1
y=4x+b
plug in the y intercept (4)
y=4x+4
What is x to the 2nd equals 9 over 16?
x2 = 9/16
It's a second-degree equation in 'x'.
The solutions are:
x = positive 3/4 .
x = negative 3/4 .
x2 + x = 1 - x
So x2 + 2x - 1 = 0
Using the quadratic formula,
x = {-2 ± sqrt[22 - 4*1*(-1)]}/(2*1)
= -1 ± sqrt(2)
You would use the FOIL method, first outer inner last, to get this answer. You multiply the first set of numbers together, then the outer set of numbers, then the inner, and finally the last set of numbers. All that's left to do is simplify if needed and in order of descending powers.
So ( a + b ) * ( c + d ) = ac + ad + bc + bd
This would give us the answer of...
( x - 2 ) ( x + 4 ) = x^2 + 4x - 2x - 8 = x^2 + 2x - 8
What is the dy over dt of y equals 7s over 2t3?
d/dt (7s/2t3) = negative 21s/2t4 (ds/dt)
(Not bad for stuff I haven't used in 30 years, eh ?)
How many inches are there in 7 millimetres?
There are 25.4 millimetres in one inch. Therefore, rounded to three significant figures, 7 inches is equal to 7/25.4 = 0.276 inches.
Direct Conversion Formula 7 mm*
1 in
25.4 mm
=
0.2755905512 in
What is D'Alembert's ratio test?
D'Alembert's ratio test, or simply the ratio test, is a way of determining whether certain series converge. It goes like this: to check if a series converges, check the sequence of ratios between consecutive terms. If that sequence converges to something less than 1, then the series converges absolutely. If it converges to something greater than 1, or diverges, then the series diverges. If it converges to 1 exactly, then the test is inconclusive.
Which is going to be the next number in the line 2 7 9 16 25 41?
The next number in the series will be 66. The next number is found by adding the two previous numbers. (2+7=9, 9+7=16, etc...)
What is the value of x 2 plus x?
X equals any number you wish.
For example, if x=1, then 1(2)+1 equals 3
-13.9x equals 5.7-12.5x what is x equal to?
-13.9x = 5.7-12.5x ( +12.5x)
-1.4x = 5.7 (/-1.4)
x = 5.7/-1.4 = -4.07 to 2 decimal points
Find the solution of this system of equations -2x equals 2 plus 1y -6x-y equals -2?
Assuming that you are giving two separate equations:
Your answer is x = 1 & y = -4
Given Equations
-2x = 2 + y
-6x - y = -2
Derived Equations
3 * (2+y) - y = -2
6 + 3y - y = -2
6 + 2y = -2
2y = -8
y = -4
-2x = 2 + (-4)
-2x = -2
x = 1
Checking Answers
-2 * (1) = 2 + (-4)
-2 = -2
-6 * (1) - (-4) = -2
-6 + 4 = -2
-2 = -2
How would you solve 6xn plus 7y equals -6 -2x-3y equals 2 using addition method?
6x+7y=-6 3(-2x-3y=2)
+________
-2y=0 => y=0
Therefore x=-1
What is the derivative of 2 to the power of 5x?
25x?
d/dx(au)=au*ln(a)*d/dx(u)
d/dx(25x)=25x*ln(2)*d/dx(5x)
-The derivative of 5x is:
d/dx(cu)=c*du/dx where c is a constant
d/dx(5x)=5*d/dx(x)
d/dx(25x)=95x*ln(2)*(5*d/dx(x))
-The derivative of x is:
d/dx(x)=1x1-1
d/dx(x)=1*x0
d/dx(x)=1*(1)
d/dx(x)=1
d/dx(25x)=25x*ln(2)*(5*1)
d/dx(25x)=25x*ln(2)*(5)
-25x can simplify to (25)x, which equals 32x.
d/dx(95x)=32x*ln(2)*(5)
Provide at least three coordinates to graph the equation 2x plus 3y equals 15 Show your work?
Plug in various values of x and solve for y. [This can be done for any value of x.]
For example, for x=0,
2*0+3y=15
3y=15
y=15/3=5
So (0,5) is one coordinate.
For x=1,
2*1+3y=15
2+3y=15
3y=13
y=13/3
So (1,13/3) is another coordinate.
For x=2,
2*2+3y=15
4+3y=15
3y=11
y=11/3
So (2,11/3) is another coordinate.
What is one over x plus eight plus six over x minus eight?
Grammar in mathematics is important so that the question cannot be misunderstood.
The question is asking for the solution to 1/(x + 8) + 6/(x - 8).
Where fractions are being added or subtracted then the denominators need converting to a common denominator. With numbers this new denominator would be the Lowest Common Multiple. With algebraic terms then simply take the product.
The common multiple of (x + 8) and (x - 8) is (x + 8)(x - 8) = x2 - 82
1/(x + 8) = 1 x (x - 8)/x2 - 82 = x - 8/x2 - 82
6/(x - 8) = 6 x (x + 8)/x2 - 82 = 6x + 48/x2 - 82
1/(x + 8) + 6/(x - 8) = x - 8/x2 - 82 + 6x + 48/x2 - 82 = 7x + 40/x2 - 82
