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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 answer to 3x to the 3rd power minus 10x equals 17x and how do you find it?
3x3 - 10x = 17x divide by x to both sides
3x2 - 10 = 17 add 10 to both sides
3x2 = 27 divide by 3 to both sides
x2 = 9
x = ±√9
x = ±3
Solve this equation using substitution 3x plus 2y equals 2 and -2 plus y equals 8?
From second equation: y = 8 + 2x
Substitute for y in first equation: 3x + 16 + 4x = 2
ie 7x = -14
ie x = -2 and y = 4
How do you solve x for 5x 2-4x-672?
You need to find two factors of 5*672 = 3360, whoxe difference is 4: these are 56 and 60.
Then 5x2 - 4x - 672 = 5x2 - 60x + 56x - 672 = 5x(x - 12) + 56(x - 12)
= (x - 12)*(5x + 56)
Difference between laplace transform and z transform?
the difference is the "S" and "Z" parameters.
S used for analog computation while Z for digital processing.
basically Z is the digital approximation of the analog frequency domain signal.
Z=exp(sT)
where T is the sampling time.
What is x2 plus 7x equals - 2x2 plus 6 in the form ax2 bx c equals 0?
x2 + 7x = 2x2 + 6
x2 - 2x2 + 7x = 6
-x2 +7x - 6 = 0 or alternatively x2 - 7x + 6 = 0
What is the solution to y equals negative x plus 2?
solving for y: y = - x + 2
solving for x: x = -y + 2
solving for an actual number: you can't. there isn't a way to get a number out of that equation.
Given the information in the question, there is no need for any inequality. the flat surface can be described as an equality.
Outer diameter = one and a half inches => outer radius = 0.75 inches.
Inner diameter = three fourths inches => inner radius = 0.375 inches.
Area = pi*(0.752 - 0.3752) square inches.
So one possible set of inequalities is 0 < area < 1,000,000,000 sq inches!
What is the value of the y in the equation 6y plus 8 equal 32?
6y + 8 = 32
6y + 8 - 8 = 32 - 8
6y = 24
6y/6 = 24/6
y = 4
They're asking you to find a value for x, which in this case is 4, since 3 times 4 equals 12.
How do you do the area of bounded y2 equals 9xand2x equals 9y?
The basic steps you must follow are:
- Simplify the two equations to be functions of y.
- Find the intersections of the two functions.
- Integrate the difference of the two functions on between the two intersection points.
Here are the steps for this specific problem:
Simplifying the equations:
Simplify y2=9x to be a function of y.
y=±√(9x)
y=±3√(x)
(Keep the ± for now.)
Simplify 2x=9y to be a function of y
(2/9)x=y
y=2/9x
Finding the intersection of the two functions:
±3√(x)=y=2/9x
±3√(x)=2/9x
±27/2√(x)=x
x=0
±27/2=√(x)
729/4=x
x=729/4
(Now, since neither of the solutions is negative, the ± may be removed from the first function.)
Integrating the difference of the two functions:
Let A=area bounded by the two curves.
Let y1=3√(x), the first function.
Let y2=2/9x, the second function.
A=∫(y1-y2)dx
(y2 is subtracted from y1 because it is the lower function on that interval. Graph the two functions; it makes sense.)
A=∫(3√(x)-2/9x)dx on [0, 729/4]
A=∫(3x1/2-2/9x)dx on [0, 729/4]
A=2x3/2-1/9x2+C on [0, 729/4]
Now, find the particular solution on the interval [0, 729/4]
A=[2(729/4)3/2-1/9(729/4)2+C]-[2(0)3/2-1/9(0)2+C]
A=19683/4-59049/16+C-C
A=19683/4-59049/16=19683/16=1,230.1875
The area of the region bounded by y2=9x and 2x=9y is 1,230.1875 units2.
Yes. According to the Commutative Property of Multiplication, 3x is = to x3 but, of course, the second term breaks the rule on "Numerical Coefficient first before Literal Coefficient"
