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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 are the application of simple harmonic motion?

Springs, sound and musical instruments, electronic oscillators, alternating electric currents, that sort of thing.

What is an expression for the product of x and y?

x times y

or, symbolically, either x*y or simply xy

(where context allows, also X x Y)

How do you solve 3x squared plus 2x minus 16 is zero?

-- Factor the left side of the equation.

-- Set one factor equal to zero, and solve it for 'x'. That gives you

one solution to the equation.

-- Set the other factor to zero, and solve it for 'x'. That gives you

the other solution to the equation.

-- If you don't get x=2 and x=-8/3 then repeat the previous steps,

because you made a mistake the first time.

What is the difference between insantaneous speend and average speed?

The instantaneous speed is the speed of a moving body at an instant. Average speed is the overall speed through a period of time. These are two important aspects of differentiation in calculus.

What is the normal body temperature of the Filipino?

98.6° F is the normal body temperature for any human, Filipino or not.

2 liters equals?

2.11 qts

1 Liter = 1.05 quart

1 guart = 0.94 liter

How do you get the second derivative of g of x equals xcscx where x equals theta?

T=theta so that it will not look so messy.

g(T)=TcscT

To find the first derivative, you must use the product rule. Product rule is derivative of the first times the second, plus the first times the derivative of the second, which will give you:

g'(T)=0xcscT + Tx-cscTcotT, which simplifies: g'(T)= -cscTxcotT

Now, take the derivative of that to get the second derivatice. In order to do that, you have to do the product rule again.

g"(T)=(cscTcotT)cotT + -cscT(-csc^2T) {that's csc squared} which simplifies:

g"(T)= cscTcot^2(T) + csc^3 (T)

Can 4D objects exist in your 3D world?

We don't actually know how many dimensions there really are. Certain theoretical considerations imply that there are at least 10 or 11, it's just that most of them are "curled up small" and we don't notice them.

That said, a 4D object cannot fully exist in a 3D space. However, a 3 dimensional "slice" of them can exist in that space, just like a 2D "slice" of a 3D object can exist in a 2D space.

What is 4 and 3 fifth x 2 thirds?

4 3/5 x 2/3 = 23/5 x 2/3 = 46/15 = 3 and one-fifteenth

What is the derivative of cos pi x plus sin pi y all to the 8th power equals 44?

(cos(pi x) + sin(pi y) )^8 = 44

differentiate both sides with respect to x

8 ( cos(pi x) + sin (pi y ) )^7 d/dx ( cos(pi x) + sin (pi y) = 0

8 ( cos(pi x) + sin (pi y ) )^7 (-sin (pi x) pi + cos (pi y) pi dy/dx ) = 0

8 ( cos(pi x) + sin (pi y ) )^7 (pi cos(pi y) dy/dx - pi sin (pi x) ) = 0

cos(pi y) dy/dx - pi sin(pi x) = 0

cos(pi y) dy/dx = sin(pi x)

dy/dx = sin (pi x) / cos(pi y)

What is the solutions when 9a2 equals 24a -16?

9a2=24a-16

9a2-24a+16=0

(3a-4)(3a-4)=0

3a-4=0

a=4/3 double root

How do you factor 10x plus 10y plus 100?

10x+10y+100

There is a common 10 in each number.

10(x+y+10)

Simplify the expression 5y-4 plus 9y-1 y plus 15?

5y - 4 + 9y - 1y + 15

= 5y + 9y - 1y + 15 - 4

= (5 + 9 - 1)y + (15 - 4)

= 13y + 9

Y equals mx plus c c?

That is the standard equation to graph a line.