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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

How do you solve -x plus 9-2x equals -21?

-x + 9 - 2x = -21

combine like terms -x and -2x

isolate -3x by subtracting 9 from both sides

divide both sides by -3

-3x + 9 = -21

- 9 - 9

-3x = -30

x = 10

How do graphs help you understand functions?

Typically, functions are graphed on x-y coordinates. A function of x means that for every x point, there must be a single y point. You can also many properties by graphing a function, such as the minimum and maximum points, slopes and inflection points, and the inverse of the function (y values plotted on x coordinate, and x values on y coordinate).

20 ml equals how many kl?

1 ml = 10^-6 kl or 0.000001 kl

So:

20 ml = 20 * 10^-6 kl = 2*10^-5 kl or 0.00002 kl

If the vertex of the parabola f x equals X 2 plus b x plus c is at 3 and 1 find b and c.?

I am used to going the other way. We will try this. (3,1) = vertex.

(X - 3)^2 + 1 = 0

X^2 - 6X + 9 + 1 = 0

X^2 - 6X + 10 = 0

b = -6

c = 10

Why does an answer to an integration problem involve a Constant of Integration?

The indefinite integral is the anti-derivative - so the question is, "What function has this given function as a derivative". And if you add a constant to a function, the derivative of the function doesn't change. Thus, for example, if the derivative is y' = 2x, the original function might be y = x squared. However, any function of the form y = x squared + c (for any constant c) also has the SAME derivative (2x in this case). Therefore, to completely specify all possible solutions, this constant should be added.

What is 1 divided by2 equals x divided by8?

1/2 = X/8

cross multiply

2X = 8

divide both sides by 2

X = 4

check 1/2 = 4/8

1/2 = = 1/2

checks

How do you work out 7y - 3y - 14 equals 14?

7y-3y-14=14

4y-14=14

4y-14+14=14+14 (adding 14 on both side)

4y=28

(4y)/4=28/4 (dividing by 4 on both side)

y=28/4=7

What is 91 x 61 centimeters?

91 cm by 61 cm is a two-dimensional area of 5551 square centimeters.

What number goes into 83 and 60?

Only 1 can evenly divide both 83 and 60.

How do you find the arc length of a minor arc?

The answer depends on the information that you have. If the arc subtends an angle of x radians in a circle with radius r cm, then the arc length is r*x cm.

What is the derivative of yXy'?

assuming that you are referring to a function:

f(y) = y×y

or better put:

f(y) = y2

Then it's derivative would be:

f'(y) = 2y

How can you calculate the length of spiral ring?

the dia meter of the pile is 750mm the pitch of the sprial rings are 100mm and how to calucualte the lentngth of the rod for the one meter lkength of pile.

What is the same between decimal and fraction?

Decimals are numbers that can be expressed like this. 10.56 or 16.4 or 46.324672462 These numbers show that the numbers are between whole numbers.

Fractions do the same thing. Fractions tell you the number between the two whole numbers, just more accurately. For example.. 3/4 is a number between 0 and 1. The fraction 23/7 is a number between 3 and 4 and if you do this on a calculator and turn it into decimal form you will get a large amount of decimals. this proves that the fraction form is more accurate.

How do you solve 3x plus 2x is equal to or less then 6?

3x + 2x < 6 Add the terms on the left side: 5x < 6

One can perform the same operation to both sides of the inequality. If one divides by a positive number then the inequality retains it 'sense'. In this case, it remains a '<'.

Divide both sides by 5: 5x / 5 < 6 / 5

x < 6 / 5 ( the answer )

Evaluate -3x2 4x plus 1 when x equals -2?

-95

-3(-2)squared times (-4)(-2) plus 1

-3(-4)(-8)+1

(12)(-8)=1

(-96)+1

-95