Calculus

geometry, Algebra , trigonometry calculus, physics

Basically, the same way you solve any inequality. However, it may be simpler if you multiply both sides of the inequality by the fraction's denominator first; that way, you will only have integers, and don't need to deal with fractions later on. If you have several fractions, you might multiply both sides of the fraction by the least common denominator.

x2 + 4x + y2 - 6y = 3

You need to be more clear about your question:

Are you trying to find the properties of the curve it defines?

x2 + 4x + y2 - 6y = 3

∴ x2 + 4x + 4 + y2 - 6y + 9 = 16

∴ (x + 2)2 + (y - 3)2 = 42

∴ This describes a circle with a radius of 4, and a center point of (-2, 3)

Did you want to solve for y?

(x + 2)2 + (y - 3)2 = 42

∴ (y - 3)2 = 16 - (x + 2)2

∴ y - 3 = ± [16 - (x + 2)2]1/2

∴ y = 3 ± [16 - (x + 2)2]1/2

Did you want to solve for x?

(x + 2)2 + (y - 3)2 = 42

∴ (x + 2)2 = 16 - (y - 3)2

∴ x + 2 = ± [16 - (y - 3)2]1/2

∴ x = -2 ± [16 - (y - 3)2]1/2

no , since there is a function which lsc but not usc.

The width of an index finger depends on the size of the person. For instance, an average size person will have an index finger that is roughly one half inch wide.

"Parallel to the x-axis" is the same as saying "a slope of zero".

In calculus, you take the derivative of f and make it equal to zero. Then solve the equation.

Taking a simple case, consider the equation f(x) = 2x2 -5x -4

To find all the places that the graph is parallel to the x-axis, take the derivative

4x - 5

and make that equal zero

4x - 5 = 0

Then solve for x. The only point where is graph is parallel to the x axis is where x=5/4. Put that back in the original equation and get the y coordinate for that point.

This class of problems makes you use a great variety of skills. All of your first year calculus will depend on your ability to thoroughly understand this and similar processes.

2x + 24 = 9x - 39

= 2x + 63 = 9x


= 63 = 7x


= x = 9

Yes it does. They both equal 72.

(7 x 9) + (9 x 9) = 16 x 9 = 144

No.

8x + 7 = 5x + 28 subtract 5x and 7 to both sides

3x = 21 divide by 3 to both sides

x = 7

1597*6=9,582

12/3+21/4+25/6... Ignore the whole numbers for a moment....

2/3+1/4+5/6. Give them all the same denominator so you have...

8/12+3/12+10/12 Now - add the top numbers of the fractions together...

8+3+10=21. 21/12 = 19/12 Finally, add all the whole numbers from the original sum (5) to give you your final sum of 69/12. Your last step is to simplify the fraction to 63/4

By antiderivative do you mean integral?

If yes, integral x^1 dx= (x^2)/2

ex3

If you mean

2x2 + 3x = (3x - 1)2 - x2

Then you can solve it this way:

Expand:

2x2 + 3x = 9x2 - 6x + 1 - x2

Group like terms:

2x2 + 3x = 8x2 - 6x + 1

6x2 - 9x - 1 = 0

Complete the square:

6x2 - 9x = 1

x2 - 3x/2 = 1/6

x2 - 3x/2 + 9/16 = 1/6 + 9/16

(x - 3/4)2 = 8/48 + 27/48

(x - 3/4)2 = 35/48

Solve for x:

x - 3/4 = ± √(35/48)

x - 3/4 = ± √(35/3) / 4

x = 3/4 ± √(35/3) / 4

x = [3 ± √(35/3)] / 4

If you mean something else, then you'll need to be clearer with your question.

2X + 5X + 4 = 25

add the X terms together

7X + 4 = 25

subtract 4 from each side

7X + 4 - 4 = 25 - 4

7X = 21

divide both sides integers by 7

(7/7)X = 21/7

X = 3

----------check in original equation

2(3) + 5(3) + 4 = 25

6 + 15 + 4 = 25

25 = 25

checks

2x2 - 9x + 3 = 0

Using the quadratic formula:

x = [9 ± sqrt(92 - 4*2*3)]/(2*2)

= [9 ± sqrt(81-24)]/4

= [9 ± sqrt(57)]/4

= 0.36254 or 4.13746 (to 5 dp)

-2x+7x=5x.

Factor out the x.

-2+7

I hope you know how to use a calculator. :D

a2

That would still be 4. If it were times 0 it would be 0.

103x6=618

Linear.

This depends on wether you want your answer in radians or degrees. If you want the answer in degrees, the highest and lowest point of the sin graph wil always be 90, 270, 450... and crosses the zero point at 180, 360, 540... If you want your answer in radians, the graph crosses the zero point, at pi, 2 pi, 3 pi... and has it's highest/lowest point at 1/2 pi, 1 1/2 pi, 2 1/2 pi...