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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 would you solve the following over the interval 0 is less than or equal to x which is less than 2pi here's the problem 2cos squared x minus 5cos x minus 3 equals 0?

2 cos2(x) - 5 cos(x) - 3 = 0

To save some writing, let's temporarily write "Q" instead of "cos(x)".

2 Q2 - 5 Q - 3 = 0

Factor the trinomial:

(2 Q + 1) (Q - 3) = 0

2Q + 1 = 0

2Q = -1

Q = - 1/2

Q - 3 = 0

Q = 3

Recalling that 'Q' is a cosine of an angle, (Q = -1/2) is the root that makes sense,

because the cosine of a real angle can never be 3 .

So now, we can get rid of 'Q' and go back to the cosine:

cos(x) = -1/2

x = 120 degrees

x = 240 degrees

What value of x when y200?

You need to give context for an answer. How are x and y correlated?

How will you compare 3x 4y equal to less than 12 and 3x 4y equal to greater than 12?

They are two regions of the Cartesian plane with the straight line 3x + 4y = 12 defining their boundary. That line is not part of either region.

What does x equal in 3x plus 9 equals 54-2x?

3x + 9 = 54 - 2x

Subtract '9' from both sides

Hence

3x = 45 - 2x

Add '2x' to both sides

5x = 45

Divide both sides by '5'

x = 9 The answer!!!!!

Verification

3(9) + 9 = 27 + 9 = 36

&

54 - 2(9) = 54 - 18 = 36

Hence both sides are equal at '36'.

What is the answer to 6y-2 equals 2y plus 18?

6y - 2 = 2y + 8 : Subtract 2y from both sides

4y - 2 = 8 : Add 2 to both sides

4y = 10 : Divide both sides by 4

y = 10/4 = 2.5 or 21/2

Who found the secrets of infinity?

Cantor found some of them. Specifically, he proved that certain infinities were greater than others.

Cantor found some of them. Specifically, he proved that certain infinities were greater than others.

Cantor found some of them. Specifically, he proved that certain infinities were greater than others.

Cantor found some of them. Specifically, he proved that certain infinities were greater than others.

-1 equals x plus 9?

-1 = x + 9

Subtract 9 from both sides of the equation: -1 - 9 = x + 9 - 9

so -10 = x

If - 3y plus 5 equals -4?

-3y+5=-4 subtract 5 from each side of the equation: -3y=-9 Divide by -3 to get the variable alone:
y=3

In maths does one minus two sine squared an equal cos squared a minus sine squared a 1-2sin2an equals sin2a-cos2a?

No.

Remember: sin2 + cos2 = 1

So, in place of (1 - 2 sin2) we can write (sin2 + cos2 - 2 sin2).

Massage that around slightly: (sin2 + cos2 - 2 sin2) = cos2 - sin2

That's not equal to (sin2 - cos2), which is the original question we were asked.

What is the answer to -16 plus 7?

The answer is -9. Simply add the numbers together arithmetically as you would for the problem two plus two. To check your work, a calculator is the best option.

How long would it take to earn 258 billion while working in a normal job?

Let's define a normal job by a job giving you a "normal" salary, for example the medium salary. In France it's €20 841 after-tax so you will need 12 379 444 years (if you don't spend any cent), about 154 743 lifes, to have in your pocket €258 billion