answersLogoWhite

0

🎒

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 vertex y equals x2 plus 10 plus 22?

Y = X^2 + 10X + 22

set to 0

X^2 + 10X + 22 = 0

subtract 22 from both sides

X^2 + 10X = - 22

Now, complete the square by halving the linear term (10), squaring it and adding it to both sides

X^2 + 10X + 25 = - 22 + 25

factor the left side, gather terms right side

(X + 5)^2 = 3

(X + 5)^2 - 3 = 0

(-5,-3)

-------------------the vertx

How do you solve the problem 3a2 -36 plus 81 equals 0?

Divide all terms by 3:-

x2-12+27 = 0

When factored:-

(x-3)(x-9) = 0

Therefore: x = 3 or x = 9

What is the slope of 2y plus 6x equals 1?

You need to rearrange the equation so that it is in the form y=mx+b. This is the slope intercept equation for a line. In this form, 'm' is the slope.

So, for 2y+6x=1 you begin by bringing the '6x' to the other side of the equation. You do this by subtracting '6x' from both sides.

Once you do this you are left with:

2y = -6x + 1

The next step is to divide both sides by 2 in order to isolate the 'y'.

Now you have:

y = -3x + 0.5

-3 = m

0.5 = b

So your slope is -3.

How do you factor with a coefiecient in front of the x squared?

A coefficient with x2 definitely adds another level of difficulty to the typical binomial factoring problem. The result is that the factors assume the form (ax+b)(cx+d). Multiplied out, we get acx2 + (bc + ad)x + bd.

Notice how a & c are factors of the original coefficient of x2.

Example:

16x2 + 10x + 1 = (2x + 1)(8x + 1)

What is x in x minus seven eighths equals negative five twelfths?

X - 7/8 = - 5/12

let's get those denominators the same; 24 looks right.

X - 3*7/3*8 = - 5*2/2*12

X - 21/24 = - 10/24

add 21/24 to both sides

X = 11/24

check

11/24 - 21/24 = - 10/24

- 10/24 = - 10/24

or

- 5/12 = - 5/12

When is a time that acceleration changes but speed can't?

Speed is a scalar quantity. This means that its value stands on its own without a direction. Something similar to speed is velocity. Velocity has the same number as speed, but also includes a direction. For example, I might be driving at a speed of 60 miles per hour, whereas my velocity is 60 miles per hour, west. This type of quantity-one that includes a direction-is called a vector quantity. Acceleration, like velocity, is a vector quantity. If I continue driving at the same speed but I follow a curve in the road that changes my direction, I might then be driving 60 miles per hour, north. Since my speed remained 60 miles per hour, the number corresponding to my acceleration was zero before and is zero after. However, the change in direction means that acceleration has changed.

What is the vertex of x 5x 8?

Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "times", "equals", "squared", etc. All that I can see is three disjoint terms.

Can skew lines cross?

Skew lines can refer to non-coplanar lines and, if that is the case, they cannot cross.

Should you use addition for the problem x plus 11 equals 36.3?

No it should be subtaction because:-

x+11 = 36.3

Subtract 11 from both sides

x = 25.3

Which one below is not a general function of optical instruments?

The question asks about something "below". In those circumstances would it be too much to expect that you make sure that there is something that is below?

X2 plus y - 52 equals 30?

x2 + y - 52 = 30

x2 - x2 + y - 52 + 52 = - x2 + 30 + 52

y = -x2 + 82

Since a = -1, the parabola open downward, and crosses the x-axis at x = +&- sq.root of 82.

0 = -x2 + 82

0 - 82 = -x2 + 82 - 82

-82 = -x2

82 = x2

+&- sq.root of 82 = x

What value of x satisfies the equation 2tan x plus 2square root3 equals 3square root3?

2tan(x) + 2√3 = 3√3

2tan(x) = √3

tan(x) = √3 / 2

x = atan(√3 / 2)

x ≈ 0.71372437894476563082

Is x2-27 equals 0 a quadratic equation?

Yes. Since 'x' appears to the 2nd power, the equation is "second degree", or 'quadratic'.

Also, since 'x' appears to the 2nd power, there are two solutions.

x = +3 sqrt(3)

x = -3 sqrt(3)

What are the rules for integration?

There are a lot of rules for integration! Plus a lot of techniques!

Here is the power rule as a simple example.

int[Xn dx]

= (Xn + 1)/(n + 1) + C

( n does not equal - 1 )

How can 7x plus 8 equal 2?

7x+8=2

.....-8..-8

7x=-6

7x/7=6/7

x=6/7

In conclusion, 7(6/7)+8=2

I'm sure you meant: x = - (6/7) or -6/7 (not 6/7).

How do you solve -9 equals 5 over 17 multipied by x?

- 9 = 5/17X

divide - 9 by 5/17, and this is the same as multiplying - 9 * 17/5

- 153/5 = X

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

- 9 = 5/17(- 153/5)

- 9 = - 765/85

- 9 = - 9

------------------because - 765/85 = - 9