Calculus

There is no single value that this equals. There could be any number of answers to it depending on the value of x.

If you want to know what x equals when a specific value is assigned to the equation, you can do this by solving the equation for a 0 value, and then factoring the result.

For example, let's say you you want to know the value of x when the equation equals negative four:

x2 + 8x + 12 = -4
∴ x2 + 8x + 16 = 0
∴ (x + 4)2 = 0
Now you simply plug in the value on the left side of the equation that would give you a result of 0. In this case, it would be negative four, as negative 4 plus 4 equals 0, which is also 0 when squared.
∴ x = -4

Similarly, if you say that the equation comes to a value of 5:
x2 + 8x + 12 = 5
∴ x2 + 8x +7 = 0
∴ (x + 7)(x + 1) = 0
In this case, there are two possible outcomes: negative 7 and negative 1. That's because either one of those will produce a zero value for this equation.
∴ x = -7 or x = -1


Alternately, what happens if the equation comes to a value of 1?

x2 + 8x + 12 = 1
∴x2 + 8x + 11 = 0

In this case, there is no simple way to solve it by factoring, so instead you can plug it into the quadratic formula, x = [-b +/- √(b2 - 4ac)] / 2a

∴ x = [-8 +/- √(82 - 4×1×11)] / (2×1)
∴ x = [-8 +/- √(64 - 44)] / 2
∴ x = (-8 +/- √20) / 2
∴ x = -4+√20, or -4-√20
∴ x ≈ 0.47214, or x ≈ -8.42714

As shown, there can be any number of correct answers to this, as there is no specified value for x. Once a value is specified, then it will always have at most two answers, and at least one.

if, for example, 0=x^2+5x+6, then:

0=(x+3)(x+2)

the numbers '3' and '2' must add to give you 5, and multiply to give you 6.

SO:

0=x^2+(a+b)x+(ab)x

0=(x+a)(x+b)

(10,13)

13.935

7

Subtract 4 from both sides and add y to both sides. This would give you 2y=14.

Then, divide both sides by 2. y=7.

52,560,000

The way you can get that number is simple:

10 x 0.10 = 1

1 x 60 = 60

60 x 24 = 1,440

1440 x 365 = 525,600

525,600 x 100 = 52,560,000

You see, you start out by multiplying the number of numbers you can count every 10 seconds, you multiple that number by the number of minutes in a hour, you multiple that number by the number of hours in a day, you multiple that number by the number of days in a year, and you multiple that number by 100 years.

So, if you constantly counted by 1 every 1 second, for 100 years, the number you would end up with is 52 billion, 560 hundred thousand.

24

Given:

a = 2πr2 + 2πrh

h = 113/r2

∴ a = 2πr2 + 2πr(113/r2)

∴ a = 2πr2 + 226π / r

∴ da/dr = 4πr + 226π ln r

a=11

5361.66

0

no

1/3 - 2/(2y + 1) = 3/y

Provided that y ≠ -1/2 and y ≠ 0,

multiply through by 3y(2y+1) to give

y(2y + 1) - 6y = 9(2y+1)

that is, 2y2 + y - 6y = 18y + 9

or 2y2 - 23y - 9 = 0

The quadratic formula then gives y = [23 ± sqrt{232 - 4*2*(-9)}]/(2*2)

= [23 ± sqrt(601)]/4

so that y = -0.3788 or y = 11.8788

-31

You seem to be unaware of the fact that you could have obtained the answer much more easily and quickly by using the calculator that comes as part of your computer. 7 - 3 - 8 - 8 = -12

It is 0.15x + 3.25

Without an equality sign it is not an equation

yearly

3/25

yes, 453 is a prime number