All Answers 358514 Answers

What is the "difference" between -8 and +8 ?

ND says that "difference" means subtract, but does that mean I calculate 8 - (-8) = 16, or do I calculate (-8) - 8 = -16 ? Is the "difference" 16 or -16 ?

Does it matter which number comes first ? That is, if I ask for the "difference" between -8 and +8, would I get a different answer than if I ask for the "difference" between +8 and -8 ? Shouldn't they be the same ?

I think that the "difference" between two numbers is the modulus of one number minus the other, that is, the "difference" between two numbers is a positive number. The "difference" between -8 and +8 is +16, not -16. They are 16 apart on the number line.

That is why I think that ND's answer to this question is wrong. ND's "difference" 2N-8 implies that 2N is greater than 8. Then, if the algebra says that N=-4, (producing a "difference" of -16), we have a contradiction, meaning that there is no N such that 2N>8 meeting the requirements of the question.

If there is no solution for which 2N>8, we have to consider the possibility that 2N<8, (and, in passing, the possibility that 2N=8, easy to reject that).

2N<8 leads to the equation 8 - 2N = 9N + 20, and the solution to that is N = -12/11.

Also,

A function that is even has the y axis (x=0) as an axis of symmetry       f(x)=f(-x)

A function that is odd has point symmetry about the origin. This means that if it is rotated 180 degrees it will be the same.     f(-x)=-f(x)

This is what 2^x looks like.  You can see that it is not symmetrical about the y axis.

And it does not have point symmetry about (0,0) 

so it is not an even function or an odd function.    

This appears to be...

1¹,  2² , 3³ , 4⁴ , 5⁵ 

So the missing value is 4⁴ = 256

You can also use the distance formula (which comes directly from pythagoras' theorem)

$$x_1=3\qquad x_2=6 \qquad y_1=-2 \qquad y_2=4$$

DragonSlayer, I sincerely hope that you are learning something by copying/repeating everybody elses answers!

Some (unknown) people have shown you how annoyed that they get when you do this.  

If you want to comment on this statement then you can do so by private message.

It is just

$$\frac{450}{6000}\times 100 \;\;percent$$

$${\frac{{\mathtt{450}}}{{\mathtt{6\,000}}}}{\mathtt{\,\times\,}}{\mathtt{100}} = {\frac{{\mathtt{15}}}{{\mathtt{2}}}} = {\mathtt{7.5}}$$

7.5%

You can draw a right angled isosceles triangle.

Let the equal sides by 1 unit

The equal angles will be 45 degrees

Using Pythagoras' theorum you can determing that the hypotenuse is sqrt(2)

Then you can reas cos 45degrees straight off the triangle

$$cos 45 = \frac{1}{\sqrt2}\\$$

if you want to have a rational denominator then

$$cos 45 = \frac{1}{\sqrt2}=\frac{1}{\sqrt2}\times \frac{\sqrt2}{\sqrt2}=\frac{\sqrt2}{2}\\$$

Aziz chooses to solve the equation 9^x=27^x+1, for which his answer x = -3 is correct, rather than the actual given equation, 9^x=27^x+1, which has no real number solution.

You have to expand it.

So for your example, the solution would be:

3(a+4)

=3a+12

Inverse sine is the same as arc sine  so just use asin   

Do you mean  

$$\\64 cm^2 = \sqrt{x^2+16} cm^2\\
or\\
64 cm^2 = \sqrt{x^2}+16 cm^2\\
or\\
something\;\;else?$$

^ the proper name for this caret

(don't confuse it with a 'carrot' that a rabbit might eat or a 'carat' which is a unit of weight for gemstones)

However when used as a 'power of', exponent symbol it is called a 'hat'

4^3 means 4³ which means 4 x 4 x 4 = 64

 You have to have something after the ^ or id doesn't make sense.  

The web2calc on the home page has log and 10^x displayed all the time at the bottom of the calculator.

If you put your curser over either of these then ln, e^x appears below and log₂,  2^x  appears below that.

So log base 10 is log and antilog base 10 is  10^x

Log base e is ln and antilog base e is e^x

Log base 2 is log₂ and antilog base 2 is 2^x

You can also type these straight into the input area at the top of the calculator.

I am sure that if I have said anything incorrect someone will correct me.  

$$\\tan(sin^{-1}\left(\frac{-\sqrt3}{2}\right))\\\\
\mbox{Consider }\qquad sin^{-1}\left(\frac{-\sqrt3}{2}\right)\\\\
\frac{-\pi}{2}\le sin^{-1}\left(\frac{-\sqrt3}{2}\right)\le \frac{\pi}{2}\\\\
\mbox{The inverse sine is negative so the angle is in the 4th quad}\\
\mbox{Keep this in mind but look for the equivalent 1st quadrant answer}\\$$

$$\\sin^{-1}\left(\frac{\sqrt3}{2}\right)=60^0\\\\
tan60^0=\sqrt3\\$$

But it is  not really 60degrees    $$\frac{\pi}{3}\;radians$$    because it is in the 4th quad i.e.  $$\frac{5\pi}{3}$$  radians

So therefore the answer is $$-\sqrt{3}$$

$$\\tan(sin^{-1}\left(\frac{-\sqrt3}{2}\right))=\;-\sqrt3$$

12% pa,

2months is 2/12 = 1/6 of a years so interest it 12/6=2%

2% of 1000 pounds = 0.02*1000 = 20 pounds

WOW IT does too.   

1) 4 / √32   ?

$$\boxed{\dfrac{4 }{ \sqrt{32} }} \\ \\
=\dfrac{\sqrt{16} }{ \sqrt{32}} \\ \\
=\sqrt{ \dfrac{16 }{ 32} } \\ \\
=\sqrt{ \dfrac{1 }{ 2} } \\ \\
=\dfrac{1}{\sqrt{2} } * \dfrac{\sqrt{2}}{\sqrt{2}}\\\\
\boxed{=\dfrac{\sqrt{2}}{2}}$$

Ahmad and Bryan saved the same amount of money. Bryan spent $114 buying a birthday gift for her friend. In the end, Ahmad had 3 times as much as Bryan. How much did Ahmad have    ?

Amount of money = M

Bryan = M - $114

M = Ahmad = 3 * Bryan

Bryan = M - $114

Bryan = 3 * Bryan - $114

2*Bryan = $114

$$\boxed{\text{Bryan} = \$\;57}$$

Ahmad = 3 * Bryan

Ahmad = 3 * $57

$$\boxed{Ahmad = \$\;171}$$

4) 3√24 / √2   ?

 $$\boxed{\dfrac{3 *\sqrt{24} }{ \sqrt{2} }} \\ \\
=3 *\sqrt{ \dfrac{24 }{ 2} } \\ \\
=3 *\sqrt{ 12 } \\ \\
=3 *\sqrt{ 4*3} \\ \\
=3 *\underbrace{\sqrt{ 4}}_{2}*\sqrt{3} \\ \\
=3 *2*\sqrt{3} \\ \\
\boxed{=6\sqrt{3}}$$  

NO NEITHER DO i!!

It's a shorthand way for expressing a number without using scientific notation directly....in this case.....

2.0574749e+21  equates to.....

2.0574749 x  10²¹   

P.S.    ......This is always confusing to me, too!!!

OK......so we have

2x^4-2x^2-12 = 0   divide everything by 2

x^4 - x^2 - 6 = 0    we can factor this directly as

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

Setting the first two factor to 0, we have that x^2 + 2 = 0  ... subtract 2 from both sides....

x^2 = -2      take the square root of both sides

x = ±√(-2) = ±i√(2) or ±√(2)i, if you prefer  .....and those are the complex roots.....

And setting  x^2 - 3 = 0 and adding 3 to both sides, we get

x^2 = 3     take the square root of both sides and we get......

x = ±√(3)  ....and those are the real roots....

I'm trying to find all real and/or complex zeroes of p(x)

What's the question???