All Answers 359165 Answers

you mean the gradient of the LINE joining those points

(5-2)/(-2-0)

unless 0! refers to 0 factorial which is 1.

I know that Heureka did not mean  this though.   LOL

domain is all possible x values and range is all possible y values 

I answered this one already - please do not repost like this we are too busy with first time questions.

If your question has not been answered then you can make another post but put the address of the original question in it instead of just rewriting the question.  That way you are not requesting us to answer the same question several times.  Do you understand what you mean?  

By the way this is your original (or other) question that i already answered (at length).

You need to draw the triangle

then

sin(25)=6.2/h

1/sin(25)=h/6.2

1/sin(25)  * 6.2 = h

Maybe it is      $$6*10^{-279}*e^{646.9708}$$     

On a calc      E ususally means 10 to the power of

I'd interprete it the other way around but either interpretatin would be valid.  

Isn't it irritating when people do not ask their questions unambiguously.    

1.   You change a numbe to a percent by multiplying by 100 and putting a percent sign.

2.  strange wording BUT  150% of 1650 is found like this

150/100*1650

3.      360 is 150% of x

          360=150/100   of x

          360=1.5  times x

           360/1.5 = x

and you can finish it.  

Do you mean that you want 10% of each of these?

Just move the point one place to the left (to make the number 10 times smaller)

so the first one would be     $.81 = 81c

If it makes you feel any better I struggled with this one - but I think it is right.  

Part a       y=f(2a)

f(-4)=4   but    f(2a)=-4    so   2a=-4     so   a=-2

f(4)=-4   but    f(2b)=4     so    2b=4      so    b=2

Part c        y=f(2a-8)

f(-4)=4  but    F(2c-8)=-4    so   2c-8=-4    so   2c=4    so    c=2

f(4)=-4  but  f(2d-8)=4  so  2d-8=4   so  2d=12     so d=6  but this is outside the domain so it does not exist

if 2<x<3  and 3<y<4 ,then the range of  $${\frac{{\mathtt{x}}}{{\mathtt{y}}}}$$  is?

Well the highest value would be the biggest x over the smallest y :  3/3=1  (not inclusive)

and the lowsest value would be smallest x over the biggest y :  2/4=0.5      (not inclusive)

So the range would be  (0.5,1)

NOW lets look at it a different way.

$$\frac{x}{y}=k\qquad\mbox{where k is a constant}$$      

if 2<x<3  and 3<y<4

------------------------

I am going to graph this useing Desmos but I will need to change the letters used

y=a/b where  2<a<3  and 3<b<4

gradient = (y2 - y1)/(x2 - x1)

 here:

$${\mathtt{gradient}} = {\frac{\left({\mathtt{7}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{\left({\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0}}\right)}} \Rightarrow {\mathtt{gradient}} = {\mathtt{3}}$$

.

I guess exposant means exponent so:

10⁴ = 10000

.

the inv tan of the calculator function

inverse tan is the same as arc tan

so press [2nd] then press atan

make sure the calculator is set to degrees (or radians) there is a botton for this on the bottom left of the calculator. 

eg

inverse tan 1.32876

enter

atan(1.32876)

and this will be your output:

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\mathtt{1.328\: \!76}}\right)} = {\mathtt{53.035\: \!563\: \!135\: \!882^{\circ}}}$$

---------------------------------------------------------

Assurez-vous que la calculatrice est réglée à degrés (ou radians) il y a un botton pourcela sur la partie inférieure gauche de la calculatrice.

par exemple

inverse tan 1.32876

Entrez

atan(1.32876)

et ce sera votre sortie :

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\mathtt{1.328\: \!76}}\right)} = {\mathtt{53.035\: \!563\: \!135\: \!882^{\circ}}}$$

heureka is correct.

.

Any real Number multiplied by 0 is 0!

$$\infty * 0 \text{ is u n d e f i n e d and not 0 }$$, because $$\infty \text{ is not a real number }$$

Actually, I also solved it algebraically at first, Melody, then realised there was a nice geometric treatment of it.

.

Note that heureka's answer and mine are different ways of expressing the same thing because

$$e^{i\theta}=cos\theta+isin\theta$$

.

To the nearest hundred this is 9600

To the nearest hundredth it is 9567.81

Look at the tens position (for hundred) or the thousandths position (for hundredths): If that number is less than 5 keep the hundred/hundredths digit the same, otherwise change it to the next higher digit.

. 

I assume you mean 

$$h(x)=2+3e^{-x-1}$$

in which case:

.

how to conert rectangle form 2+3i to polar form :

$$z = x + y i \quad | \quad z = 2 + 3i$$

polar: $$x = r*\cos{(\phi)} \quad and \quad y = r*\sin{(\phi)}$$

set into z = x + yi:  $$z = r*\cos{(\phi)}+ r*\sin{(\phi)}i = r \left[ \cos{(\phi)}+ \sin{(\phi)}i \right] = r \left[ \cos{(\phi)}+ i\sin{(\phi)} \right]$$

r:  $$r=\sqrt{x^2+y^2} \quad | \quad r = \sqrt{2^2+3^2} = \sqrt{4+9} = \sqrt{13}$$ 

$$\phi$$ : $$\phi = \tan^{-1}{ ( \frac{y}{x} )} \quad | \quad \phi = \tan^{-1}(\frac{3}{2}) = 56.3099324740\ensurement{^{\circ}}$$

z(polar): $$z=r \left[ \cos{(\phi)}+ i\sin{(\phi)} \right] \quad | \quad z = \sqrt{13} \left[ \cos{(56.3099324740\ensurement{^{\circ}})}+ i*\sin{(56.3099324740\ensurement{^{\circ}})} \right]$$

Distrubute the 8 over the terms in brackets and collect like terms:

$$9m^6+8(m^6+16)\rightarrow 9m^6+8m^6+8\times16\rightarrow17m^6+128$$

.

Anything multiplied by 0 is 0.

.

rectangular form: x + iy

polar form: re^iθ

r = √(x² + y²)

θ = tan^-1(y/x)

$${\mathtt{r}} = {\sqrt{{{\mathtt{2}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{3}}}^{{\mathtt{2}}}}} \Rightarrow {\mathtt{r}} = {\mathtt{3.605\: \!551\: \!275\: \!463\: \!989\: \!3}}$$

$${\mathtt{theta}} = \underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)} \Rightarrow {\mathtt{theta}} = {\mathtt{56.309\: \!932\: \!474\: \!02^{\circ}}}$$

.