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ok i will post my answers with the question next time

Yes it is.

Well you show us what you have done and we will tell you if they are right, or we will help you understand where you did something wrong.

u think about this very hard

-12,000 because when u multiply the negative three times it becomes a negative and then u multiple 40 x 3 which equals 120 then u multiply it by 100 which equals 12000 and dont forget to put the negative sign in front so its -12,000

i have done them all im just checking my work

Well it they multiply to a positive then the 2 numbers must both be positive OR both be negative

BUT

they add to a negative  OR they must both be negative.

look at the multiply first

-1*-15=15

-3*-5=15

I do not think that there are any others

which of these pairs of numbers add to -16?

what can i multiply to get 15 but adds to negative 16

The answer is 19.

Yuk, yuk. Very much.

$$\\\frac{(80000-y^2)}{200}=\frac{(3210-ky)}{5}\\\\
$multiply both sides by 200$\\\\
80000-y^2=40(3210-ky)\\\\
80000-y^2=128400-40ky\\\\
0=y^2-40ky+128400-80000\\\\
y^2-40ky+48400=0\\\\$$

Now, if you want to make y the subject you can use the quadratic formula.  :)

There isn't one

$$\\cos(2x)=\frac{\sqrt2}{2}=\frac{1}{\sqrt2}\\\\
2x=45, 360-45, 360+45, 720-45, .....\\\\
x=22.5, 180-22.5, 180+22.5, 360-22.5,....\\\\
x=180n\pm 22.5\;degrees \qquad n\in Z$$

This is the description of what e is

$$\displaystyle\lim_{n\rightarrow\infty}\left(1+\frac{1}{n}\right)^n=2.718281828.....\qquad=e\\$$

it just doesn't make much sense to you yet. :))

You are very welcome MathsGod.  I am glad that we are helping you to learn. :)

$35,800 at 8.2% for 3 years simple and compound interest.

i=r=0.082    n=t=3     P=35800

compound interest

FV=P(1+r)^n

simple interest

I=Prt

FV=P+I

Now you can do it yourself :)

Are you asking how much water that will be over 151.19m²  ?

It is probably best to put them both in cm

79.3mm=79.3/10 = 7.93cm

100*100=10,000cm² in a m²

151.19 * 10,000 = 1,511,900 cm²

$${\mathtt{1\,511\,900}}{\mathtt{\,\times\,}}{\mathtt{7.93}} = {\mathtt{11\,989\,367}}$$ cm³   =  11,989,367ml =  11,989.367 Litres

so that is 11,989 Litres which is almost 12Kilolitres

Yep...equally easy......

I shall show you the calculus solution

$$\\\ddot{y}=9.8\\\\
\dot{y}=9.8t+c\\\\
when \;\;t=0\;\;\dot{y}=0\;\;so\;\;c=0\\\\
\dot{y}=9.8t\\\\
$Find t when $\;\dot{y}=12.55\\\\
12.55=9.8t\\\\
t=\frac{12.55}{9.8}=1.28sec$$

There you go - that was pretty simple too.  :)

$$\\y=\sqrt{25-x^2}\\\\
y=(25-x^2)^{0.5}\\\\
\frac{dy}{dx}=0.5(25-x^2)^{-0.5}\times -2x\\\\
\frac{dy}{dx}=-x(25-x^2)^{-0.5}\\\\
when \;\;x=3\\\\
\frac{dy}{dx}=-3(25-3^2)^{-0.5}\\\\
\frac{dy}{dx}=-3(16)^{-0.5}\\\\
\frac{dy}{dx}=-3\times\frac{1}{4}\\\\
\frac{dy}{dx}=-\frac{3}{4}\\\\$$

$$\\$Gradient of the tangent is $ -\frac{3}{4}\\\\
$Gradient of the normal is $ +\frac{4}{3}\\\\\\
\frac{4}{3}=\frac{y-4}{x-3}\\\\
4(x-3)=3(y-4)\\\\
4x-12=3y-12\\\\
$the equation of the normal at (3,4) is $
4x-3y=0$$

That linear formula looks pretty straight forward to me, Melody......

Is it more confusing with calculus???

y = (25 - x^2)^1/2    taking the derivative, we have

y' = (1/2)(25 -x^2)^(-1/2) (-2x) =  -x / √[25 - x^2]

And the slope of the line when x = 3 = -3/ √[25 - 3^2]  = -3/ √16 = -3/4

And the slope of the normal line will be the negative reciprocal of this = 4/3

So we have

y - 4 = (4/3)(x -3)

y = (4/3)x - 4 + 4

y = (4/3)x       and that's the equation of the normal line to the function at (3, 4)

See the pic here of the function, the tangent line to the function at (3, 4) and the normal line to the function going through the same point

My original amswer wasn't entirely correct.....you actually helped me to see MY dumb error...!!

did you need to use physics formula or calculus?

If a ball is dropped, how long must it fall to attain a velocity of 12.55m/s?

I will assume that you are on Earth near seal level      gravity=9.8m/s^2

a=9.8,   u=0,   v=12.55,   t=?

v=u+at

12.55=0+9.8*t

12.55=9.8t

$${\frac{{\mathtt{12.55}}}{{\mathtt{9.8}}}} = {\frac{{\mathtt{251}}}{{\mathtt{196}}}} = {\mathtt{1.280\: \!612\: \!244\: \!897\: \!959\: \!2}}$$

1.28 seconds

If you need to use calc you can ask and it shall be done.