All Answers 358110 Answers

$15.74 / 3.8 =$4.14 cost per pound.

3:00

What is the size of the yard?

If we take the average year to be 365.25 days(because of leap year), then we have:

52,560 / 365.25 =143.90 years, or 143 years and ~329 days.

! means factorial.

Ex. 4!=1*2*3*4

9=10 is an incorrect statement because 9 does NOT equal 10.

z = (4 - 2i) - (-1 + 3i)

Algebraic form:
z = 5-5i

Exponential form:
z = 7.0710678 × ei (-45°)

Trigonometric form:
z = 7.0710678 × (cos (-45°) + i sin (-45°))

Polar form:
r = |z| = 7.07107
φ = arg z = -45° = -0.25π

It is 33

Simplify the following:
i^35

i^35  =  i^(4×8+3)  =  (i^4)^8 i^3:
(i^4)^8 i^3

i^3 = i^2×i = (-1) i = -i:
(i^4)^8 -i

i^4 = (i^2)^2 = (-1)^2 = 1:
-1^8 i

1^8 = 1:
Answer: |   -i

Thx Miss Melody :D

I had the answers but i just needed 2 know if they were right, n they were!

So thank u

(^_^)

Hi Eloise :)

I think it is probably easiest to use a unitary method for these. 

1. It takes 3 pumps 15 hours to fill a swimming pool. How many pumps would it take to fill the pool in 9 hours?

3   pumps       take       15 hours

so 1 pump must take 3 times longer than that.      15*3=45hours

1pump         takes      45 hours

Now 45 divided by 5 = 9 hous which is the number you want.

If you are going to do it 5 times faster then it will take 5 times more pumps   1*5=5 pumps

So

it will take 5 pumps to fill the pool in 9 hours

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

2. It takes 200 tiles to tile a room when each tile covers 36cm2. If I use tiles which covers 25cm2, how many tiles would I       use?

200 tiles    when each is    36cm^2         

If the tiles are only 1cm^2 then the tiles are 36 times smaller and you will need 36 times 200 tiles   36*200 = 7200 tiles (if they are really little just 1cm^2 each)

But the ones we want are 25cm^2 each, that is 25 times bigger than the really little ones.  They are a 25 times bigger so we will need to divide the number of tiles by 25

7200 divided by 25 = 288 tiles.

So if the tiles cover 25cm^2 each, you will need 288 tiles.

You had best buy some extra ones because there will be some cut peices that you will not want to use ;)

This is the formula you would use for this purpose:

PV=FV[1 + R]^-N=PV OF $1 IN THE FUTURE. Where R=Interest rate per period, N=number of periods, PV=Present value, FV=Future value.

PV=68,000(1 + .025)^-22

PV=39,498.80
 

nice question

hey nm

Hey,

Sup?

(2M)/(2M+3)-(2M)/(2M-3)=1 How many extraneous solutions does the equation have.

\(\small{ \begin{array}{rcll} \frac{2M}{2M+3}-\frac{2M}{2M-3} &=& 1 \quad & | \quad :2M \\ \frac{1}{2M+3}-\frac{1}{2M-3} &=& \frac{1}{2M} \quad & | \quad \cdot (2M+3) \cdot (2M-3) \\ \frac{(2M+3) \cdot (2M-3) }{2M+3}-\frac{(2M+3) \cdot (2M-3) }{2M-3} &=& \frac{(2M+3) \cdot (2M-3) }{2M} \\ (2M-3) - (2M+3) &=& \frac{(2M+3) \cdot (2M-3) }{2M} \\ 2M-3 - 2M-3 &=& \frac{(2M+3) \cdot (2M-3) }{2M} \\ -6 &=& \frac{(2M+3) \cdot (2M-3) }{2M} \quad & | \quad (2M+3) \cdot (2M-3) = (2M)^2-3^2 = 4M^2-9 \\ -6 &=& \frac{4M^2-9}{2M} \quad & | \quad \cdot 2M \\ -6\cdot 2M &=& 4M^2-9\\ 4M^2-9 &=& -6\cdot 2M\\ 4M^2-9 &=& -12M\quad & | \quad +12M \\ 4M^2+12M-9 &=& 0\\ \end{array} }\)

\(\boxed{~ \begin{array}{rcll} a\cdot M^2+b\cdot M+c &=& 0 \\ M &=& \dfrac{-b \pm \sqrt{b^2-4ac} }{2a} \end{array} ~}\)

\(\small{ \begin{array}{rcll} 4M^2+12M-9 &=& 0 \quad | \quad a=4 \quad b = 12 \quad c = -9 \\ M &=& \dfrac{-12 \pm \sqrt{12^2-4\cdot 4 \cdot (-9) } }{2\cdot 4} \\ M &=& \dfrac{-12 \pm \sqrt{144+144 } }{2\cdot 4} \\ M &=& \dfrac{-12 \pm \sqrt{ 2\cdot 144 } }{2\cdot 4} \\ M &=& \dfrac{-12 \pm \sqrt{ 2\cdot 12^2 } }{2\cdot 4} \\ M &=& \dfrac{-12 \pm 12\cdot\sqrt{ 2} }{2\cdot 4} \\ M &=& \dfrac{-3 \pm 3\cdot\sqrt{ 2} }{2 } \\\\ M_1 &=& \dfrac{-3 + 3\cdot\sqrt{ 2} }{2 } \\ \mathbf{M_1} & \mathbf{=} & \mathbf{0.62132034356} \\\\ M_2 &=& \dfrac{-3 - 3\cdot\sqrt{ 2} }{2 } \\ \mathbf{M_2} &\mathbf{=} & \mathbf{-3.62132034356 } \end{array} }\)

I really struggle with fraction multiplying little help?

This one is MUCH harder than you have made it Solviet.

Nauseated might come up with a neat formula for you but if you want to work it out logically that might be a real challenge ://

I'll think on it ://

aa ok i understand :)

I think this is an English understanding problem Solviet.

If a pink card is next to a green card it can mean in either order.  Either pink,green or green,pink

If I cared about the order I might say that the pink is to the left (or right) of green

Do you understand this ?

wait but it is saying "do not include a pink card next to a green card" only pink card next to green