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square root

\(\sqrt{500}=\sqrt{100*5}=10\sqrt{5}\)

3y + 5 = -10

3y = -10 - 5 ---  Shift 5 to right side of equal which changes it from a positive 5 to a negative 5
3y = -15 ---  -10 - 5 = -15

 y = -5 ---  Since both sides are divisible by 3, we divide them by 3 to simplify the answer. 3y / 3 = y & -15 / 3 = -5

arc tan is the same as inverse tan

so use

[2nd] [atan]

10^x=x^16

This cannot easily be done .

There are some values of theta for which it is true. I guess the aim is to find those values.

The two sides are not generally equal!

Try a few example values (say 20 and 25 degrees) to check.

Each year a property increases by 10.5%. What is the value of a $600000 property after 5 years?

\(FV=600000*(1.105)^5\)

600000*1.105^5 = $ 988468

\(\sqrt{144}\)

\(\sqrt{{12}^{2}}\)

\({12}^{\frac{2}{2}}\)

\({12}^{1}\)

\(12\)

\(2.5d+9.25=3+3.75d\)

\(-1.25d+9.25=3\)

\(-1.25d=-6.25\)

\(d=5\)

\(4\times\sqrt{196}\)

\(4\times14\)

\(56\)

If 6.1% IS NOT fresh water, then 100% - 6.1%  IS freshwater = 93.9%

93.9% x 3.4 x10^6 =  .939 (3.4) x 10^6 = 3.1926 x 10^6 gallons =  3,192,600 gallons

you fill a water tank with 3.4*10^6 galoons of water. about 6.1% of water is not fresh water.

how many gallons of fresh water is there?

The percentage of fresh water is:

100% - 6.1% =93.9%

(93.9/100) x 3.4 x 10^6=3,192,600=3.1926 x 10^6 gallons of fresh water in the tank.

The answer is 3x because the 3 cubed is 9 and multiply that to x square will be =9x^2 then divide the whole equation by 3x.

what is 4 square of 196

Do you mean

\(\sqrt[4]{196}\qquad?\)

the square root of 196 is 14 so the 4th root is

 \(\sqrt{14}\)

on any calc you can put it in as        14 ^  (1/4)

to get an approximation

The answer is 12.

f(x) = (x-2)/(x^2+2x-8)

\(f(x) =\frac{(x-2)}{(x+4)(x-2)}\\ f(x) =\frac{1}{x+4}\\\)

To factorize   x^2+2x-8

the trick is to find two numbers that multiply to -8 and add to 2

since they multiply to a negative they must have opposite signs and since the add to a positive the big one must be positive.

4 and -2      easy peazy :))

(4x^2)(2xy)^3

4x^2*8x^3*y^3

32x^5 y^3

arc tan is the same as inverse tan.

use [2nd] [atan]

?im confused?

Hi Goaterino,

Welome to the Web2.0calc forum   

My answer is really just the same as Heureka's and Max's.        Thanks Heureka and Max :)

If you still do not understand it would be helpful if you try to explain which bit you do not understand :)

5(sqrt5) can be written in the form 5^k

What is the value of k

Things you must know

\(\sqrt5=5^{1/2}\\ 5=5^1\\ 5^a*5^b=5^{a+b} \)

so

\(5(sqrt5)\\ =5^1*\sqrt5\\ =5^1*5^{1/2}\\ =5^1*5^{0.5}\\ =5^{1+0.5}\\ =5^{1.5}\)

So k=1.5

Heureka has used a comma instead of a decimal point - some countries do that :)

3*(n+2*m)-n+m

3(n+2m)-n+m

3n+6m-1n+1m

2n+7m

Probability is the chance  that something will happen.

Numerically it has to be between 0 and 1

0 if  the even simpley cannot happen and 1 if if absolutely has to happen and all other possibilities are inbetween.

State the amplitude , period, phase shift, and vertical shift of y=sin (4x + pi) - 1.

y=sin (4x + pi) - 1

\(y+1=1sin [4 (x +\frac{ pi}{4})] \\ Amplitude=1\\ period=\frac{2\pi}{4}=\frac{\pi}{2}\\ \mbox{phase shift is given by the solution to}\\ x +\frac{ pi}{4}=0\\ x= -\frac{ pi}{4}\\ \mbox{Vertical displacement is given by the solution to }\\ y+1=0\\ y=-1\qquad \mbox{The centre of the oscillation will be }y=-1\)