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what is 100/1.09765432

\(\frac{100}{1.09765432}=91.1033630333\)

You forgot a solution. If cos(x)=1/2 then sin(x)=(3/4)^1/2 OR sin(x)=-(3/4)^1/2

That means tan(x)=-(3^1/2) OR tan(x)=3^1/2

Can someone explain substitution method when there are more than two parts?
ie)

\( 9m - 2n - 42 = 0 \)

and

5m - 2n - 26 = 0

\(9m - 2n - 42 = 0 \\m= \color{red}\frac{2n+42}{9}\)     

\(5m - 2n - 26 = 0\\5({\color{red}\frac{2n+42}{9}})-2n-26=0\\10n+210-18n-234=0\\-8n=24\\{\color{blue}n=-3}\)         [ substitute  \(m=\color{red}\frac{2n+42}{9}\)

\(9m - 2n - 42 = 0 \\9m-2(-3)-42=0\\9m=42-6\\m= \frac{36}{9}\\\color{blue}m=4\)

  !

Note that \(x^{-y} \implies \frac{1}{x^y}\)

Yep.....you have the correct function

Note, when x = 0, y = 5....so we have

5  = ab^(0)  =  a

So, since b^(0) = 1,  then.....a = 5

And we know that

3125 = 5b^(4)    divide both sides by 5

625  = b^4         take the 4th root of both sdes and we have

625^(1/4)  = b    =   5

So.....our function is

y = 5*5^(x)

TY

I was doing practice problems at ramdoms so this helps get rid of some of my mis conseptions.

Yep.....this only has one real root [ one x intercept]  at x  = 3

The other factor , x^2 + 5    has  two non-real solutions

Since this is a 3rd power polynomial, we will have either three real roots or one real root and two non-real roots, as in this situation.

We can split this into two series......

The first is 

 1 + 4/49 +16/2401 + 64/ 117649 ...........

And the sum of this series =         1 /  [ 1 - (2/7)^2 ] =   49/45

The second series can be written as

- [ 2/7, 8/343, 32/16807........]

And the sum of this series =  -  [  [2/7] / [1 - (2/7)^2 ] ]   =  -14/45

So.......the sum  is    (49/45) - (14/45)   =   35/45  =  7/9

You need the amplitude of the oscilation to find the frequency, or the period.

\(6^{-10}=\frac{1}{6^{10}}=\frac{1}{60,466,176}\approx 0.0000000165381717\approx1.654\times10^{-8}\)

If you just want to put it into the calculator, you can type it like this:

6^(-10)

6^-10=1/6^10

sqrt3

cos    = x / r      sin  = y / r   and tan  = y / x

We know x and r and we need to find y =  sqrt (r^2 - x^2)  = sqrt (2^2 - 1^2) =

sqrt (4 - 1)   =  sqrt (3)

So

sin (x)  = y/r =  sqrt (3) / 2       and tan (x) = y/x   =  sqrt (3)  / 1  = sqrt (3)

Here is a drawing of what cos(x)= 1/2 really means:

We can find sin(x) just using the Pythagorean Theorem.

\((\frac12)^2+(\sin (x))^2=1^2 \\~\\ \mathbf{sin(x)}=\sqrt{1-\frac14}=\sqrt{\frac34}\mathbf{=\frac{\sqrt3}{2}}\)

tan = sin / cos, so...

tan(x) = sin(x) / cos(x) = \(\frac{\sqrt3}{2}\div\frac{1}{2}=\frac{\sqrt3}{2}\cdot\frac{2}{1}\mathbf{=\sqrt3}\)

Q: What is condensation on grass?

A: dew

Q: What makes the water cycle continue? (hint: gives heat at summer)

A: the sun (and other things too, like gravity... but I think the sun is it)

Those are the only ones I really know...

CAN YOU PLEASE TELL ME THE ANSWER FOR THIS

 P=100(1/2)^(t/5730)

a.

After 2500 years  ≈ 73.9%

After 5000 years ≈  54.6%

After 10,000 years ≈ 29.8%

b.  Here's the graph : https://www.desmos.com/calculator/229ckgarkg

c. 37% remains after about 8200 years

5(-3x - 2) - (x - 3) = -4(4x + 5) + 13

Distribute.

-15x - 10 - x + 3 = -16x - 20 + 13

Combine like terms.

-16x - 7 = -16x - 7

Both sides say the exact same thing.

So yes, it is true for all values of x.       :)

6/1 =6 

160.07 calc

Is it like this?

(The position of the red square inside the blue square doesn't matter.)

To find the area of the shaded region, all we need to do is find the area of the bigger, blue square, and subtract from it the area of the smaller, red square.

shaded area = blue square area - red square area

blue square area = side² = (x + 5)²

red square area = side² = (x - 2)²

shaded area = (x + 5)² - (x - 2)²

shaded area = (x + 5)(x + 5) - (x - 2)(x - 2)

shaded area = [x² + 10x + 25] - [x² - 4x + 4]

shaded area = x² + 10x + 25 - x² + 4x - 4

shaded area = 14x + 21 sq. units.

160.07