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The amount doesn't matter....we have

2P = P(1.05)^t    divide both sides by P ... (see why the amount doesn't mattter??)

2 = (1.05)^t       take the log of both sides

log 2 = log(1.05)^t     and by a log property, we have

log 2 = t log(1.05)    divide both sides by  log(1.05)

log 2 /  log(1.05) = t = about 14.2 years

There is a calculator on the home page. :)

$${\mathtt{5}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}} = {\mathtt{11}}$$

Notice if we have

(1/3)ⁿ and n = 2, we have (1/3)² = 1/9

But notice if we have n + 1 and n = 2.....we have (1/3)^{2+ 1} = (1/3)³ = 1/27

So....as long as n > 0 ......a _n > a_n+1 because a_n+1 multiplies a_n by another (1/3).....thus making a_n+1 < a_n

Thus....this is a decreasing function as n gets larger......

Does that make sense??

sin(theta/2)-cos(theta)=0     add cos(theta) to both sides and square both sides

[1 - cos(Θ]/2  =  cos²Θ    mutiply both sides by 2

1 - cos(Θ) =  2cosΘ        rearranging, we have

2cos²Θ + cos(Θ) - 1  =  0    factor

(2cos(Θ) - 1) (cos(Θ) +1 ) = 0

So. setting both factors to 0, we have

(2cos(Θ) - 1) = 0       add 1 to both sides

2cos(Θ) = 1               divide both sides by 2

cos(Θ) = 1/2        and this happens at  60 degrees  and at 300 degrees   on [0, 360]

And setiing the other factor to 0, we have

cos(Θ) +1  = 0   subtract  1 from both sides

cos(Θ)  = -1        and this happens at 180 degrees on [0, 360]

However, confining ourselves to [0, 360]......180 degrees is not a solution to the original equation .... (because we squared both sides, we sometimes get extraneous solutions in the interval !!)......however..... .-180 degrees would work ...!!!

Thank you so much! 

[4 - (3c - 1)][6 - (3c - 1)]

=  [4 - 3c + 1][6 - 3c + 1]

=  [5 - 3c][7 - 3c]

=  35 - 21c - 15c + 9c²

=  35 - 36c + 9c²

Why do I feel like the person who posted this always posts this question? It is really annoying. Please stop it whoever you are. You probably know the answer by heart even if your were three months old.

Hello guys! The answer IS 19 like jillybean said!! :)

sin(θ/2) - cos(θ/2)  =  0

--->   sin(θ/2)  =  cos(θ/2) 

--->   sin(θ/2) / cos(θ/2)  =  cos(θ/2) / cos(θ/2)

--->   tan(θ/2)  =  1

--->   θ/2  =  45° or   θ/2  =  135°

--->   θ  =  90°  or   θ  =  270°

Right now we have:$${\mathtt{x}}{\mathtt{\,\times\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}$$

While we cannot solve for x, we can simplify it to $${\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{3}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}$$, because, $${\mathtt{x}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}} = {{\mathtt{x}}}^{{\mathtt{3}}}$$.

A percent is basical a number out of a hundred. So 33% is 33/100, which is .33 as a decimal.

Then you can multiply it with 2575 to get your answer:

$${\mathtt{0.33}}{\mathtt{\,\times\,}}{\mathtt{2\,575}} = {\frac{{\mathtt{3\,399}}}{{\mathtt{4}}}} = {\mathtt{849.75}}$$

The lateral area is given by the side length times the height times five =  (12in)(4in)(5) = 240 in²

Approx 8,333

How do they choose what goes into n? I mean how do you know to pick an odd or even sequence. Or neither? They chose 5, 6, 7, 8. When they asked in its original question format all it said was to give the following sequence and determine whether it's increasing, decreasing, or neither. 

175 / 500  = .35 = 35%

We can use the sine inverse to find this......

sin^-1(.577) = about 35.24°   ....Note this could also be a second quadrant angle = (180- 35.24)° = about 144.76 °

Very nice, happy7  .......  !!!!

The inverse f is  y = x - 1      And the inverse of g is y = x/2

g(f(5) sanys to put 5 into f and then evaluate this in g =  2(5 +1) = 2(6)  = 12

And we want to put this result into the inverse of f = 12 - 1 = 11

And we want to put this result into f inverse, again  = 11 - 1 = 10

And we want to put this result into g inverse = 10/2 = 5

Finally, we want to put this result into f  = 5 + 1 = 6

T.Q.M Jerry eres el amor de mi vida nunca te olvidare te amo mucho 

30 6 9 5 and 8

30 + (6-5) + (9-8) =

30 + 1 + 1   =

32

(&4)  means to put 4 into x + 5  = 4 + 5   = 9

And #(&4)  means to put the result of &4 into #....so we have.....

#(&4) = #(9) = (9)²  = 81

Notice that when n is odd....then  (-3)ⁿ is negative......and when n is even, (-3)ⁿ is even.....thus, as n increases (or decreases), (-3)ⁿ  neither increases or decreases......it "oscillates"  between "negative" and "positive"

Nothing shows up.......!!!

We have

3[8x + 7 ] + 8 = 7   simplify

24x + 21 + 8  = 7

24x + 29  = 7    subtract 29 from both sides

24x = -22         divide both sides by 24

x = -22/24 = -11/12