AzizHusain

24 = 32x --> 24/32 = x; reduce to 3/4 by dividing both the numerator and denominator by 8 -->

x = 3/4

1/2*1/3*1/4=?

The numerators are all 1's so we only have to worry about multiplying the denominators:

1/(2*3*4) = 1/(24) = 1/24 or 0.0416666666666667.

Sorry for the late reply...had so many extra things happening yesterday and thought it would only take a few hours but time flew by!

For this question: we use proportions to solve for some unit given a conversion. In this case, we are asked to solve for # of minecraft days that can be played in 2 hours and are given the conversion of 1 minecraft day = 24 mins. 

Now, we have minecraft days, hours, and mins as our units; however, we need 2 units since we want to have #minecraft day/#minute = #minecraft day/#minute. We convert the hours --> 2 hours --> 120 mins.

For proportions, we have the format just like above but the units can vary dramatically depending on what we want to find.

Plugging in what we already know: 1 minecraft day / 24 mins = #minecraft day [x] / 120 mins -->

Now, let's call what we want to find "x". By cross multiplying and noticing that we can cancel the mins units since we will end up with 120 minecraft day*mins / 24 mins = x, we get an x value of 5 minecraft days.

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Another method: Dimensional analysis

In science, especially chemistry, we use dimensional analysis to convert units and start out with something we already know, but not a conversion.

So, we will start with "2 hours" since that is the only available information we are given that is not a conversion.

2 hours X (60 mins / 1 hour) X (1 minecraft day / 24 mins) = 5 minecraft days.

By doing this, we can see that the hours cancel out, the mins cancel out, and we are left with minecraft days as the only unit. We simply multiply the numerator out and then divide by the numerator, just like a fraction to obtain our answer.

Notice that if we were asked for a dfferent unit and were given more more conversions, we could keep on continuing our dimensional analysis chain until we reach that desired unit.

Probably in a few hours.

Sorry, I have to go out right now...I will be back later..

Proportions: 1 day/24 mins = x / 120 mins (2 hours = 120 mins, we need same units)

x = 120 mins*day / 24 mins = 5 days.

8 2/3 = 26/3 = 8,666.... es mayor de 8,6.

Use the "cos" button that is the third key in the 1st column of the scientific calculator on this website.

For the second question, relating the graph to f(x) = cosx with interval -2pi <= x <= 2pi:

Notice that for f(x) = cosx, if x = 0, then f(0) = 1. But, in this graph at cos(0), the value is 2 which suggests that the graph had to have been shifted up one unit. This graph is f(x) = cosx + 1 = cos(0) + 1 = 1 + 1 = 2.

lxl + lyl = 1

if x = 0, then y = 1,

and if y = 0, then x = 1.

So (0,1) and (1,0) are definitely points.

Also, we can also do the same for:

if x = 0, then y= -1 as well since we have the absolute value sign,

and if y = 0, then x = -1 as well since we have the absolute sign.

So, we now have 4 main points (0,1), (1,0), (0, -1), & (-1,0). 

Now, we know x or y cannot be greater than 1 since lxl + lyl must be equal to 1 [if x = 2, then there would be no value for y that would satisfy the equation].

Furthermore, we notice that 0.5 + 0.5 also equals 1 so we get more points: (0.5, 0.5), (-0.5, 0.5), (-0.5, -0.5), & (0.5, -0.5).

We now have 8 points and if you connect them together, you get a square.

So, these 8 points create a square with sides of sqrt(2).