helperid1839321

I'm not entirely confident this answer is correct, as I got a different answer when I did my calculations. Also, it's not terribly helpful to recieve an answer without an explanation to go with it.

If the person doesn't know how to solve the problem, then they don't learn how to solve it in the future. The objective of most teachers is self-obsoletion (in effect, they are tryhing to do their job, so they aren't necessary, in order to succeed.) This forum could also be viewed the same way, as we would like to answer the questions in a way that lets the people solve the remaining ones on their own.

I started by observing the height-of-object to length-of-shadow ratio. We're given both values for the tree, so we simply divide: 40 foot height/10 foot shadow = 4:1 ratio of height:shadow size.

Andrea's shadow is 18 inches long, so we place it into the ratio. 18 inches (Andrea's shadow)/1 (ratio component relating to shadow size) = 18 inches, so we multiply the first value by 18 inches.

This yields 72 inches, rather than 68, as the guest below suggested.

On an exit note, being a little bit taller than normal, I would be somewhat intimidated by someone who's a full 6 feet tall.

Interesting, it seems like that might have been rolled back. It doesn't seem like it's a filter anymore either. That's on me for not keeping up to date with the site

Did you know that there is an "off-topic" option for making posts to the forum? It's usually nice for things like this so it doesn't bury math questions ;)

First thing to answer: What are we solving for?
From the last part of the prompt, we can assume we are solving for the proportion of red bean ice cream cones sold, versus the total number of ice cream cones.

Second thing: What are the knowns, and the unknowns?

We know how many durian ice-cream sales were completed, and how many red bean ice-cream cups were sold.
The only unknown we have here is the number of red bean ice-cream cones sold. However, this has the side effect of leaving the total number of ice-cream sales completed unknown.

How might we calculate the total number of red-bean ice cream cones sold?
We're given a relation between the total number of red bean ice cream sales completed, and the number of red bean ice cream cones. We're also given a relationship between this and the total number of red bean ice-cream cups sold, which we're also given an exact number for. Source:
"The remaining 24 red bean ice-cream were sold in cups."

Our ratio here is: 1/5 of red bean ice-cream sales in cones, and the remainder (24) in cups.
The remainder after subtracting 1/5 from a whole is 4/5, so we can say that 4/5 of the red-bean ice-cream sales were in cups.
Reducing this to the smallest factor and multiplying to get the value of the whole, we first divide 24 by 4 (the numerator), then multiply by 5 (the denominator).

This leaves us with a total of 30 red-bean ice cream sales.

Now, we multiply the total number of red-bean ice cream sales (30) by the proportion of those sales that are in cones (1/5) to get the number of red-bean ice cream cones sold. (6)

We must return now to the total number of ice cream cones sold, which we can assume to be limited to the information provided. We add the durian ice cream purchases (10) to the number of red-bean ice cream purchases (30) to get the total ice cream purchases (40).

Now, we have our proportion: 6 red bean ice-cream cones :: 40 ice-cream sales.

This may be represented by the fraction, 6/40.

We can also reduce this fraction to 3/20, simply because they are equal quantities. This makes it easier to convert to a percent, as 20 is a factor of 100.

If we want to get a percentage from a fraction, we can use a conversion ratio. In this case, our conversion ratio is \(\frac{100\%}{1}\).

This might look odd, but the term "percent" can be traced back to a definition meaning "out of 100" (from the latin "per centum" [that's latin right?]), so 100% would be equal to 100/100, or 1.
In any case, we can then do some multiplication. \(\frac{3}{20} \times \frac{100\%}{1} = \frac{15\%}{1} = 15\%\)

To expand the multiplication, I first divided the 100% value by the denominator, in order ot figure out the value I multiply the numerator by. 100/20 = 5, so I multiplied the 3 on the top left by 5%.
 

This gives me 15%, which I believe to be the answer.

On a side note, it would be appreciated if you were to post how far you got into the problem before getting stuck next time, so that it might be possible to avoid a massive wall of text. I think that doing so would help both of us :)

I'll assume that b and c are non-zero for the purposes of solving, or the answer might be unobtainable. I also think I need to assume them to be finite.

(a+b)/b = a/b + b/b = 5
b/b = 1
a/b + b/b - b/b = 5 - 1
a/b = 4

First, I split the fraction into 2 parts. It isn't helpful immediately, but was helpful with something else, namely...

Second, I used to identity property of division. Namely, dividing a finite, non-zero quantity by itself will yield 1.
Then, I subtract the second equation from the first. This is a very finicky thing to do, but because I know that the values apply the same in both places, I'm doing it anyways.

I could have also written: \(\frac{a}{b} + \frac{b}{b} = \frac{a}{b} + 1 = 5\), then subtracted 1 from each side to get a/b = 4. Different method, same result.

(b+c)/c = b/c + c/c = 4
c/c = 1
b/c + c/c - c/c = 4 - 1
b/c = 3

The numbers and letters are different here, but the steps from above apply the same here.

(a+c)/c = n = a/c + c/c
c/c = 1

a/c + c/c - c/c = n - 1
a/c = n-1
a/c = a/b * b/c
n-1 = 4 * 3
n-1 = 12
n = 13

The important thing that happened here, is I created a "placeholder" variable I named n. I set it equal to the initial quantity that we were solving for, so as to reduce the number of times I write out (a+c)/c, and to also allow operations related to it easier.
The third part of this might look odd, but I chose not to change n, and leave (n-1) in place. This helps, as I note that a/c = n-1, and also equal to a/b * b/c. The b in the numerator and denominator cancel out, and the remaining values match up, thus n-1 = a/b * b/c. However, we don't have a or c, so we keep a/b and b/c, since we have those values and can then find a/c.

From there, we then find n, and with it, the value it represented, as seen below:

(a+c)/c = n = 13
 

Hi, not sure this really breaches any forum rules, but putting the link of the problem in the question as having a link as the only content is not the most accessible way that we might be able to help you. If you wanted to point out that the other question got buried, and didn't get an answer, one option might be to put the link as "previous post: ", and then post the problem again.

Answers posted here would seem notably out of context, and would also require lots of tabbing back and forth, making this content primarily a filler on the forum page, burying other people's questions.

If you rewrite your second equation as (1-x)x^0.5, you'll notice it doesn't actually equal the same thing. That's because it was in the bottom of a fraction before, meaning it should have a *negative* derivative.
Also, you forgot about all constants turning into 0 when you take the derivative, meaning the derivative should look a bit more like (0-1)(-0.5)(x^-1.5).

Hope this is able to help! ;)

This isn't as much calculus as it is geometry, but I'll explain here.

Areas of sectors are in general the area of the circle times the proportion of the circle you are measuring the area of.

For question (a), given a radius of 7 (7² being 49), it would be \(49\pi\times\frac{71^\circ}{360^\circ}\), or 49pi*71/360 ≈ 30.360002338441363

For question (b), given a radius of 10 (10² being 100), it would be \(100\pi\times\frac{0.3\text{ rad}}{2\pi\text{ rad}}\), or 100pi*0.3/(2pi) = 15.

Hope I managed to get the answer to you in time :)

I will assume consecutive to mean that the integers have a difference between them of 1.

We can now define 2 integers, a and b, and say that a > b.

From this we know that, given the difference is equal to one: a + 1 = b.

We also know that a + b = 129.

Substituting the alternative form of b in, we have: a + (a + 1) = 129.

After combining terms (grouping), we have: 2a + 1 = 129.

After isolating variables (getting a alone on one side), we get 2a = 128, which, when dividing each side, resolves into a = 64.

Plugging a back into the above equation, we find b = (64) + 1, or b = 65.

The consecutive integers are therefore 64 and 65.

I'll assume that given how we are given an incomplete value for x we can assume that the point is 6 distance from the x axis, leaving us with a y-value of + or - 6.

Given how the most y-negative value possible is -2 (assuming straight negative y travel), we can safely eliminate -6 as a possibiility for y, and find y to be +6.

Solving for a point with y=6 a distance of 5 units away from (8,3), by using a memorized pythagorean triple of 3-4-5, you can know that the x value is 8 plus or minus 4 units.

Given that x is less than 8, the lower answer of 4 is the only one that is possible, hence x = 4.

We now know that (x,y) is located at (3,4).

Solving for distance from the origin, we could use the pythagorean theorem, but this is another use of the same pythagorean triple. We know that it is 5 units from the origin.

Putting this back with n, we now have sqrt(n) = 5

Squaring each side to solve for n alone, we find n = 25.

If use of the pythagorean theorem is required I will be happy to supply it.