How To Solve Calculus Word Problems

How To Solve Calculus Word Problems-73
Of course, cheating at math is a terrible way to learn, because the whole point isn't to know the answer to 2x 2 = 7x - 5, it's to understand the learn?

Of course, cheating at math is a terrible way to learn, because the whole point isn't to know the answer to 2x 2 = 7x - 5, it's to understand the learn?

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It has trouble with word problems, but if you can write down a word problem in math notation it shouldn't be an issue.

I also tried it on a weird fraction from an AP algebra exam, which it kind of failed at, but then I swiped over and it was showing me this graph, which included the correct answer: I love this app, not just because it would've helped 8th grade Paul out of a jam, but because it's such a computery use of computers.

We’ve already found the relevant radius, $r = \sqrt[3]\,.$To find the corresponding height, recall that in the Subproblem above we found that since the can must hold a volume of liquid, its height is related to its radius according to $$h = \dfrac\,.

$$ Hence when $r = \sqrt[3]\,,$ \[ \begin h &= \frac\,\frac \\[8px] &= \frac\,\frac \\[8px] &= \frac\,\frac \\[8px] &= 2^\frac \\[8px] h &= 2^\sqrt[3] \quad \triangleleft \end \] The preceding expression for is correct, but we can gain a nice insight by noticing that $$2^ = 2 \cdot\frac$$ and so \[ \begin h &= 2^\sqrt[3] \\[8px] &= 2 \cdot\frac\,\sqrt[3] \\[8px] &= 2 \sqrt[3] = 2r \end \] since recall that the ideal radius is $r = \sqrt[3]\,.$ Hence the ideal height (height and radius) will minimize the cost of metal to construct the can?

On about half the middle school science problems I tried, the app was able to identify the topic at question and show me additional resources about the concepts involved, but for others it was no more powerful than a simple web search.

How To Solve Calculus Word Problems

But for algebra this thing is I pointed it at 2x 2 = 7x - 5, which I wrote down at random, and it gave me a 10 step process that results in x = 7/5.Typical phrases that indicate an Optimization problem include: Before you can look for that max/min value, you first have to develop the function that you’re going to optimize.There are thus two distinct Stages to completely solve these problems—something most students don’t initially realize [Ref]. Now maximize or minimize the function you just developed.Notice, by the way, that so far in our solution we haven’t used any Calculus at all.That will always be the case when you solve an Optimization problem: you don’t use Calculus until you come to Stage II.Above, for instance, our equation for $A_\text$ has two variables, We can now make this substitution $h = \dfrac$ into the equation we developed earlier for the can’s total area: \[ \begin A_\text &= 2\pi r^2 2 \pi r h \[8px] &= 2\pi r^2 2 \pi r \left( \frac\right) \[8px] &= 2\pi r^2 2 \cancel \cancel \left(\frac\right) \[8px] &= 2\pi r^2 \frac \end \]We’re done with Step 3: we now have the function in terms of a single variable, , and we’ve dropped the subscript “total” from $A_\text$ since we no longer need it.This also concludes Stage I of our work: in these threes steps, we’ve developed the function we’re now going to minimize!In this problem, for instance, we want to minimize the cost of constructing the can, which means we want to use .So let’s write an equation for that total surface area:\begin A_\text &= A_\text A_\text A_\text \[8px] &= \pi r^2 2\pi r h \pi r^2 \[8px] &= 2\pi r^2 2 \pi r h \end That’s it; you’re done with Step 2!You'll see a button "View steps" and this takes you to the developer's site where you can purchase the full version of the solver (where you can see the steps). I was homeschooled (that's not the confession part), and in 8th grade my algebra textbook had the answers to half the problems in the back. That seems to be the premise behind app called Socratic. The app lets you take a picture of a problem (you can also type it in, but that's a little laborious), and it'll not only give you an answer, but the steps necessary to to arrive at that answer — and even detailed explanations of the steps and concepts if you need them.

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