andhereicome said: Hi! Um, I was hoping to get some help with my math homework... I'm supposed to solve the equation y=-2x^2+16x-30 by graphing by hand, using my calculator, factoring, and by using the quadratic formula, and I'm pretty lost. Thank you!

Basically its asking you to find for what x values will y = 0 using various methods.

First set the equation to zero giving us: 0=-2x^2+16x-30
Next we can immediately notice we can immediate factor out the -2 from the right side. This gives us 0=-2(x^2-8x+15)

Now we have to figure out what two numbers can we multiply together to get 15 and add together to get -8. Well the factors of 15 are (-1,-15) (1,15) (3,5) (-3,-5) (-1,-15) and (1,15). Of all of these we will use -3 and -5 because they both add to negative 8 and multiply to make 15. This means the equations they can be factored as (x-3)*(x-5). So now we have found the 0=-2(x-5)(x-3)

Now all we have to do is solve for x, but we have two solutions. First divide by -2 on both sides, giving us 0=(x-5)(x-3). Now we have to take each expression and solve for x, so now we have:

x-5=0

x-3=0

This gives us

x=5

x=3

You have completed the problem by factoring.

To graph by hand. since we already know the answer you can simply graph by plugging in integer values. Since we already know the answer it would be best to plug in x=0 to x=5. After getting your values, plot them, and you can see that y=0 at x=3 and x=5

Your graph should look like this.

To do the quadratic formula method, use the quadratic formula make -2=a, 16=b, -30=c
Use this equation:

\

Lots of algebra later you have x=3 and x=5. If you need help solving the equation let me know. (+/-) by the way means there are two solutions, one solution using the addition and a separate solution using subtraction.

Using your calculator will vary by your model of calculator but I’d suggest graphing the function and finding where the function crosses y=0. This will be at x=3 and x=5. Similar to graphing by hand but much faster.

Hope this helps if you need anything more in depth, feel free to ask.

And if anyone else on tumblr needs help with math, chemistry, physics, or biology, feel free to contact me!

@11 months ago
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I need help with this problem Draw the graph of a differentiable function that is increasing at a decreasing rate over the interval (0,8)

First off, thank you for asking a question. The short answer is to sketch a graph like in the first or second picture. In needs to be concave down and increasing as in the third picture on a range from x=0 to x=8.
Conceptual questions like these are hard because they don’t have a set formula, but once you really understand the math, they are the easiest.
Let’s breakdown what it asked you:
Draw the graph of a differentiable function that is increasing at a decreasing rate over the interval (0,8)
If you want to approach it analytically. You need to make a function that is increasing. This means that the derivative is positive
Our next clue is that it needs to be increasing at a decreasing rate. This means that the 2nd derivative is negative.
Or in other words you need to sketch a function that is Concave down and increasing from [0,8]. Outside of [0,8]  it can be pretty much whatever you want, as long as it is continuous.
So lucky you don’t need to find the function but you need.

But if you’re interested in how to answer it if a more in depth answer to your question would be y=-(x-8)^2, the good thing is you don’t need to provide a function just a sketch. Please refer to my first photo.
To be accurate though you could’ve used any number as long as it was greater than or equal to 8. For instance y=-(x-100)^2 would have worked also.

An easier way to see it would be y=100-(x-8)^2 This also would’ve worked. And I will use it to explain how to solve them problem since it is visually nicer. Please refer to the second picture.

I hope this helps, if you have any more questions feel free to ask.

And if anyone else on tumblr needs help with math, chemistry, physics, or biology, feel free to contact me!

@11 months ago with 2 notes
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someone…….pls………help

I found this out using Wolfram Alpha. I’m here to help students who want to succeed in math and science, if you would’ve read my post on website  "4 Top websites you’re not using, and it’s hurting your grade." You could’ve saved yourself some trouble so I highly recommend checking it out. If you need more homework help let me know!

@11 months ago with 3 notes

Many students might know about one or two of these sites, the resourceful students know all of them. Whether if you do or don’t could easily be the difference between a letter grade or two. Even if they cost money I’d highly recommend investing in these web resources.

Cost: Free!!!
What is it?: According to their website, “Khan Academy is a non-profit educational website created in 2006 by educator Salman Khan, a graduate of MIT and Harvard Business School. The stated mission is to provide ‘a free world-class education for anyone anywhere.’” Salman Khan is a highly accomplished academic having three degrees from MIT (BS Math, BS Electrical Engineering & Computer Science, and a Masters in Electric Engineering & Computer Science) not to mention him going to Harvard for his MBA. Basically his website contains lectures from him and newly other experts in various fields of education (History, Mathematics, Physics, Organic Chemistry, etc. ).
What can you gain from it?:Salman Khan’s video lectures are perfect for when your class didn’t cover the issue enough or if you’re still having trouble understanding some concepts. He has a remarkable way of explaining things conceptually and often can explain things in a way that suddenly makes things click in your head. I would maybe use this for test review, but I would mostly use it to supplement in-class lectures. This is not a substitute for taking notes!
Pros: Many different topics, not just STEM, and very thorough. Great for conceptual understanding.
Cons: Very long winded, can talk a long time to explain a subject because he explains it in such detail, if you just need a little bit of help and not a lot, it wouldn’t be my first choice. No specific advice for your homework problems.

PatrickJMT

Cost: Free

What is it: Patrickjmt.com is a lot like KhanAcademy except it focuses on Math and to a lesser extent physics. Rather than explaining to you all of the theoretical basis behind mathematics, Patrick simply does an example problem. His video’s tend to be a lot shorter and more to the point than compared to Khanacademy, because he is not diving deep into the theories and intuition behind the solutions.

What can you gain from it?: This website is indispensable when you’re just having trouble with a very specific problem, he tends to do many different examples so this can definitely speed up any homework problem or test review.

Pros: A lot faster, may sometimes answer your questions, concise, more detail.

Cons: Still not extremely specific though more specific than khanacademy.

Chegg

Cost: Textbook Solutions – \$14.95/month  includes Homework help | Textbook renting: Varies

What is it: Chegg should be a name every college student knows for a number of reasons. First of all you can rent books as opposed to buying them saving you tons of money, you can even rent the etextbook saving you space and your back. But more importantly for \$14.95 a month you can access the solutions manual for any textbook in the world. Step by step solutions to all the problems in your textbooks. If you don’t know what a solutions manual is, you need to, especially if you’re taking a STEM class. A solutions manual offers the step by step answer to every problem, rather than just the number. The homework help section is also amazing since there are tons of people on the website who will answer the questions you ask, or the question may have already been asked and you can look up the previous solutions.
What can you gain from it?: Chegg’s resources aren’t great note supplements but in terms of homework help they’re hard to beat. You can use this website to help you solve your homework and understand the solutions if you don’t have a solutions manual.

Pros: Very specific to your HW, A large data base of answered questions. Can answer questions that are not straight forward. Sells and rents books.

Cons: Can have many wrong answers or solutions, can often be unhelpful. Still might be cheaper to get the solutions manual(s). Pretty specific but may not be extremely helpful with online homework due to the questions having different numbers.

WolframAlpha

Cost: Free – \$2.99/Month for unlimited Access

What is it: WolframAlpha is a “computational knowledge engine” it can tell you thing from the “number of colon cancer deaths in japan” to  .  We are very lucky as math students that not only can it answer almost any math question you can type into it, but it also offers step by step solutions.

What can you gain from it?: It functions as an extremely powerful calculator, and can be used for doing your homework whenever you don’t need a lesson and checking your answers.

Pros: Very specific, can answer almost any question you put into it, fast.

Cons: Very limited but still helpful free service, Can offer much theoretical or intuitive insight.

@11 months ago with 18 notes
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So just what is all this anyways?

This is me giving back. I want to continue to provide guidance and support to all the students out there who want to succeed at no matter what the cost. I can teach youhow to get excellent grades, I can show a failing student how to get a 4.0 in the hardest majors. You don’t have to be exceptionally smart either but all you simply need to do is make minor changes in how you study and how you think about your education.

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@11 months ago
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help please! “Find the second derivative of y with respect to x for the following implicit functions: 9x^2+16(y-4)^2=144

Full solution coming soon

@11 months ago with 2 notes
#math #math help #math tutor #mathematics #calculus #trig

it says to solve the equation for theta (0 ≤ θ < 2pi)

2 sin^2 θ = 1

If you could explain the steps to solving this, it would help out a lot with this whole worksheet. Again thank you so much! “

First, thanks for coming to me with this problem as I love trig. Secondly I would like to let you know that I made a post I suggest you read called "4 Top websites you’re not using, and it’s hurting your grade."  It brings up an amazing website called Wolfram Alpha that as able to solve your question and even give you a step-by-step solution (go solution and click step-by-step solution.

None the less I will guide you through this fun problem!

First you have : 2 sin^2 (θ) = 1

Our goal here is to isolate the variable
θ.
So, m
y first step would be to get rid of the 2 on your function dividing both sides by 2 resulting in: sin^2 (θ) = 1/2

Next, in order to get rid of the square, we square root both sides giving us:
sin(θ)= +/- 1/root(2)

Protip: The +/- (plus or minus) is very important in order to get the correct answer. In order to understand why we have +/- instead of just 1/root(2) we must think of the square root function itself. You might not know this but the square root function by its definition does not tell the full story. By definition the square root function only spits out positive numbers. So if you put into you calculator the square root of 4, it will only give you two because that is its mathematical definition.

So what does this mean? That means whenever you are solving a problem and you use the square root function to solve a square, you have to add in the negative solution also in order to be correct. Important: This does not include square roots that are given in the problem, only square roots you introduce in solving the problem.

Okay, Anyways. Now we have the more manageable:
sin(θ)= +/- 1/root(2).

You may also recognize this as sin(θ)= +/- root(2)/2

Quick Tip: We get the root(2) out of the denominator of 1/root(2) by multiplying by root(2)/root(2) (which is actually just a 1) to get root(2)/2

Solving this is still tricky, the natural impulse is to simply use arcsin(root(2)/2)). But this would be forgetting that it’s range is only -pi/2 to pi/2.

At this point is best to simply look at the unit circle. Hopefully you have it memorized, if not, know it simply must be done. But if you have trouble, come to me, there’s lots of tricks to get around it.

If you look at the unit circle we need to find the angles that give us y-values of root(2)/2 and negative root(2)/2.

So if you look at the (x,y) coordinates of different angles, the angles in radians from 0 to 2pi giving you pi/4, 3pi/4, 5pi/4 and 7pi/4.

I hope this helps, if you have any more questions feel free to ask.

And if anyone else on tumblr needs help with math, chemistry, physics, or biology, feel free to contact me!

@11 months ago
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## ...And then you shall know peace.: ...Math...

I wish I could do better in math. I’ve never really struggled in school before, getting all A’s in high school and A’s and B’s in college. Now that I’ve transferred as an undergraduate, my first math class in almost 3 years is threatening my GPA. I am freaking out. I’ve never failed quizzes and…

I’ve started my blog for people like you. I have a lot of information and I’m not sure yet where to start. Do you have any questions about how to excel in math?

@11 months ago with 1 note

The tangent line will be horizantal where ever the slope is 0.

so, do I set x^3-18x^2 equal to 0?

You need to take the derivative of this function, then find where the derivative equals zero.

Using the power rule you get f`(x) = 3x^2-36x you can then factor out the x and the 3.

f`(x) = 3x(x-12)

This is your derivative, now solve for zero. This will give you the horizontal tangent line. Since a slope of zero is a horizontal line.

0 = 3x(x-12)

We can break the solution into to two parts since they are multiplied by each other:

a. 3x = 0

b. x-12 = 0

If you solve them you get your two solutions. x=0 and x=12. If you put them into the original function you get the answers (0,0)  and (0,-864)