"I need help with integers. what is the rule in subtracting and adding them?" by Rowlanda

"Hi ms.young i need help with integers. what is the rule in subtracting and adding them?"

Hi, Rowlanda. The rules for adding integers are as follows:

• If the signs are the same, add and keep the sign.

Examples:

4 + 5 = 9

-4 + (-3) = -7

-4 - 4 = -8 (this one is tricky, but remember + (-4) and -4 means the same thing)

• If  the signs are different, subtract the digits and keep the sign of the "larger" number.

Examples:

-9 + 5 = -4

9 + (-4) = 5 (Remember: this means the same thing as " 9 - 4 ")

The one that confuses students is the following:

-7 - (-2); this is better understood as  -7 + 2 because "the opposite of negative 2" [-(-2)] is positive 2.
once this is rewritten, just follow your rules to arrive at the answer of -5.

Get it?  Good!

Mrs. Young

Algebra I question ((5y-)-(-4y+6)=3) by Marquitta

Hi, Marquitta.


I’m assuming your question is how to solve this problem for y. Let me give you a similar question to walk you through the challenging parts of this equation.

Consider:                                                 (3x)-(-8x+2)=4, solve for x

The first thing I’d want to do is eliminate that irritating double negative. So, I’m going to rewrite the problem.

                                                                       (3x)-1(-8x+2) = 4

When you recognize that there is really a (-1) multiplying the expression (-8x-2), you can see that we can go ahead and use the distributive property to make those negatives go away:



                                                     (3x)-1(-8x+2)=4            -1( -8x) = 8x

                                                                                          -1(2) = -2
                                                     3x + 8x -2 = 4

Now, we can combine like terms and solve:

                                         3x + 8x -2 = 4         3x + 8x = 11x 
                                                                 
                                         11x -2 = 4              add 2 to both sides

                                         11x=6                   divide by the coefficient of x, 11

                                           x = 6/11            fractional answer!

Your problem is very similar. If you get stuck, just do what I did. The numbers are different, but the process is exactly the same.

Let me know if you need more help! Thanks for the question!



Mrs. Young

higher order derivatives question by Unknown

Question: I'm trying to solve for t given:


y''''(t)-10y'''(t)+35y''(t)-50y'(t)+24y(t) = e^(5t)

and that

y'''(0) = y''(0) = y'(0) = y(0) = 0



any hints??



Answer:
Thank you for your question. I don’t get a lot of cal. questions…so this will be fun!

In general, when we’re dealing with finding higher order derivatives, it is important to simplify the process in your mind by only thinking in terms of first order derivatives. In other words,

f'' (x) = f ' (f ' (x) )

Or in words, “the 2nd derivative of x is the derivative of the first derivative”

“the 3nd derivative of x is the derivative of the 2nd derivative”

Etc…

Also, look at the given information:

y'''(0) = y''(0) = y'(0) = y(0) = 0

Why was this given? What information does this give you that is necessary to solve for t?

Next, the exponential term is a real headache. How could you eliminate it?



I hope this helps. If you need further help, you can email me or leave a comment to this post. I can provide a sample problem.



Thanks.



Mrs. Young

Questions below

Hi, everyone. Mrs. Young here. As you can probably tell, this archive is in a new format, so today's date shows as the "post date". Therefore, I have included the date the question was actually asked by the student. All post after this point will be posted on the day submitted. If you find a partial answer to a question you have, feel free to comment on the related post and I'll expand on the matter.


Thanks!


Mrs. Young

What is Cosine, tangent and adjacent all for? (05/15/10 by Alton)

Hi, Alton.

Sine, cosine, and tangent are the basic trigonomic functions. They describe the relationship between the sides of a right triangle and its angles. As you know, if you know any two sides of a right triangle, you can find the third by using the Pythagorean Theorem. That's algebra...triginometry says that if you know any one side and one of the acute angles you can find the remaining side lengths.
 Look at the diagram below:

 

If given angle 0 (theta), then:     

 sine 0 = opposite/hypoteneuse

                                          

  cosine  0= adjacent/hypoteneuse

                                          

   tangent 0 = opposite/adjacent

Once you have your equation set up, use your calculator to finish up. You're either finding the anlge measure of theta, or finding one of the side lengths.

This is the purpose of triginometry.

Hope this answers your question.

Mrs. Young

Q: How do you find the arc of an angle if the degree is 75 and the radius is 36 in.? (04/27/10 by Alton)

Hi, Alton.



I'm assuming that the central angle is 75 degrees, hence the arc measure is also 75 degrees. Given that, we can do a proportion using the circumference of the circle:



How many degrees in a circle?

If the radius is 36 in, what is the circumference?



So,



75 degrees/degrees in circle = x/(pi)(r)^2



Got it?



Mrs. Young

Q: I have question about the combinations home work; it says how many different combinations of 3 books can be chosen from a list of 10 recommended books? can you help me? (03/10/10 by Stephanie)

Certainly.


Remember that combinations are a collection of items where order does not matter.

So if you were given the problem:



C(9,3) which is read "nine choose 3" that means, "If you have nine items, how many different combinations, or sets of 3, can you have?". Order doesn't matter because {1,2,3} is the same thing as {3,1,2}, or {1,3,2}, etc. The formula is:

C(n,r)=(P(n,r))/(P(r,r))



You’ll remember that “P” stands for permutation.

For the given example:

C(9,3) = (P(9,3))/(P(3,3))=(9∙8∙7)/(3∙2∙1)=504/6=84



Now, for the specific problem you asked, “how many different combinations of 3 books can be chosen from a list of 10 recommended books,” what would be the question using the notation?

C(10,3)

Once you’ve got the problem written correctly, follow the steps above to complete the problem.



Thanks for your question!



Mrs. Young

Q: What is the difference between experimental and theoretical probability? (03/03/10 by Cynthia)

Hi, Cynthia. These can be a little confusing at first, but this is the concept:




Theoretical probability is the chances that something should happen-based upon the math, not reality.



Experimental probability is what the data (collected through an experiment) says would or did happen.



For example, if you have a number cube (dice) it has 6 sides, with numbers 1-6. If I ask the question, "what is the probability that I'll roll a 3?", in theory the chances of me getting a 3 is 1/6. However, let's say I actually roll the dice 6 times and get a "3" three times. My experimental probabilty would be 3/6, or 1/2, because it's based on the results of my experiment, not number theory.



Does that answer your question? Are you asking about just simple, independent events?



Let me know if this doesn't cover it, and I'll get back to you.



Thanks for your question!



Mrs. Young

Q: If it says -x does it mean 1(-x)? (03/02/10 by Axel)

Hi, Axel. Well, yes, it does mean that, but that isn't very helpful. The more useful way of looking at it is that -x = (-1)x

Usually, you are being asked to solve for x, so if you recognize that x is being multiplied by -1, you can divide both sides of the equation by it and get the value for x; which is what you want.



I hope this helped.

Q: How can you determine which variant (variable) is independent and which is dependent? (03/01/10 by Alton)

Hi, Alton. Thank you for your question:




Let's look at our problem:



An ice-cream vendor made a table showing the relationship between the daily high temperature and the number of ice-cream cones sold per day. What is the dependent quantity in this relationship?



So, if you were to make a table, what are the two quanties being compared?



The daily high temperatures and the number of ice creams sold



Now, Alton, you're a very intellegent young man. Let me ask you...which statement is true?



Does the number of ice creams sold depend on the daily high temp?



or



Does the daily high temp depend on the number of ice creams sold?



Obviously, the temperature isn't going to check in with the ice cream stand to see how high to get, right? That makes the daily high temperature independent; by default that makes the number of ice creams sold the dependent quantity. This makes sense because it is logical to believe that the hotter it gets the more ice creams the vendor would sell.



Therefore, if you let were to write an equation where I represnets the number of ice creams sold, and t represents the daily temperature, you would have a function that would be in the form:

I = at + c





Make sense?

Q: How do you read a formula? (02/08/10 by Karla)

Hi, Karla. There are many formulas, but I suspect the particular one you're asking about is that of surface area and lateral surface area of a prism or cylinder:




L = Ph; which is read, "lateral surface area equals the perimeter of the base times the height of the figure"



and



S = Ph + 2B; which is read, "surface area equals the perimeter of the base times the height of the figure plus two times the area of the base."



The formulas the perimeter and area of the base is dependent upon the type of figure that it is. A cylinder, for example, has a base that is a circle, while a rectangular prism has a base that is a rectangle, etc.



I hope this helps.



Mrs. Young

Q: How do you find the surface area of a prism? (02/05/10 by Alejandro)

Hi, Alejandro. Sorry I didn't get your request until tonight (the email correction was after 9). The formula for total surface area of any prism or cylinder is




SA= Ph+2B, that is "perimeter of the base, times the height of the prism, plus two times the area of the base".



So, let's say you have a triangular prism whose base has sides that are 3 inches with an altitude of 3.5 inches. The prism has a height of 5 inches. The perimeter of the base is 9 inches because you find the perimeter of a triangle by adding all the sides. The area of base is (1/2) x 3 x 3.5 which gives us an area of 5.25 inches. Now we are ready to substitute into our formula:



SA = 9(5)+2(5.25)



Now, we simplify our equation:



SA = 45 + 10.5

SA = 55. 5



This means that our surface area is 55.5 square inches.





I hope this helps. If you are still confused write me back. I will do a video and send you the link!



Mrs. Young



P.S. Don't forget: b mean the length of a side(the base of a polygon); B means the area of a surface (the base of the prism). Don't get them confused.

Q: How do you find the volume of a pyramid? (02/02/10 by Alex)

Hi, Alex.




You don't need to me to answer this. If you look at your formula chart, you'll see it there. The formula is:



V= (1/3)Bh



Volume = one third the area of the base times the height of the pyramid.



Does that answer your question? Or are needing an example as how to solve the problem?