Problem: Write an article based on this summary: Refrain from responding. Set boundaries. Remain calm.

Answer: This is a common way that people express disapproval. Sometimes when people say something offensive, they’re hoping for a response. When you don’t give them what they want, they may register that they’ve offended you.  This is different than simply pretending they didn’t say something offensive. You must actively refrain from giving the response they want. If someone tells an offensive joke, refusing to laugh or smile shows that you don’t approve of their humor. If some asks you a question and uses a slur or offensive language, you can opt to not answer. Instead of simply not responding, you can respond directly to the offensive comment. Let the person know that if they want to converse with you, they’ll have to honor your boundaries. You can say, “I’m sorry, but I can’t continue this conversation if you’re going to use that language” or “I need you to use a different tone so that I can hear what you’re saying without taking offense.” This is important in order to not escalate the situation. Use a measured, casual tone when expressing your boundaries. You don’t want to come off as threatening.   Remember that you’re not telling them what they need to do; you’re telling them what your needs are in order for the conversation to continue. Even if someone has said something highly offensive, becoming visibly upset will not help the situation.


Problem: Write an article based on this summary: Differentiate the x terms as normal. Differentiate the y terms and add "(dy/dx)" next to each. Use the product rule or quotient rule for terms with x and y. Isolate (dy/dx).

Answer: When trying to differentiate a multivariable equation like x2 + y2 - 5x + 8y + 2xy2 = 19, it can be difficult to know where to start. Luckily, the first step of implicit differentiation is its easiest one. Simply differentiate the x terms and constants on both sides of the equation according to normal (explicit) differentiation rules to start off. Ignore the y terms for now. Let's try our hand at differentiating the simple example equation above. x2 + y2 - 5x  + 8y + 2xy2 = 19 has two x terms: x2 and -5x. If we want to differentiate the equation, we'll deal with these first, like this:  x2 + y2 - 5x + 8y + 2xy2 = 19 (Bring the "2" exponent in x2 down as a coefficient, remove the x in -5x, and change the 19 to 0) 2x + y2 - 5 + 8y + 2xy2 = 0 As your next step, simply differentiate the y terms the same way as you differentiated the x terms. This time, however, add "(dy/dx)" next to each the same way as you'd add a coefficient. For instance, if you differentiate y2, it becomes 2y(dy/dx). Ignore terms with both x and y for now. In our running example, our equation now looks like this: 2x + y2 - 5 + 8y + 2xy2 = 0. We would perform this next y-differentiating step as follows:  2x + y2 - 5 + 8y + 2xy2 = 0 (Bring the "2" exponent in y2 down as a coefficient, remove the y in 8y, and place a "dy/dx" next to each). 2x + 2y(dy/dx) - 5 + 8(dy/dx) + 2xy2= 0 Dealing with terms that have both x and y in them is a little tricky, but if you know the product and quotient rules for differentiating, you're in the clear. If the x and y terms are multiplied, use the product rule ((f × g)' = f' × g + g' × f), substituting the x term for f and the y term for g. On the other hand, if the x and y terms are divided by each other, use the quotient rule ((f/g)' = (g × f' - g' × f)/g2), substituting the numerator term for f and the denominator term for g.  In our example, 2x + 2y(dy/dx) - 5 + 8(dy/dx) + 2xy2 = 0, we only have one term with both x and y — 2xy2. Since the x and y are multiplied by each other, we would use the product rule to differentiate as follows:  2xy2 = (2x)(y2)— set 2x = f and y2 = g in (f × g)' = f' × g + g' × f (f × g)' = (2x)' × (y2) + (2x) × (y2)' (f × g)' = (2) × (y2) + (2x) × (2y(dy/dx)) (f × g)' = 2y2 + 4xy(dy/dx)    Adding this back into our main equation, we get 2x + 2y(dy/dx) - 5 + 8(dy/dx) + 2y2 + 4xy(dy/dx) = 0 You're almost there! Now, all you need to do is solve the equation for (dy/dx). This looks difficult, but it's usually not — keep in mind that any two terms a and b that are multiplied by (dy/dx) can be written as (a + b)(dy/dx) due to the distributive property of multiplication. This tactic can make it easy to isolate (dy/dx) — just get all the other terms on the opposite side of the parentheses, then divide them by the terms in parentheses next to (dy/dx). In our example, we might simplify 2x + 2y(dy/dx) - 5 + 8(dy/dx) + 2y2 + 4xy(dy/dx) = 0 as follows:  2x + 2y(dy/dx) - 5 + 8(dy/dx) + 2y2 + 4xy(dy/dx) = 0 (2y + 8 + 4xy)(dy/dx) + 2x - 5 + 2y2 = 0 (2y + 8 + 4xy)(dy/dx) =  -2y2 - 2x + 5 (dy/dx) = (-2y2 - 2x + 5)/(2y + 8 + 4xy) (dy/dx) = (-2y2 - 2x + 5)/(2(2xy + y + 4)


Problem: Write an article based on this summary: Spend time with your friend. Share laughs. Learn to listen.

Answer:
Hang out on the weekends or plan activities together every now and then, do some homework together, and chat during the break at school. You don't have to live in each others' pockets, but make sure you spend some quality time together with your best friend to make the friendship grow and become stronger.  Know that you'll probably have to sacrifice some of your time and maybe effort to be your best friend. It should feel like something you want to be doing, even when it's hard. Invite other people to hang out with you. Being best friends doesn't mean you have to isolate yourselves from other people. Sometimes, it's nice to be alone; you don't need anybody else to have fun together. Other times, your enjoyment is increased by including other people into the fold. There is nothing like laughing and smiling to bring people together. Besides, when they're really friends, you guys can laugh at the dumbest, smallest, weirdest stuff and it doesn't really matter. Take time out of your day to appreciate the funny things in life. Nobody likes a best friend who just talks and talks but never listens. If you're a chatterbox, try to develop good listening skills. Whenever your best friend says something, listen carefully and say something. Don't just say "yeah" and move on. Don't interrupt or fidget continually while they're talking to you. If they ask for advice, listen carefully and give them the best advice you can. It'll earn you respect and of course, make them come to you more.   Be an active listener. Being an active listener means reading in between the lines. Sometimes it means knowing what the other person feels or is thinking before they do. If you're an active listener, you might know who your friend likes before they do. Know when not to talk. There's an old saying out there: The dumb person talks; the wise person listens. While that's definitely an overstatement, it has some truth in it. Begin to feel comfortable just being with your bestie, not constantly having to talk to fill the silence.