Problem: Write an article based on this summary: Don't take it personally. Respond to the rumor quickly. Find the source of the rumor. Make it known the rumor was false. Understand that it may take time for the rumor to fade.

Answer: Some people live life in bitterness or malice, and will spread rumors because they think it will make them feel better about themselves. Others hear information incorrectly and without meaning to harm someone, will spread that information. Either way, rumors aren't usually a sign that you have done something wrong. They usually communicate that the people spreading them are struggling with insecurities or boredom, so don't take it personally.  While this can be difficult to do because some rumors can be very hurtful, just remember that people spread rumors for a reason. Most people who are kind and care about others won't spread malicious rumors to harm someone. Those who spread rumors usually do so because they feel jealousy or envy towards you, or they are upset with their current state in life and want to add some drama to it to make it more interesting. Stay above these rumors and don't encourage them by taking them personally and getting really upset. Some people spread rumors just to get a rise out of someone else. When rumors start to spread about you, act like nothing has happened and that you aren't affected by these lies. This can also help show people that the rumor isn't true, because you think it's so ridiculous that you don't even see a need to be upset about it. When a rumor is told about you, the best thing to do is respond to the rumor quickly. If you allow the rumor to fester and continue to be spread it may become worse or more exaggerated. Talk to the people who you have heard spread the rumor and explain to them that it is false, or go to an authority and let them know that the rumor isn't true.   Some people choose to ignore rumors instead of responding to them. This can be a good option, depending on the extent of the rumor. If the rumor is something so outlandish that very few people actually believe it, it could be good to just ignore it and over time people will stop talking. However, if the rumor is believable or is something that could get you into trouble, you need to address it quickly. You don't want to end up in a position where you are at fault because others have spread lies about you. For example, if there is a rumor going around your workplace that you haven't been working efficiently or are doing something against company policy, you should address that rumor quickly. If not, you may be in great trouble with your boss. You want to denounce a rumor by addressing it before you are confronted and asked if it is true. It's easier for someone to believe you when you come to them first. When you hear about a rumor, sometimes it's best to go to the source of the rumor to understand why it was spread. This can help you from being hurt and can also prevent you from judging someone incorrectly. As people are spreading the rumor ask them who they heard it from, and hopefully you will be able to find the source of the rumor.  Once you have found the source or creator of the rumor, ask them why they spread it and where they got their information. If it was a friend, you might ask them if you did something that upset them that caused them to spread the rumor. You should also figure out if the rumor was spread in malice or because information was communicated incorrectly. Although neither are good things, someone may have spread a rumor, not knowing it was a rumor. In this case, the person wasn't doing it out of malice, so you don't want to create unnecessary drama. If you find out someone did do the rumor out of malice, ask them why they started it. As stated earlier, people often start rumors because they are insecure about themselves. In this situation try to understand the person and practice giving them grace and forgiving them. Although this can be hard, the best way to love someone and help change them is by showing them grace when they don't deserve it. If you react kindly to this person, they may feel guilt or shame for spreading the rumor and then it may be easier to convince them to tell people the real truth. The best way to denounce a rumor is by proving to people that it can't possibly be true. You can do this by explaining to people what is actually true, or you can show it to them by your actions. If the rumor involves you and someone else, ask that other person to help you prove that the rumor is false. Sometimes it can be helpful to have a third party refute the rumor.  If someone spread a rumor that you were cheating on your significant other, then be more faithful to them. Don't flirt with other people and spend more time with your significant other so that people begin to question the truth of the rumor. If someone spread a rumor at your work about your laziness or that you were going against company policy, then try your best to show people you are a hard worker and that you are totally in line with company policy. Make it so hard for people to believe that the rumor is true. While this step isn't always fun or enjoyable, because you may feel like you are having to prove yourself when you shouldn't be, it can be effective. Telling people a rumor isn't true may work, but when you show it to them, they have undeniable evidence and proof. Unfortunately, even if you have addressed the rumor, not all rumors fade quickly or immediately. Some people will believe you or will become uninterested while others may take some sort of twisted joy in hurting your reputation and will continue to discuss the rumor or the events surrounding it. Don't let these things bother you, but keep your head held high. Once you have addressed the rumor, there is not much you can do except to continue living life as you were. It may take time and patience, but eventually people will have moved onto another source of gossip.ignore the person who started it.


Problem: Write an article based on this summary: Construct a rough sketch of the original vector. Sketch and label the component vectors. Use the sine function to calculate the vertical component. Use the cosine function to calculate the horizontal component.

Answer:
By relying on mathematical calculations, your graph does not need to be as neatly drawn. You do not need to determine any measurement scale. Just sketch a ray in the general direction of your vector. Label your sketched vector with its magnitude and the angle that it makes from the horizontal.  For example, consider a rocket that's being fired upwards at a 60-degree angle, at a velocity of 1,500 meters (5,000 ft) per second. You would sketch a ray that points diagonally upward. Label its length “1500 m/s” and label its base angle “60°.” The diagram shown above indicates a force vector of 5 Newtons at an angle of 37 degrees from the horizontal. Sketch a horizontal ray beginning at the base of your original vector, pointing in the same direction (left or right) as the original. This represents the horizontal component of the original vector. Sketch a vertical ray that connects the head of your horizontal vector to the head of your original angled vector. This represents the vertical component of the original vector. A vector's horizontal and vertical components represent a theoretical, mathematical way of breaking a force into 2 parts. Imagine the child's toy Etch-a-Sketch, with the separate "Vertical" and "Horizontal" drawing knobs. If you drew a line using only the "Vertical" knob and then followed with a line using only the "Horizontal" knob, you would end at the same spot as if you had turned both knobs together at exactly the same speeds. This illustrates how a horizontal and vertical force can act simultaneously on an object. Because the components of a vector create a right triangle, you can use trigonometric calculations to get precise measurements of the components. Use the equation:  sin⁡θ=verticalhypotenuse{\displaystyle \sin \theta ={\frac {\text{vertical}}{\text{hypotenuse}}}} For the missile example, you can calculate the vertical component by substituting the values that you know, and then simplifying, as follows:  sin⁡θ=verticalhypotenuse{\displaystyle \sin \theta ={\frac {\text{vertical}}{\text{hypotenuse}}}} sin⁡(60)=vertical1500{\displaystyle \sin(60)={\frac {\text{vertical}}{1500}}} 1500sin⁡(60)=vertical{\displaystyle 1500\sin(60)={\text{vertical}}} 1500∗0.866=vertical{\displaystyle 1500*0.866={\text{vertical}}} 1,299{\displaystyle 1,299}   Label your result with the appropriate units. In this case, the vertical component represents an upward speed of 1,299 meters (4,000 ft) per second. The diagram above shows an alternate example, calculating the components of a force of 5 Newtons at a 37 degree angle. Using the sine function, the vertical force is calculated to be 3 Newtons. In the same way that you use sine to calculate the vertical component, you can use cosine to find the magnitude of the horizontal component. Use the equation:  cos⁡θ=horizontalhypotenuse{\displaystyle \cos \theta ={\frac {\text{horizontal}}{\text{hypotenuse}}}} Use the details from the missile example to find its horizontal component as follows:  cos⁡θ=horizontalhypotenuse{\displaystyle \cos \theta ={\frac {\text{horizontal}}{\text{hypotenuse}}}} cos⁡(60)=horizontal1500{\displaystyle \cos(60)={\frac {\text{horizontal}}{1500}}} 1500cos⁡(60)=horizontal{\displaystyle 1500\cos(60)={\text{horizontal}}} 1500∗0.5=horizontal{\displaystyle 1500*0.5={\text{horizontal}}} 750{\displaystyle 750}   Label your result with the appropriate units. In this case, the horizontal component represents a forward (or left, right, backward) speed of 750 meters (2,000 ft) per second. The diagram above shows an alternate example, calculating the components of a force of 5 Newtons at a 37 degree angle. Using the cosine function, the horizontal force is calculated to be 4 Newtons.