Using the Δy/Δx idea, we choose two points on our non-linear graph of some function. For a straight line, the slope is the exact rate of change. 36. b Anticipated drawdown and decline in the water levels c Stratification of the. 3-2 rate of change and slope answer key. What Does a Slope Represent? If y is directly proportional to x and y = 24 when x = 4, the proportion equation is. The formula for the rate of change using a graph is given by; m=((y2 - y1))/((x2 - x1)).
How much thread did she use? If the constant of proportionality for a given directly. The student applies mathematical process standards to explain proportional and non-proportional relationships involving slope. The rate of change is 30/3, or 10/1, the same rate of change as in the first example. Introduction to average rate of change (video. In time, you will learn how to calculate the instantaneous rate of change of a curvy graph of some function - that is, the exact slope (via a tangent line) at a point on the graph. Linear Rate of Change. On a graph it represents a measure of the change in the vertical distance between a series of measurements taken along the same line. Can anyone give me an explanation of what that is and how it can be used to find average rate of change. Document Information. X=3, for our example is. Quiz 3 - Karen has 12 dolls.
It is also not a function, as there are multiple values of y for one value of x. Slope Formula. He was making ice tea at the rate of 4 liters of ice tea in 3 hours. F(x)=x², the derivative of. The slope is the rate of change from one month to the next. This example is notable because typically Frankish commanders have been. What Does the Slope of a Graph Tell Us? To learn more about how we help parents and students in Grand Forks, ND: visit: Tutoring in Grand Forks, ND. Practice 3 - Rex owns a strawberry farm. Math Review of Rate of Change and Slope | Free Homework Help. The x-intercept is -3.
We offer tutoring programs for students in K-12, AP classes, and college. What relationship does a tangent line in graphs have with the tangent of a circle? Well, the slope of our secant line is going to be our change in distance divided by our change in time, which is going to be equal to, well, our change in time is one second, one, I'll put the units here, one second and what is our change in distance? Milky Problem Step-by-step Lesson- See if you can make sense of how Andrew drinks milk. Linda's average annual rate of change if $9, 182 dollars per year. As I mentioned, we will build the tools to later think about instantaneous rate of change, but what we can start to think about is an average rate of change, average rate of change, and the way that we think about our average rate of change is we use the same tools, that we first learned in algebra, we think about slopes of secant lines, what is a secant line? The steep slope is associated with more radical changes in language, and the gradual slope is associated with more progressive changes. Rate of change and slope answer key template. Please Note: This review follows the outline of unit 9. test VERY closely. Reward Your Curiosity. The amount of the paycheck depends on the number of hours worked, so that worker is paid $160. Graphs are a visual representation of information, typically used to show relationships between different data sets. Does it lack imagination? The slope becomes steeper and the y-intercept. So, if you have a graph about weight loss with weight plotted on the y axis, the slope will tell you how fast the weight changes over time.
She uses an additional 2 kg of potatoes for each person that will be eating chips. The line gets steeper as the slope increases. We can't count the rise over the run like we did in the calculating slope lesson because our units on the x and y axis are not the same. 00 for 8 hours the next week. As we have seen, this value of a graph remains the same along the line.
We can now use the slope formula to find the slope of the line. P is always constant. Moreover, we can even use a graph to find the distance between two points. By taking just two points, we lost all the information about what happened between those points. Shane's insulation company charges an initial fee of $25, plus $1. Rate of change and slope answer key class 10. 0% found this document not useful, Mark this document as not useful. But since infinity is hard to do, let's just use a "large" number instead. Her mascara were $2. The total amount owed. Which function best describes the graph shown below? Therefore, we must find two ordered pairs within the context of this problem.
But that's actually what we do we turn the curve ( not the whole curve we part the curve which its points near each other and easy to be turned to a straight line) to a straight line then take the slope by two points on it. After 2 hours, she had 12 fresh flowers. For this problem, we don't have a graph to refer to in order to identify the two ordered pairs. Fbetween the two values we selected. 576648e32a3d8b82ca71961b7a986505. If the amount of your pay check, p, is directly. We must pay close attention to the graph in order to solve the problem. 1-3 Skills_Practice_Rate_of_Change_and_Slope Ans key.pdf - NAME _ DATE _ PERIOD _ 1-3 Skills Practice Rate of Change and Slope Find the slope of the | Course Hero. That being said, a close approximation may provide a good enough answer for your work.
At3:02, Sal talks about slope-intercept form. Proportional to the number of hours you. Y = t^2+1 which is the same as y = t * t + 1. t = m = slope of the line at time = t? The y variables are the dependent variables and the x variables are the independent variables. Represent the cost of car if it was driven 80 miles with an equation. Homework 3 - Flora uses 10 kg of potatoes for making chips. Let's take a look at John's graph again. B is the y intercept, which is the point at which the line crosses the y axis. In fact, there is no difference, the two ways will give exactly the same answer! Teaching Methods & Materials. A gradual slope can be associated with a more gradual increase in order.
However, if the relationship is a vertical line, the slope is undefined. Step 1: Write two ordered pairs: (8, 144, 000) (In 1998, she purchased the house for $144, 000). Proportional relationship is 8, graphically the 8 is. Round your answer to the nearest dollar. If we just took 2 points (the start and the end), we might get some idea of the average but this would likely be a bad representation of the true average. Suppose a plane is landing.
Husband of Andromache. He held his round shield and his spear in front of him, resolute to kill any who should dare face him. Last of all came Agamemnon, king of men, he too wounded, for Coon son of Antenor had struck him with a spear in battle. Would he be demanding but understanding?
However valiant I may be, I cannot give chase to so many and fight all of them. Co-commander, with his brother, of the Thessalians who hail from Tricca and Oechalia. Meanwhile the fleet runner Antilochus, who had been sent as messenger, reached Achilles, and found him sitting by his tall ships and boding that which was indeed too surely true. His participation in the war was crucial to the Greeks' victory. The siege lasted for more than 10 years until the Greeks came up with a strategy to abduct Helen from the palace. His own feet never bore him back to gladden his wife and parents. THUS, then, did the Achaeans arm by their ships round you, O son of Peleus, who were hungering for battle; while the Trojans over against them armed upon the rise of the plain. Behind them fought Automedon full of sorrow for his comrade, as a vulture amid a flock of geese. Menelaus most strongly affects the epic plot through his . the two. While this image is presented during the aftermath of the Trojan war, Euripides also uses Hecuba as a representative of contemporary Hellenic women as this archetype is universal for all circumstances. He is an important counselor to Agamemnon. Often in his brother's shadow, Menelaus is still a strong warrior and at times an effective leader. Twelve filly foals did they conceive and bear him, and these, as they sped over the rich plain, would go bounding on over the ripe ears of corn and not break them; or again when they would disport themselves on the broad back of Ocean they could gallop on the crest of a breaker.
Therefore I am suppliant at your knees if haply you may be pleased to provide my son, whose end is near at hand, with helmet and shield, with goodly greaves fitted with ancle-clasps, and with a breastplate, for he lost his own when his true comrade fell at the hands of the Trojans, and he now lies stretched on earth in the bitterness of his soul. Greatest of the Trojan warriors, he is the champion of his people. Menelaus most strongly affects the epic plot through historia. Even if you're using similar ideas that you've already seen, the trick is to explain and frame your analysis in a way that answers every prompt specifically. Beloved of Athena, Odysseus is the shrewd counselor and skilled diplomat. Was it that you might share the sorrows that befall mankind? First he killed Iphition son of Otrynteus, a leader of much people whom a naiad nymph had borne to Otrynteus waster of cities, in the land of Hyde under the snowy heights of Mt.
The Trojan war occurred as a result of the conflict between Greece and Troy and was said to last for over 10 years. Including captive women in the Achaean encampment. When Achilles is dead you may then fight among the foremost undaunted, for none other of the Achaeans shall slay you. On this he struck Dryops with his spear, about the middle of his neck, and he fell headlong at his feet. While the Trojan war is the setting of many famous classical works being examined by various different angles, not many focus on the consequences suffered by women. He helps Hera to put Zeus out of the action, so that Poseidon can help the Achaeans. His own he sent to the strong city of Ilius and to the Trojans, while he put on the immortal armour of the son of Peleus, which the gods had given to Peleus, who in his age gave it to his son; but the son did not grow old in his father's armour. When Jove, lord of the storm-cloud, saw Hector standing aloof and arming himself in the armour of the son of Peleus, he wagged his head and muttered to himself saying, "A! Menelaus most strongly affects the epic plot through his - Brainly.com. Asteropaeus flew forward to avenge him and attack the Danaans, but this might no longer be, inasmuch as those about Patroclus were well covered by their shields, and held their spears in front of them, for Ajax had given them strict orders that no man was either to give ground, or to stand out before the others, but all were to hold well together about the body and fight hand to hand. Then Achilles also rose and said to the Argives, "Father Jove, of a truth you blind men's eyes and bane them.
Consequently the perfection of our nature and capability of happiness, must be estimated by the degree of reason, virtue, and knowledge, that distinguish the individual, and direct the laws which bind society: and that from the exercise of reason, knowledge and virtue naturally flow, is equally undeniable, if mankind be viewed collectively. Brother and husband of Hera. The simile comparing herself to a woman 'dragged as a slave' in her lamentation further fortifies Hecuba's portrayal as a victim of a play. Menelaus most strongly affects the epic plot through his . exe. Swift goddess messenger of Zeus. Talthybius is also governed by both his sense of duty and integrity. First he shaped the shield so great and strong, adorning it all over and binding it round with a gleaming circuit in three layers; and the baldric was made of silver. Meriones gathered them up from the ground and took them into his own hands, then he said to Idomeneus, "Lay on, till you get back to the ships, for you must see that the day is no longer ours. However, Menelaus did not believe what Helen had to say and decided to bring her back to her home on a separate ship.
For of a truth we two, I and Pallas Minerva, have sworn full many a time before all the immortals, that never would we shield Trojans from destruction, not even when all Troy is burning in the flames that the Achaeans shall kindle. To what extent do you agree with the statement? At dawn we can arm and take our stand on the walls; he will then rue it if he sallies from the ships to fight us. Meanwhile Apollo set Aeneas on to attack the son of Peleus, and put courage into his heart, speaking with the voice of Lycaon son of Priam. The contention for this one will be: the Trojan War undoubtedly has its winners and losers, and few of these characters agree on who the responsible villains are, with some blaming Helen (P1) while she herself blames the gods (P2).
Let, then, Achilles wait, though he would fain fight at once, and do you others wait also, till the gifts come from my tent and we ratify the oath with sacrifice. Nevertheless I will go, that I may see my dear son and learn what sorrow has befallen him though he is still holding aloof from battle. I have held you so far as a man of more understanding than any in all Lycia, but now I despise you for saying that I am afraid of Ajax. When he and Little Ajax are grouped together, they are called the Aeantes. So long as the gods held themselves aloof from mortal warriors the Achaeans were triumphant, for Achilles who had long refused to fight was now with them. Thus through the livelong day did they wage fierce war, and the sweat of their toil rained ever on their legs under them, and on their hands and eyes, as they fought over the squire of the fleet son of Peleus. His chastisement is further bolstered by Cassandra's rhetorical question asking 'they kept on dying, for what reason'. Since this play primarily focuses on the cost of war and how women, as innocent bystanders, have to suffer as a result of the Trojan war, it should not be difficult finding evidence related to women's suffering. Is it that you hope to reign over the Trojans in the seat of Priam? NOW when Dawn in robe of saffron was hasting from the streams of Oceanus, to bring light to mortals and immortals, Thetis reached the ships with the armour that the god had given her. Hamlet:... but tell. "My friends, " he cried, "princes and counsellors of the Argives, all you who with Agamemnon and Menelaus drink at the public cost, and give orders each to his own people as Jove vouchsafes him power and glory, the fight is so thick about me that I cannot distinguish you severally; come on, therefore, every man unbidden, and think it shame that Patroclus should become meat and morsel for Trojan hounds. Women of Troy explores the ways in which a character's true self might emerge in times of tragedy.
Resource to ask questions, find answers, and discuss the novel. These words stirred the heart of Ajax, and he made his way among the front ranks, Menelaus going with him. As he spoke he called loudly on the Trojans saying, "Trojans, Lycians, and Dardanians, fighters in close combat, be men, my friends, and fight might and main, while I put on the goodly armour of Achilles, which I took when I killed Patroclus. Paris is a strong fighter, but he has little appetite for battle. Swift of foot, Little Ajax is a great warrior in his own right. These last moreover would rest for a while and leave off fighting, for they were some distance apart and beyond the range of one another's weapons, whereas those who were in the thick of the fray suffered both from battle and darkness. The protagonist Hecuba, for example, is portrayed as the archetypal mother. The light around the body of Patroclus.
You must see with your own eyes that heaven is heaping calamity upon the Danaans, and giving victory to the Trojans. By allowing the Trojan women to express their indignation and enmity as a response to their impending slavery, Euripides is able to present a critique on the ways in which women were oppressed in Ancient Greece. But Achilles dear to Jove arose, and Minerva flung her tasselled aegis round his strong shoulders; she crowned his head with a halo of golden cloud from which she kindled a glow of gleaming fire. There is, of course, plenty of other evidence out there such as the way in which Cassandra is portrayed as a 'poor mad child', her helplessness in surrendering to her 'wretched' fate with Agamemnon who wanted her for himself. When he had thus spoken he took with him the sons of Nestor, with Meges son of Phyleus, Thoas, Meriones, Lycomedes son of Creontes, and Melanippus, and went to the tent of Agamemnon son of Atreus.