Indices with variables

Number 4: Working with Indices

Give me two questions with surds and one question with indices and one linear equation including one fraction

Problem solving with the laws of indices

Advanced problem solving with the laws of indices

Create 50 item mathematical problems about describing patterns involving indices and recurring decimals, identifying commonalities between operations with algebra and arithmetic, connecting rules for linear relations with their graphs, explaining the purpose of statistical measures and explaining measurements of perimeter and area.

Il était une fois un garçon nommé Maxime. Maxime avait 15 ans et il vivait dans une petite ville française. Il aimait passer son temps à jouer aux jeux vidéo et à regarder des films d'action. Un jour, Maxime découvrit un mystérieux coffret dans le grenier de sa maison. Il l'ouvrit avec curiosité et à l'intérieur se trouvait une vieille carte au trésor. Maxime était excité et décida de partir à l'aventure pour trouver ce trésor caché. Il rassembla ses amis, Camille et Lucas, et ensemble, ils suivirent les indices sur la carte. Ils traversèrent des forêts sombres, escaladèrent des montagnes escarpées et naviguèrent sur un lac profond. La quête était difficile, mais ils ne se découragèrent pas. Finalement, ils arrivèrent à l'endroit indiqué sur la carte. Ils creusèrent profondément et découvrirent un coffre rempli de pièces d'or et de bijoux étincelants. Ils étaient émerveillés par leur découverte. Maxime partagea le trésor avec ses amis. Ils décidèrent d'utiliser l'argent pour réaliser leurs rêves. Maxime acheta une nouvelle console de jeux, Camille réalisa un voyage qu'elle avait toujours voulu faire, et Lucas décida d'investir dans une caméra pour poursuivre sa passion pour la photographie. C'était une aventure incroyable pour ces trois amis. Ils réalisèrent qu'il était important de travailler en équipe, de rester courageux et de poursuivre ses rêves. Ils gardèrent précieusement les souvenirs de cette aventure pour toujours. Can you make 5 easy multiple option reading and comprehension questions with answers they can find literally in the text?

Contact with the Americas In 1001, Viking sailors led by Leif Erikson reached the eastern tip of North America. Archaeologists have found evidence of the Viking settlement of Vinland in present-day Newfoundland, Canada. The Vikings did not stay in Vinland long and no one is sure why they left. However, Viking stories describe fierce battles with Skraelings, the Viking name for the Inuit. Evidence suggests that Asians continued to cross the Bering Sea into North America after the last ice age ended. Some scholars believe that ancient seafarers from Polynesia may have traveled to the Americas using their knowledge of the stars and winds. Modern Polynesians have sailed canoes thousands of miles in this way. Still others think that fishing boats from China and Japan blew off course and landed on the western coast of North or South America. Perhaps such voyages occurred. If so, they were long forgotten. Before 1492, the peoples of Asia and Europe had no knowledge of the Americas and their remarkable civilizations. The Voyages of Columbus Portuguese sailors had pioneered new routes around Africa toward Asia in the late 1400s. Spain, too, wanted a share of the riches. King Ferdinand and Queen Isabella hoped to keep their rival, Portugal, from controlling trade with India, China, and Japan. They agreed to finance a voyage of exploration by Christopher Columbus. Columbus, an Italian sea captain, planned to reach the East Indies by sailing west across the Atlantic. Finding a sea route straight to Asia would give the Spanish direct access to the silks, spices, and precious metals of Asia. The spice trade was a major cause for European exploration and a reason the Spanish rulers supported Columbus’s voyage. They also wanted wealth from any source. “Get gold,” King Ferdinand said to Columbus. “Humanely if possible, but at all hazards—get gold.” Crossing the Atlantic In August 1492, Columbus set out with three ships and about 90 sailors. As captain, he commanded the largest vessel, the Santa María. The other ships were the Niña and the Pinta. After a brief stop at the Canary Islands, the little fleet continued west into unknown seas. Fair winds sped them along, but a month passed without the sight of land. Some sailors began to grumble. They had never been away from land for so long and feared being lost at sea. Still, Columbus sailed on. On October 7, sailors saw flocks of birds flying southwest. Columbus changed course to follow the birds. A few days later, crew members spotted tree branches and flowers floating in the water. At 2 a.m. on October 12, the lookout on the Pinta spotted white cliffs shining in the moonlight. “Tierra! Tierra!” he shouted. “Land! Land!” At dawn, Columbus rowed ashore and planted the banner of Spain. He was convinced that he had reached the East Indies in Asia. He called the people he found there “Indians.” In fact, he had reached islands off the coasts of North America and South America in the Caribbean Sea. These islands later became known as the West Indies. For three months, Columbus explored the West Indies. To his delight, he found signs of gold on the islands. Eager to report his success, he returned to Spain. Columbus Claims Lands for Spain In Spain, Columbus presented Queen Isabella and King Ferdinand with gifts of pink pearls and brilliantly colored parrots. Columbus brought with him many things that Europeans had never seen before: tobacco, pineapples, and hammocks used for sleeping. Columbus also described the “Indians” he had met, the Taino (ty noh). The Taino, he promised, could easily be converted to Christianity and could also be used as slaves. The Spanish monarchs were impressed. They gave Columbus the title Admiral of the Ocean Sea. They also agreed to finance future voyages. The promise of great wealth, and the chance to spread Christianity, gave them a reason to explore further. Columbus made three more voyages across the Atlantic. In 1493, he founded the first Spanish colony in the Americas, Santo Domingo, on an island he called Hispaniola (present-day Haiti and the Dominican Republic). A colony is an area settled and ruled by the government of a distant land. Columbus also explored present-day Cuba and Jamaica. He sailed along the coasts of Central America and northern South America. He claimed all of these lands for Queen Isabella of Spain. Columbus proved to be a better explorer than governor. During his third expedition, settlers on Hispaniola complained of his harsh rule. Queen Isabella appointed an investigator, who sent Columbus back to Spain in chains. In the end, the queen pardoned Columbus, but he never regained the honors he had won earlier. He died in 1506, still convinced that he had reached Asia. The Impact of Columbus’s Voyages Columbus has long been honored as the bold sea captain who “discovered America.” Today, we recognize that American Indians had discovered and settled these lands long before 1492. We also recognize that Columbus and the Europeans who followed him treated the ancient inhabitants of the Americas brutally. Still, Columbus’s voyages did change history. They marked the beginning of lasting contact among the peoples of Europe, Africa, and the Americas. For a great many American Indians, contact had tragic results. Columbus and those who followed were convinced that European culture was superior to that of the Indians. The Spanish claimed Taino lands and forced the Taino to work in gold mines, on ranches, or in Spanish households. Many Taino died from harsh conditions or European diseases. The Taino population was wiped out. Still, the voyages of Columbus signaled a turning point for the Americas. A turning point is a moment in history that marks a decisive change. Curious Europeans saw the new lands as a place where they could settle, trade, and grow rich. Spanish Exploration Continues After the voyages of Columbus, the Spanish explored and settled other Caribbean islands that Columbus had found. They sought gold, land for crops, people to enslave, and converts to Christianity for the Spanish crown. By 1511, they had conquered Puerto Rico, Jamaica, and Cuba. They also explored the eastern coasts of North America and South America in search of a western route to Asia. In 1513, Vasco Núñez de Balboa (bal boh uh) crossed the Isthmus of Panama. American Indians had told him that a large body of water lay to the west. With a party of Spanish soldiers and Indians, Balboa reached the Pacific Ocean and claimed the ocean for Spain. The Spanish had no idea how wide the Pacific was until a sea captain named Ferdinand Magellan (muh jel un) sailed across it. The expedition—made up of five ships and about 250 crew members—left Spain in 1519. Fifteen months later, it cut through the stormy southern tip of South America by way of what is now known as the Strait of Magellan and entered the Pacific Ocean. Crossing the vast Pacific, the sailors ran out of food: Primary Source “We remained 3 months and 20 days without taking in provisions or other refreshments and ate only old biscuit reduced to powder, full of grubs and stinking from the dirt which rats had made on it. We drank water that was yellow and stinking.” —Antonio Pigafetta, The Diary of Antonio Pigafetta Magellan himself was killed in a battle with the local people of the Philippine Islands off the coast of Asia. In 1522, only one ship and 18 sailors returned to Spain. They were the first people to circumnavigate, or sail completely around, the world. In doing so, they had found an all-water western route to Asia. Europeans became aware of the true size of the Earth. How Did the Columbian Exchange Affect the Rest of the World? The encounter between the peoples of the Eastern and Western Hemispheres sparked a global exchange of goods and ideas. Because it started with the voyages of Columbus, this transfer is known as the Columbian Exchange. The Columbian Exchange refers to a biological and cultural exchange of animals, plants, human populations, diseases, food, government, technology, the arts, and languages. The exchange went in both directions. Europeans learned much from American Indians. At the same time, Europeans contributed in many ways to the culture of the Americas. This exchange also brought about many modifications, or changes, to the physical environment of the Americas, with both positive and negative results. Changing Environments Europeans introduced domestic animals such as chickens from Europe and Africa. European pigs, cattle, and horses often escaped into the wild and multiplied rapidly. Forests and grasslands were converted to pastures. As horses spread through what would become the United States, Indians learned to ride them and used them to carry heavy loads. Plants from Europe and Africa changed the way American Indians lived. The first bananas came from the Canary Islands. By 1520, one Spaniard reported that banana trees had spread “so greatly that it is marvelous to see the great abundance of them.” Oranges, lemons, and figs were also new to the Americas. In North America, explorers also brought such plants as bluegrass, the daisy, and the dandelion. These plants spread quickly in American soil and modified American grasslands. Tragically, Europeans also brought new diseases, such as smallpox and influenza. American Indians had no resistance to these diseases. Historians estimate that within 75 years, diseases from Europe had killed almost 90 percent of the people in the Caribbean Islands and in Mexico. American Indian Influences on Europe, Africa and Asia American Indians introduced Europeans to valuable food crops such as corn, potatoes, sweet potatoes, beans, tomatoes, manioc, squash, peanuts, pineapples, and blueberries. Today, almost half the world’s food crops come from plants that were first grown in the Americas. Europeans carried the new foods with them as they sailed around the world. Everywhere, people’s diets changed and populations increased. In South Asia, people used American hot peppers and chilies to spice stews. Chinese peasants began growing corn and sweet potatoes. Italians made sauces from tomatoes. People in West Africa grew manioc and corn. European settlers often adopted American Indian skills. In the North, Indians showed Europeans how to use snowshoes and trap beavers and other fur-bearing animals. European explorers learned how to paddle Indian canoes. Some leaders studied American Indian political structures. In the 1700s, Benjamin Franklin admired the Iroquois League and urged American colonists to unite in a similar way. Positive and Negative Consequences Through the Columbian Exchange, Europeans and American Indians modified their environments and gained new resources and skills. At the same time, warfare and disease killed many on both sides. Europeans viewed expansion positively. They gained great wealth, explored trade routes, and spread Christianity. Yet their farming, mining, and diseases took a toll on the physical environment and left many American Indians dead. Despite these negatives, the Columbian Exchange shaped the modern world, including what would become the United States.

Chapter 22 Antihypertensive Drugs Hypertension Defined (JNC-8) Pharmacology Overview 7 main categories of drugs to treat HTN Adrenergic drugs (old friend) Angiotensin-converting enzyme (ACE) inhibitors Angiotensin II receptor blockers (ARBs) Calcium channel blockers (CCBs) Diuretics Vasodilators Direct renin inhibitors A. Adrenergic Drugs: 5 Subcategories and where they act A1. Adrenergic neuron blockers (central and peripheral)- we won’t talk about this A2. Alpha1 receptor blockers (peripheral) A3. Alpha2 receptor agonists (central) A4. Beta receptor blockers (peripheral) A5. Combined α and β receptor blockers (peripheral) A2. Peripherally Acting Adrenergic DrugAlpha1 Blockers (we’ve met these) Doxazosin, prazosin, alfuzosin Block alpha1-receptors which causes BP to decrease Reduces peripheral vascular resistance and BP by dilating both arterial and venous blood vessels Main Use: benign prostatic hyperplasia (BPH) Alpha1 Blockers REMEMBER Tamsulosin (Flomax)* is an α1 blocker BUT *Tamsulosin is not used to control BP, just for BPH. A3. Centrally Acting Adrenergic DrugsAlpha 2 agonist Clonidine and methyldopa 1- Stimulate alpha2-adrenergic receptors. in the brain Decreases sympathetic outflow from the CNS which decreases NE production 2. Stimulate alpha2-adrenergic receptors in kidneys remember alpha 2 opposes alpha 1 Dilates peripheral blood vessels → lowers peripheral resistance → Results in decreased BP So ….Clonidine (Catapres) Used primarily for its ability to decrease blood pressure in an urgent setting Also use in opioid withdrawal as previously discussed Oral (multiple times a day), and topical patch formulations Do not stop abruptly as it may lead to rebound hypertension In reality, Clonidine and methyldopa Not prescribed as first-line home antiHTN drugs High incidence of unwanted adverse effects: orthostatic hypotension, fatigue, and dizziness MIGHT be uses as adjunct drugs after other drugs have failed, in conjunction with other antiHTN such as diuretics A4. Adrenergic Drugs Selective Beta 1 Blockers Metoprolol, Atenolol Reduction of HR through β1 receptor blockade (remember adrenergic blocking of this receptor???) HR results in BP Cause reduced secretion of renin = BP A4. Adrenergic Drugs Selective Beta1 Blockers Nebivolol (Bystolic) Uses: hypertension and HF Action: blocks β1 receptors and produces vasodilatation, which results in a decrease in SVR High doses loses selectivity and blocks both β1 and β2 Less sexual dysfunction All BB- Do not stop abruptly; must be tapered over 1 to 2 weeks A4. Adrenergic Drugs NONSelective Beta Blockers Propranolol Acts equally on β1 and β2 Other uses include situational anxiety associated with public speaking, test taking As mentioned on previous slide, nebivolol at high doses becomes beta nonselective A5. Dual-Action Adrenergic Drugs α1 and β Receptor Blockers Dual antihypertensive effects of reduction in heart rate (beta1 receptor blockade) and vasodilation (alpha1 receptor blockade) Examples are carvedilol (common) and labetalol (not as common) A5. Dual-Action Adrenergic Drugs α1 and β Receptor Blockers Carvedilol (Coreg) Widely used drug that is well tolerated Uses: HTN, mild to moderate HF in conjunction with digoxin, diuretics, and ACE inhibitors Contraindications: severe bradycardia or unstable HF, bronchospastic conditions such as asthma, and various cardiac conduction problems Adrenergic Drugs Indications - HTN But also for Glaucoma (topical) BPH: doxazosin, prazosin, and terazosin (2 for 1) Management of severe HF when used with cardiac glycosides and diuretics Contraindications Acute HF- have to stabilize first MOAIs- yeah doesn’t everything interact with MAOIs? Peptic ulcers Severe liver/kidney disease Asthma (with beta blockers) Adrenergic Drugs: Adverse Effects Orthostatic hypotension 1st-dose syncope Rebound hypertension with abrupt discontinuation Most common: Dry mouth, drowsiness, constipation, sedation Interactions- always check for specific drug interactions Can cause additive CNS depression with alcohol, benzodiazepines, opioids Question #1 When administering an alpha-adrenergic drug for hypertension, it is most important for the nurse to assess the patient for the development of what response? Hypotension Hyperkalemia Oliguria Respiratory distress Answer A Hypotension This is a key point in patient education These drugs have strong vasodilating properties and may cause severe hypotension, especially at the beginning of therapy. B. Angiotensin-Converting Enzyme Inhibitorsaka ACE Inhibitors or ACEi Large group of safe and effective drugs Currently are 10 ACEi Often used as first-line drugs for HF and hypertension May be combined with a thiazide diuretic, loop diuretic, or Calcium Channel Blocker (CCB) You need to understand the basics ACE Inhibitors: Review RAAS ACE converts angiotensin I, formed through the action of renin, to angiotensin II Angiotensin 2 is a potent vasoconstrictor and also induces aldosterone secretion by the adrenal glands Aldosterone stimulates sodium resorption (H20 follows Na Both act to raise BP which causes kidneys to reduce renin production ACEi= Great drug to treat HTN BUT contraindicated in pregnancy (2nd,3rd trimester due to fetal renal damage) and breastfeeding first few weeks after birth B. ACE Inhibitors - PRIL Lisinopril (Prinivil) super common, often the 1st drug Enalapril (Vasotec) also common Captopril (Capoten) great if liver disease present Benazepril (Lotensin) Fosinopril (Monopril) Perindopril (Aceon) Quinapril (Accupril) Ramipril (Altace) Trandolapril (Mavik) Primary Effects of the ACE Inhibitors Prevent Na (and H2O) resorption by inhibiting aldosterone secretion (volume reduction) (GO BACK TO RAAS DIAGRAM) blood volume decreases work of the heart preload, or the left ventricular end-diastolic volume which is important in HF ACE SUMMARY OF ACTIVITY 1) Prevent vasoconstriction caused by angiotensin 2 (2) Prevent aldosterone secretion  less sodium and water resorption Cardioprotective Effects of ACEi They slow progression of left ventricular hypertrophy (ventricular remodeling) after MI so considered cardioprotective ACE inhibitors have been shown to decrease morbidity and mortality in patients with HF Renal Protective Effects of ACEi ACE inhibitors: reduce glomerular filtration pressure by volume reduction Cardiovascular drug of choice for patients with diabetes since it helps protect kidneys by reducing pressure. Sometimes used low dose for kidney protection with DM without HTN B. ACEi Enalapril (Vasotec) Only ACEi available in both oral and IV Enalapril IV does not require cardiac monitoring Oral enalapril: prodrug (metabolized in liver) Improves patient’s chances of survival after an MI Reduces the incidence of HF B. ACEi Captopril (Capoten) Uses: prevention of ventricular remodeling after MI; reduce the risk of HF after MI Shortest half-life Must be administered multiple times throughout the day so this limits its use Not a prodrug so good for patient with liver disease Question #2 A patient with diabetes has a new prescription for the ACE inhibitor lisinopril. She questions this order because her provider has never told her that she has hypertension. What is the best explanation for this order? The doctor knows best The patient is confused This medication has cardioprotective properties This medication has a protective effect on the kidneys for patients with diabetes Answer D ACE inhibitors have been shown to have a protective effect on the kidneys because they reduce glomerular filtration pressure. This property makes them the cardiovascular drug of choice for patients with diabetes. Question #3 A patient with a history of pancreatitis and cirrhosis is also being treated for hypertension. Which drug will most likely be ordered for this patient? Clonidine Prazosin Diltiazem Captopril Answer D Captopril Captopril is not a prodrug; therefore, it does not need to be metabolized by the liver to be effective. This is an advantage in patients with liver disease. ACE Inhibitors: Adverse Effects *Dry, nonproductive cough, which reverses when therapy is stopped. This is a class effect Dizziness- Note: First-dose hypotensive effect may occur Headache & Fatigue Possible hyperkalemia ** Angioedema: rare but potentially fatal Not safe in pregnancy-are contraindicated during the second and third trimesters of pregnancy because of increased risk of fetal renal damage C. Angiotensin II Receptor Blockers(ARB) Considered an alternative to ACEi Less likely to cause a dry cough and hyper K+ that is common with ACE inhibitors Angiotensin II Receptor Blockers: Mechanism of Action Go back to RAAS diagram! ARBs affect primarily 2 places 1. Vascular smooth muscle - blocks vasoconstriction 2. Adrenal gland -Selectively blocks the binding of Ang 2 to certain Ang 2 receptors inhibiting secretion of aldosterone Lowers volume retention and BP Angiotensin II Receptor Blockers -ARTAN Losartan (Cozaar)- very common Eprosartan (Teveten) Valsartan (Diovan) Irbesartan (Avapro) Candesartan (Atacand) Olmesartan (Benicar) Telmisartan (Micardis) Azilsartan (Edarbi) C. ARB Losartan (Cozaar) Beneficial in patients with HTN and HF Used with caution in patients with kidney or liver dysfunction and in patients with renal artery stenosis ***Not safe for breastfeeding women and should not be used in pregnancy (Cat C 1st trimester, Cat D 2nd-3rd trimester), potential fetal toxicity Appear to be equally effective for the treatment of hypertension and well tolerated ARBs less likely to cause cough and hyperK+ but can still happen Evidence that ARBs are associated with lower mortality after MI than ACE inhibitors Never take ACEi and ARBs at the same time* 5. Calcium Channel Blockers (CCB) Primary use: HTN, angina, some dysrhythmias Cause smooth muscle relaxation by blocking the binding of calcium to its receptors, preventing muscle contraction Results in: Relaxed blood vessels to the heart Decreased peripheral smooth muscle tone Decreased SVResistance Decreased BP E. Diuretics First-line antiHTN in JNC 8 guidelines Decreases fluid volume The results from diuresis: preload, Peripheral resistance Overall effect  Decreased workload of the heart and decreased BP Thiazide diuretics are the most commonly used diuretics for HTN Ie hydrochlorothiazide (HCTZ), chlorthalidone We will discuss diuretics further in the chapter on diuretics F. Vasodilators Directly relax arterial or venous smooth muscle (or both) Results in: Decreased SVR Decreased afterload Peripheral vasodilation Indicated for treatment of HTN May be used in combination with other drugs F. Vasodilators Hydralazine (Apresoline) Orally: routine cases of essential hypertension Injectable: hypertensive emergencies BiDil: specifically indicated as an adjunct for treatment of HF in African-American patients F. Vasodilators Sodium Nitroprusside (Nitropress) *Sodium nitroprusside and IV diazoxide are reserved for the management of hypertensive emergencies. Contraindications: severe HF, known inadequate cerebral perfusion (especially during neurosurgical procedures) F. Vasodilators Adverse Effects Hydralazine: dizziness, headache, tachycardia, edema, dyspnea, N/V/D, vitamin B6 deficiency, rash Sodium nitroprusside: hypotension, bradycardia, decreased platelet aggregation, rash G. Direct Renin Inhibitors Aliskirin (Tekturna) Blocks the RAS pathway at the point of activation. Inhibiting renin production prevents the downstream production of Ang II (potent vasoconstrictor) Adverse effects: N/V, severe hypotension, hyponatremia, hyperkalemia… Contraindicated in patients with DM taking ACEi or ARB Miscellaneous Antihypertensives Eplerenone (Inspra) Newer class of drugs called selective aldosterone blockers (remember RAAS?) Reduces BP by blocking the actions of aldosterone at its corresponding receptors in the kidney, heart, blood vessels, and brain Indications: routine treatment of hypertension and for post-MI HF Contraindicated if serum potassium levels are high (above 5.6 mEq/L) A Special Form of HTNTreatment of Pulmonary Hypertension Sildenafil and Tadalafil Commonly used for erectile dysfunction Used for pulmonary hypertension but with different trade names Sildenafil: Revatio* (Viagra for ED) Tadalafil: Adcirca* (Cialis for ED)

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