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Topic 5 / Section 1: Practice Problems

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Page 1 of 6 Topic 5 / Section 1: Practice Problems Temperature is measured in the US in degrees Fahrenheit, while the temperature in man other places is measured in degrees Celsius. The relationship between
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Page 1 of 6 Topic 5 / Section 1: Practice Problems Temperature is measured in the US in degrees Fahrenheit, while the temperature in man other places is measured in degrees Celsius. The relationship between these units is linear, as epressed in the equation below, where is temperature in Fahrenheit and is the temperature in Celsius. 9 = Recall that is Fahrenheit and is Celsius, and that the slope m = using the words Fahrenheit and Celsius instead of and. m =. Rewrite this epression 3. We can interpret the slope above b saing that increasing degrees Celsius means we increase degrees Fahrenheit. 4. What is the intercept of this line? 5. Freezing is measured as degrees Celsius. Find freezing in Fahrenheit b plugging ( = ) into the equation above. Write our answer as an ordered pair (, ). 6. Boiling is measured as 1 degrees Celsius. Find boiling in Fahrenheit b plugging ( = 1 ) into the equation above. Write our answer as an ordered pair (, ). 7. Graph the line. - Fill in the table with the points ou found above and at least 2 other points. - Fill in our labels for and as Celsius and Fahrenheit Page 2 of 6 One cubic inch of water weighs approimatel pounds (or 1 gram). The relationship between these units is linear, as epressed in the equation below, where is weight in pounds and is the size of the water in of cubic inches. = Recall that is weight and is size, and that the slope m = the words Size and Weight instead of and. m =. Rewrite this epression using 3. We can interpret the slope above b saing that increasing cubic inch means we increase pounds. 4. What is the intercept of this line? 5. Describe what the intercept is telling ou about the weight of water measuring cubic inches 6. Find the weight of 1 cubic inches of water b plugging ( = 1 ) into the equation above. Write our answer as an ordered pair (, ). 7. Graph the line. - Fill in the table with the point ou found above and at least 2 other points. - Fill in our labels for and as Size and Weight Page 3 of 6 Mass is a fundamental concept in phsics, roughl corresponding to the intuitive idea of how much matter there is in an object. In informal everda usage, mass is more commonl referred to as weight, but in phsics and engineering weight strictl means the size of the gravitational pull on the object; that is, how heav it is, measured in units of force. In everda situations, the mass of an object is proportional to its weight, which usuall makes it unproblematic to use the same word for both. Distinguishing them becomes important for measurements with a precision better than a few percent, due to slight differences in the strength of the Earth's gravitational field at different places, and is essential when one considers places far from the surface of the Earth, such as in space or on other planets. - The following is a list of the weights of a mass on the surface of some of the bodies in the solar sstem, relative to its weight on Earth: Mercur.378 Venus.97 Earth 1 Moon.165 Mars.377 Jupiter Saturn 1.64 Uranus.889 Neptune On which of the planets would ou weigh the least? Page 4 of 6 Let s take the eample of the moon. There ou would weigh.165 times our weight on earth. The relationship between these units is linear, as epressed in the equation below, where is our moon weight in pounds and is our earth weight in pounds. = Recall that is moon weight and is earth weight, and that the slope m =. Rewrite this epression using the words Earth weight and Moon weight instead of and. m = 3. We can interpret the slope above b saing that increasing pound in earth weight means we increase pound in moon weight. 4. What is the intercept of this line? 5. Graph the line. - Fill in the table with at least 3 points. - Fill in our labels for and as moon weight and earth weight Page 5 of 6 Wh does it take such a small flotation device to keep ou afloat? Well, approimatel 8% of our bod is made up of water which has no weight when ou are swimming. Also, our bodies have fat, on average about 15%, and fat weighs less than water. So when ou are floating in water, onl 5% of our bod weight needs to be kept afloat This relationship is linear, as epressed in the equation below, where is our water weight in pounds and is our dr weight in pounds. =.5 2. What is the intercept of this line? 3. Graph the line. - Fill in the table with least 3 points. - Fill in our labels for and as water weight and dr weight Page 6 of 6 The following eample is NOT linear. It is an eample of how to calculate our bod mass inde (BMI) given our weight and height. BMI is a internationall used measure of obesit. BMI (weight in pounds) 73 = 2 (height in inches) - First ou will notice that we are looking for = m+ b. We have too man inputs! We have an input for weight and another input for height. So the BMI equation above is not linear. However, it is not without use, so let s investigate. in 1. If I weigh 145 pounds and am 5 feet 5 inches tall ( 5ft in = 65in ), m BMI is ft (145) BMI = = (65) The following table indicates the BMI weight status categories as fied b the US Department of Health and Human Services. BMI Weight Status Below 18.5 Underweight Normal Overweight 3 & Above Obese 3. Given the BMI calculated in (1), what do I fall under? 4. Calculate our own BMI.
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