Mathematics For Elementary Teachers With Activities
5th Edition
ISBN: 9780134423401
Author: Sybilla Beckmann
Publisher: PEARSON
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Chapter 7.2, Problem 7P
Fertilizer problem: A type of fertilizer is made by mixing nitrogen and phosphate in an 8 to 3 ratio. For 35 kilograms of nitrogen, how many kilograms of phosphate are needed to make the fertilizer?
Solve the Fertilizer Problem in two ways by reasoning about multiplication and division with quantities, once from the multiple-batches perspective and once from the variable-parts perspective. In each case, describe the number of kilograms of phosphate as a product A . B, where A and B are suitable whole numbers, fractions, or mixed numbers that you derive from 8, 3, and 35. Attend carefully to our definition of multiplication when discussing A B. In each case, use a math drawing to support your explanation.
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☐
Part 1:
A linear electrical load draws 1₁ A at a 0.72 lagging power factor. See the table to find ½ for your
student ID. When a capacitor is connected, the line current dropped to 122 A and the power factor
improved to 0.98 lagging. Supply frequency is 50 Hz.
a. Let the current drawn from the source before and after introduction of the capacitor be 1₁ and I₂
respectively. Take the source voltage as the reference and express 11 and 12 as vector
quantities in polar form.
b. Obtain the capacitor current, Ic = 12 − I₁, graphically as well as using complex number
manipulation. Compare the results.
c. Express the waveforms of the source current before (į (t)) and after (i2(t)) introduction of the
capacitor in the form Im sin(2лft + 0). Hand sketch them on the same graph. Clearly label your
plots.
d. Analytically solve i̟2(t) − i₁ (t) using the theories of trigonometry to obtain the capacitor current
in the form, ic(t) = Icm sin(2πft + 0c). Compare the result with the result in Part b.
= x³, y = 8, x = 0.
Let R be the region bounded by the curves y = x³
1. Sketch the region and find the area. Write your answer in simplest fractional form.
2. Sketch the solid you obtain by rotating the region R about the x-axis.
3. Find the volume of the solid obtained by rotating the region R about the x-axis
using the disk/washer method. Write the formula you are using. Write your answer
in terms of π. Draw the approximating rectangle that you rotate.
4. Find the volume of the solid obtained by rotating the region R about the x-axis
using the shell method. Write the formula you are using. Write your answer in
terms of π. Draw the approximating rectangle that you rotate.
5. Which method did you find easier and why? [There is no wrong answer for what
you find easier, but explain.]
6. Sketch the solid you obtain by rotating the region R about the y-axis.
7. Find the volume of the solid obtained by rotating the region R about the y-axis
using the disk/washer method. Write the formula…
Chapter 7 Solutions
Mathematics For Elementary Teachers With Activities
Ch. 7.1 - Use the multiple-batches perspective to discuss...Ch. 7.1 - Use the variable-parts perspective to discuss and...Ch. 7.1 - John is driving at a constant speed of 10 miles...Ch. 7.1 - You can make grape juice by mixing 1 can of frozen...Ch. 7.1 - Use ratio tables to determine in two ways which of...Ch. 7.1 - Explain how to reason about ratio tables to...Ch. 7.1 - Allie, Benton, and Cathy are planning to mix red...Ch. 7.1 - Company A charges $6 for every 100 silly bands....Ch. 7.1 - You can make a pink paint by mixing 212 cups white...Ch. 7.2 - Walking at a constant speed, a person walks 34 of...
Ch. 7.2 - In a terrarium, the ratio of grasshoppers to...Ch. 7.2 - At a zoo, the ratio of king penguins to emperor...Ch. 7.2 - On a farm, the ratio of grey goats to white goats...Ch. 7.2 - An orange-lemon juice mixture can be made by...Ch. 7.2 - Explain how to solve parts a—d of Problem 5 by...Ch. 7.2 - Fertilizer problem: A type of fertilizer is made...Ch. 7.2 - Brad made some punch by mixing 12 cup of grape...Ch. 7.2 - To make grape juice by using frozen juice...Ch. 7.2 - You can make a soap bubble mixture by combining 2...Ch. 7.2 - You can make concrete by mixing 1 part cement with...Ch. 7.2 - Marge made light blue paint by mixing 212 2 cups...Ch. 7.2 - A batch of lotion was made at a factory by mixing...Ch. 7.2 - If a 34 cup serving of snack food gives you 60% of...Ch. 7.2 - If $6000 is 75% of a company’s budget for a...Ch. 7.2 - Amy mixed 2 tablespoons of chocolate syrup in 34...Ch. 7.2 - A 5-gallon bucket filled with water is being...Ch. 7.2 - Explain how to reason about quantities to solve...Ch. 7.2 - * The ratio of Frank’s marbles to Huang’s marbles...Ch. 7.2 - * Asia and Taryn each had the same amount of...Ch. 7.2 - * An aquarium contained an equal number of...Ch. 7.3 - A company mixes different amounts of blue paint...Ch. 7.3 - A company mixes different amounts of grape and...Ch. 7.3 - a. Which of the following two mixtures will have a...Ch. 7.3 - a. Snail A moved 6 feet in 7 hours. Snail B moved...Ch. 7.3 - A dough recipe calls for 3 cups of flour and 114...Ch. 7.3 - A recipe that serves 6 people calls for 112 cups...Ch. 7.3 - Explain how to reason with unit rates to solve the...Ch. 7.3 - Buttercup the gerbil drinks 23 of a bottle of...Ch. 7.3 - If you used 212 truck loads of mulch for a garden...Ch. 7.3 - If 212 pints of jelly filled 312 jars, then how...Ch. 7.3 - * A standard bathtub is approximately 412 feet...Ch. 7.4 - Goblin Green Paint is made by mixing blue and...Ch. 7.4 - Aqua Regia is an acid that can dissolve gold. It...Ch. 7.4 - A type of dark chocolate is made by mixing cocoa...Ch. 7.4 - A type of chemical solution is 6% sodium chloride...Ch. 7.4 - As in the text, consider biodiesel and petrodiesel...Ch. 7.4 - Peacock Purple Paint is made by mixing red paint...Ch. 7.4 - A company mixes fertilizer and soil in a 4 to 9...Ch. 7.4 - Consider ramps whose length and height are in the...Ch. 7.4 - Consider the line through the origin and the point...Ch. 7.4 - A company makes mixtures of acetic acid and water...Ch. 7.5 - Suppose that 6 people can stuff flyers into 500...Ch. 7.5 - Make up two examples of relationships between two...Ch. 7.5 - A Sewing Problem: If 10 workers take 8 hours to...Ch. 7.5 - A Driving Problem: Driving at 50 mph, you covered...Ch. 7.5 - For each of the following relationships, determine...Ch. 7.5 - Suppose that you have two square garden plots: One...Ch. 7.5 - If a crew of 3 people takes 212 hours to clean a...Ch. 7.5 - If you can rent 5 DVDs for 5 nights for $5, then...Ch. 7.5 - If 6 people take 3 days to dig 8 ditches, then how...Ch. 7.5 - * A candy factory has a large vat into which...Ch. 7.5 - * Jay and Mark run a lawn-mowing service. Mark’s...Ch. 7.5 - * If liquid pouring at a steady rate from hose A...Ch. 7.5 - * Suppose that there are 400 pounds of freshly...Ch. 7.6 - Last year, the population of South Skratchankle...Ch. 7.6 - Last year’s sales were $7.5 million. This year’s...Ch. 7.6 - Jayna and Lisa are comparing the prices of two...Ch. 7.6 - Are the two problems that follow solved in the...Ch. 7.6 - The price of play equipment for the school has...Ch. 7.6 - How much should Swanko Jewelers charge now for a...Ch. 7.6 - If sales taxes are 7%, then how much should you...Ch. 7.6 - Connie and Benton bought identical plane tickets,...Ch. 7.6 - Of the five statements that follow, which have the...Ch. 7.6 - Explain the difference between a 150% increase in...Ch. 7.6 - Every week, DollarDeals lowers the price of items...Ch. 7.6 - * The SuperDiscount store is planning a “35%-off...Ch. 7.6 - * One box of cereal contains 12% more cereal than...Ch. 7.6 - * One box of cereal contains 25% more cereal than...Ch. 7.6 - * In a box of chocolate candies, 40% of the...Ch. 7.6 - * In a box of chocolate candies, 30% of the...Ch. 7.6 - * There are two elementary schools in a county....Ch. 7.6 - * There are two middle schools in a county. The...Ch. 7.6 - * One school had 10% more children than another...Ch. 7.6 - * Sue and Tonya started the same job at the same...Ch. 7.6 - * Suppose that the sales tax is 7%, and suppose...Ch. 7.6 - * A dress is marked down 25%, and then it is...Ch. 7.6 - * Frank’s Jewelers runs the following...Ch. 7.6 - * The following information about two different...Ch. 7.6 - * According to the 2000 Census, from 1990 to 2000...Ch. 7.6 - * In 2000, Washington County had a total...
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