goldenleanna

goldenleanna

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University of Toronto Scarborough

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Project Management5Science1Mechanical Engineering1Geography4Information Technology2Computer Science1Accounting2Calculus2Biology11Mathematics2Statistics2Physics1Chemistry1
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Let's start by solving for p and q using the given equations:

 

Given:

x = va(sinu + cosv)

y = va(cosu - sinv)

z = 1 + sin(u - v)

 

To find p and q, we need to eliminate u and v from the equations. Here's how we can do it:

 

1. Square both sides of the first equation:

x^2 = v^2a^2(sinu + cosv)^2

 

2. Square both sides of the second equation:

y^2 = v^2a^2(cosu - sinv)^2

 

3. Add the squared equations together:

x^2 + y^2 = v^2a^2(sinu + cosv)^2 + v^2a^2(cosu - sinv)^2

 

4. Expand and simplify the equation:

x^2 + y^2 = v^2a^2(sin^2u + 2sinucosv + cos^2v) + v^2a^2(cos^2u - 2sinvcosu + sin^2v)

 

5. Combine like terms:

x^2 + y^2 = v^2a^2(sin^2u + cos^2u + sin^2v + cos^2v) + 2v^2a^2(sinucosv - sinvcosu)

 

6. Simplify further using trigonometric identities:

x^2 + y^2 = v^2a^2 + 2v^2a^2(sin(u + v))

 

7. Now, let's look at the equation for z:

z = 1 + sin(u - v)

 

8. Square both sides of the equation:

z^2 = (1 + sin(u - v))^2

 

9. Expand and simplify the equation:

z^2 = 1 + 2sin(u - v) + sin^2(u - v)

 

10. Substitute the value of z from the original equation:

z^2 = 1 + 2sin(u - v) + sin^2(u - v)

 

11. Simplify further:

z^2 = 1 + 2sin(u - v) + (1 - cos^2(u - v))

 

12. Simplify even more:

z^2 = 2 - cos^2(u - v) + 2sin(u - v)

 

13. Rearrange the equation:

cos^2(u - v) = 2 - z^2 - 2sin(u - v)

 

14. Substitute the value of sin(u - v) from the equation derived in step 6:

cos^2(u - v) = 2 - z^2 - 2v^2a^2

 

15. Take the square root of both sides:

cos(u - v) = ±√(2 - z^2 - 2v^2a^2)

 

16. Now, let's find sin(u - v) using the equation derived in step 6:

sin(u - v) = (x^2 + y^2 - v^2a^2) / (2va^2)

 

17. Substitute the values of cos(u - v) and sin(u - v) into the equation for x:

x = va(sinu + cosv)

 

18. Substitute the values of sin(u - v) and cos(u - v) into the equation for y:

y = va(cosu - sinv)

 

19. Simplify the equations further and solve for p and q:

p = arcsin((x - y) / (2va))

q = arccos((x + y) / (2va))

 

These are the values of p and q based on the given equations. Please note that there may be other solutions or constraints depending on the specific values of x, y, z, v, and a.

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QUESTION 9

How did this experiment with Benedict's solution demonstrate the digestion of starch by amylase? In other words, how did you know the starch was digested?

We compared control samples with samples that had been treated with amylase and measured the pH using a pH indicator. When the solution becomes orange or red, it indicates that the starch has been digested.

We compared control samples with samples that had been treated with amylase and used a Benetict's test for Reducing Sugar. When Benedict's turns orange/red it indicates that starch has been digested.

We compared control samples the sample to been treated with amylase and observed which had become liquefied. The solution becomes liquefied, it indicates that the starches have been digested.

Compare control samples with samples that had been treated with amylase. Benedict's turns light blue it indicates that starch has been digested.

QUESTION 10

What happens to saliavry amylase when it arrives with the bolus in the stomach? Because of this, what happens to charbohydrate digestion? (Hint: Look up the optimum pH for amylase and what is the pH of the gastric juices)

When the bolus hit the stomach, the amylase enyzmes continue to function and starch digestion continues.

When the bolus hit the stomach, the amylase enyzmes denature and cease to function and starch digestion stops.

When the bolus hit the stomach, the amylase enyzmes denature and cease to function. However, starch digestion continues because pepsin continues the digestion of starch.

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Experiment 2: Osmosis - Direction and ConcentrationGradients

In this experiment, we will investigate the effect of soluteconcentration on osmosis. A semi-permeable membrane (dialysistubing) and sucrose will create an osmotic environment similar tothat of a cell. This selective permeability allows us to examinethe net movement of water across the membrane. You will begin theexperiment with a 30% sucrose solution, and perform a set of serialdilutions to create lower concentration solutions. Some of thesucrose concentrations will be membrane permeable; while otherswill not be permeable (can you determine why this is?).

Materials

(3) 250 mL Beakers

(1) 10 mL Graduated Cylinder

(1) 100 mL Graduated Cylinder

Permanent Marker

*8 Rubber Bands (2 blue, 2 green, 2 red, and 2 yellow)

60 g Sucrose (Sugar) Powder, C12H22O11

4 Waste Beakers (any volume)

*Paper Towels

*Scissors

*Stopwatch

*Water

*(4) 15 cm. Pieces of Dialysis Tubing

*Contains latex. Please handle wearing safety gloves if you have alatex allergy.



*You Must Provide

*Be sure to measure and cut only the length you need for thisexperiment. Reserve the remainder for later experiments.

Procedure

1. Use the permanent marker to label the three 250 mL beakers as 1,2, and 3.

2. Cut four strips of dialysis tubing, each 15.0 cm long. FillBeaker 3 with 100 mL of water and submerge the four pieces ofdialysis tubing in the water for at least 10 minutes.

3. After 10 minutes, remove one piece of tubing from the beaker.Use your thumb and pointer finger to rub the tubing between yourfingers; this will open the tubing. Close one end of the tubing byfolding over 3.0 cm of one end (this will become the bottom). Foldit again and secure with a yellow rubber band (use

4. Tie a knot in the remaining dialysis tubing just above or justbelow the rubber band. This will create a seal and ensures thatsolution will not leak out of the tube later in theexperiment.

5. To test that no solution can leak out, add a few drops of waterto the tubing and look for water leakage. If any water leaks,tighten the rubber band and/or the knot in the tubing. Make sureyou pour the water out of the tubing before continuing to the nextstep.

6. Repeat Steps 4 - 5 with the three remaining dialysis tubes,using each of the three remaining rubber band colors.

7. Reconstitute the sucrose powder according to the instructionsprovided on the bottle�s label (your kit contains 60 g of sucrosein a chemical bottle) . This will create 200 mL of a 30% stocksucrose solution.

8. Use Table 2 to create additional sucrose solutions that are 30%,15% and 3% concentrated, respectively. Use the graduated cylinderand waste beakers to create these solutions. Set these solutionsaside.

Table 2: Serial Dilution Instructions

Sucrose Solution mL of Stock Sucrose Solution Needed mL of WaterNeeded

30% 10 0

15% 5 5

3% 1 9

3% 1 9

9. Pour 150 mL of the remaining stock sucrose solution into Beaker1.

10. Use some of the remaining stock sucrose solution to create anadditional 200 mL of a 3% sucrose solution into Beaker 2.

Hint: Use your knowledge of serial dilutions to create this final,3% sucrose solution.

11. Measure and pour 10 mL of the remaining 30% sucrose solutioninto the dialysis bag with the yellow rubber band. Seal the top ofthis tubing with the remaining yellow rubber band.

12. Measure and pour 10 mL of the 15% sucrose solution in the bagwith the red rubber band, and seal the top of the dialysis tubingwith the remaining red rubber band. 10 mL of the 3% sucrosesolution in the bag with the blue rubber band, and seal thedialysis tubing with the remaining blue rubber band. The final 10mL of 3% sucrose solution in the bag with the green rubber band.Seal the dialysis tubing with the remaining green rubberband.

13. Verify and record the initial volume of solution from each bagin Table 3.



Figure 8: The dialysis bags are filled with varying concentrationsof sucrose solution and placed in one of two beakers.

14. Place the yellow, red, and blue banded tubing in Beaker 2.Place the green banded tubing in Beaker 1 (Figure 8).

15. Hypothesize whether water will flow in or out of each dialysisbag. Include your hypotheses, along with supporting scientificreasoning in the Hypotheses section at the end of thisprocedure.

16. Allow the bags to sit for one hour. While waiting, pour out thewater in the 250 mL beaker that was used to soak the dialysistubing in Step 1. You will use the beaker in Step 19.

17. After allowing the tubing to sit for one hour, remove them fromthe beakers.

18. Carefully open the tubing. The top of the tubing may need to becut off/removed as they tend to dry out over the course of an hour.Measure the solution volumes of each dialysis bag using the 100 mLgraduated cylinder. Make sure to empty and dry the cylindercompletely between each sample.

19. Record your data in Table 3.

Data Tables and Post-Lab Assessment

Table 3: Sucrose Concentration vs. TubingPermeability

Table 3: Sucrose Concentration vs. TubingPermeability

Band Color

% Sucrose in Beaker

% Sucrose in Bag

Initial Volume (mL)

Final Volume (mL)

Net Displacement (mL)

Yellow

Red

Blue

Green

Hypothesis:

For each of the tubing pieces, identify whether the solutioninside was hypotonic, hypertonic, or isotonic in comparison to thebeaker solution in which it was placed.

Which tubing increased the most in volume? Explain why thishappened.

What do the results of this experiment this tell you about therelative tonicity between the contents of the tubing and thesolution in the beaker?

What would happen if the tubing with the yellow band was placedin a beaker of distilled water?

How are excess salts that accumulate in cells transferred to theblood stream so they can be removed from the body? Be sure toexplain how this process works in terms of tonicity.

If you wanted water to flow out of a tubing piece filled with a50% solution, what would the minimum concentration of the beakersolution need to be? Explain your answer using scientificevidence.

How is this experiment similar to the way a cell membrane worksin the body? How is it different? Be specific with yourresponse.

Answer: Hypotheses: 1. For each of the tubing pieces, identify whether the sol...

Note: The color results of these controls determine theindicator reagent key. You must use these results to interpret therest of your results. 6. After at least 10 minutes have passed,remove the dialysis tube and close one end by folding over 3.0 cmof one end (bottom). Fold it again and secure with a rubber band(use two rubber bands if necessary). 7. Make sure the closed endwill not allow a solution to leak out. You can test this by dryingoff the outside of the dialysis bag with a cloth or paper towel,adding a small amount of water to the bag, and examining the rubberband seal for leakage. Be sure to remove the water from the insideof the bag before continuing. 8. Using the same pipette which wasused to mix the solution in Step 3, transfer eight mL of thesolution from the Dialysis Bag Solution beaker to the prepareddialysis bag. Figure 4: Step 9 reference. 9. Place the filleddialysis tube in beaker filled with 80 mL of water with the openend draped over the edge of the beaker as shown in Figure 4. 10.Allow the solution to sit for 60 minutes. Clean and dry allmaterials except the beaker with the dialysis bag. 11. After thesolution has diffused for 60 minutes, remove the dialysis tube fromthe beaker and empty the contents into a clean, dry beaker. Labelit dialysis bag solution. 12. Test the dialysis bag solution forthe presence of glucose and starch. Test for the presence ofglucose by dipping one glucose test strip into the dialysis bagdirectly. Again, wait one minute before reading the results of thetest strips. Record your results for the presence of glucose andstarch in Table 4. Test for the presence of starch by adding two mLIKI. Record the final color in Table 4 after one minute has passed.13. Test the solution in the beaker for glucose and starch. Use apipette to transfer eight mL of the solution in the beaker to aclean beaker. Test for the presence of glucose by dipping oneglucose test strip into the beaker. Wait one minute before readingthe results of the test strip and record the results in Table 4.Add two mL of IKI to the beaker water and record the final color ofthe beaker solution in Table 4. Table 3: Indicator Reagent DataIndicator Starch Positive Control (Color) Starch Negative Control(Color) Glucose Positive Control (Color) Glucose Negative Control(Color) IKI Solution n/a n/a Glucose Test Strip n/a n/a Table 4:Diffusion of Starch and Glucose Over Time Indicator Dialysis BagAfter 1 Hour Beaker Water After 1 Hour IKI Solution Glucose TestStrip Post-Lab Questions 1. Why is it necessary to have positiveand negative controls in this experiment? 2. Draw a diagram of theexperimental set-up. Use arrows to depict the movement of eachsubstance in the dialysis bag and the beaker. 3. Which substance(s)crossed the dialysis membrane? Support your response withdata-based evidence. 4. Which molecules remained inside of thedialysis bag? 5. Did all of the molecules diffuse out of the baginto the beaker? Why or why not?

Answer: Two beakers, A and B, and two dialysis tubes are used in the experimen...
Answer: Phenolphthalein: This molecule does not pass through the dialysis tubi...
Answer: The beaker's amber color is due to a chemical indicator solution, such...

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