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erma4kov [3.2K]

2 years ago

11

jack wants to find out which laundry detergent cleans the best ( Gain, Tide, or Purex). So, he takes a cotton sheet and cuts it

up into equal squares. He stains four squares with chocolate, and four with grape juice. He washes one of each of the squares in each of the 3 detergents. One from each set of squares is washed in water alone. For each wash load, he used: the same amount of water, the same amount of detergent, and the same temperature of water. Find the independent variable, dependent variable, control (constants) and write a hypothesis for the outcome.

2 answers:

Aloiza [94]2 years ago

7 0

Answer:

A scientific experiment should contain three variables:

1 Dependent variable: the variable which has to be studied in the experiment.

2 Independent variable: the variable which can be manipulated or gets changed in the experiment.

3. Control variable: the variable which is kept constant or the same throughout the experiment.

In the given question.

1. Independent variable is the type of laundry reagent.

2. Dependent variable- the clean cloth after washing.

3. Control variable- the amount of water, the temperature of the water and the amount of detergent.

dezoksy [38]2 years ago

6 0

the independent variables are the different laudry detergent

the dependent variable is color of the cloth after washing

the control variables are the amount of water added and by washing one cloth b just water

<span>hypothesis: the cloth washed with laundry detergent is cleaner than the cloth that is just washed by water. </span>

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Complete Question

The complete Question is shown on the first uploaded image

Answer:

a

The torque acting on the particle is $\tau = 48t \r k$

b

The magnitude of the angular momentum increases relative to the origin

Explanation:

From the equation we are told that

The position of the particle is $\= r = 4.0 t^2 \r i - (2.0 t - 6.0 t^2 ) \r j$

The mass of the particle is $m = 3.0 kg$

The time is t

The torque acting on the particle is mathematically represented as

$\tau = \frac{ d \r l }{dt}$

where $\r l$ is change in angular momentum which is mathematically represented as

$\r l = m (\r r \ \ X \ \ \r v)$

Where X mean cross- product

$\r v$ is the velocity which is mathematically represented as

$\r v = \frac{d \r r }{dt}$

Substituting for $\r r$

$\r v = \frac{d }{dt} [ 4 t^2 \r i - (2t + 6t^2 ) \r j]$

$\r v = 8t \r i - (2 + 12 t) \r j$

Now the cross product of $\r r \ and \ \r v$ is mathematically evaluated as

$\r r \ \ X \ \ \r v = \left[\begin{array}{ccc}{\r i}&{\r j}&{\r k}\\{4t^2}&{-2t -6t^2}&0\\{8t}&{-2 -12t}&0\end{array}\right]$

$= 0 \r i + 0 \r j + (- 8t^2 -48t^3 + 16t^2 + 48t^3 ) \r k$

$\r r \ \ X \ \ \r v = 8t^2 \r k$

So the angular momentum becomes

$\r l = m (8t^2 \r k)$

Substituting for m

$\r l = 3 * (8t^2 \r k)$

$\r l =24t^2 \r k$

Substituting into equation for torque

$\tau = \frac{d}{dt} [24t^2 \r k]$

$\tau = 48t \r k$

The magnitude of the angular momentum can be evaluated mathematically as

$|\r l| = \sqrt{(24 t^2) ^2}$

$|\r l| = 24 t^2$

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