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3 years ago

How should variables be depicted on a graph?

Physics

1 answer:

nignag [31]3 years ago

4 0

Answer:

D.) independent variable on the x-axis

Explanation:

Normally in an x-y plane, the value of x is taken as an independent variable, i.e. it is independent because it can assume any value (real number), while y depends on the value x. for example for the following equation.

y = x

Where:

x = independent value.

y = dependent value of x

This is the equation of a line, inclined with slope equal to 1.

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A student performs a reaction twice. In the second trial, he increases the temperature of the reaction and notes that the reacti

mihalych1998 [28]

Answer: higher temperature increases reaction rates for both endothermic and exothermic reactions

Explanation: i took the test

6 0

3 years ago

The rate at which heat enters an air conditioned building is often roughly proportional to the difference in temperature between

erma4kov [3.2K]

Answer:

Considering first question

Generally the coefficient of performance of the air condition is mathematically represented as

$COP = \frac{T_i}{T_o - T_i}$

Here $T_i$ is the inside temperature

while $T_o$ is the outside temperature

What this coefficient of performance represent is the amount of heat the air condition can remove with 1 unit of electricity

So it implies that the air condition removes $\frac{T_i}{T_o - T_i}$ heat with 1 unit of electricity

Now from the question we are told that the rate at which heat enters an air conditioned building is often roughly proportional to the difference in temperature between inside and outside. This can be mathematically represented as

$Q \ \alpha \ (T_o - T_i)$

=> $Q= k (T_o - T_i)$

Here k is the constant of proportionality

since 1 unit of electricity removes $\frac{T_i}{T_o - T_i}$ amount of heat

E unit of electricity will remove $Q= k (T_o - T_i)$

$E = \frac{k(T_o - T_i)}{\frac{T_i}{ T_h - T_i} }$

=> $E = \frac{k}{T_i} (T_o - T_i)^2$

given that $\frac{k}{T_i}$ is constant

=> $E \ \alpha \ (T_o - T_i)^2$

From this above equation we see that the electricity required(cost of powering and operating the air conditioner) is approximately proportional to the square of the temperature difference.

Considering the second question

Assuming that $T_i = 30 ^oC$

and $T_o = 40 ^oC$

Hence

$E = K (T_o - T_i)^2$

Here K stand for a constant

$E = K (40 - 30)^2$

=> $E = 100K$

Now if the $T_i = 20 ^oC$

Then

$E = K (40 - 20)^2$

=> $E = 400 \ K$

So from this see that the electricity require (cost of powering and operating the air conditioner)when the inside temperature is low is much higher than the electricity required when the inside temperature is higher

Considering the third question

Now in the case where the heat that enters the building is at a rate proportional to the square-root of the temperature difference between inside and outside

We have that

$Q = k (T_o - T_i )^{\frac{1}{2} }$

$E = \frac{k (T_o - T_i )^{\frac{1}{2} }}{\frac{T_i}{T_o - T_i} }$

=> $E = \frac{k}{T_i} * (T_o - T_i) ^{\frac{3}{2} }$

Assuming $\frac{k}{T_i}$ is a constant

Then

$E \ \alpha \ (T_o - T_i)^{\frac{3}{2} }$

From this above equation we see that the electricity required(cost of powering and operating the air conditioner) is approximately proportional to the square root of the cube of the temperature difference.

4 0

3 years ago

In a Hydrogen atom an electron rotates around a stationary proton in a circular orbit with an approximate radius of r =0.053nm.

VLD [36.1K]

Answer:

(a) 8.2 x 10^-8 N

(b) 3.6 x 10^-47 N , 2.27 x 10^39

Explanation:

charge of proton, q1 = 1.6 x 10^-19 C

charge of electron, q2 = - 1.6 x 10^-19 C

radius of orbit, r = 0.053 nm = 0.053 x 10^-9 m

mass of electron, me = 9.1 x 10^-31 kg

mass of proton, mp = 1.67 x 10^-27 kg

Gravitational constant, G = 6.67 x 10^-11 Nm^2/kg^2

(a) The electrostatic force between two charges is given by

$F_{e}=\frac{Kq_{1}q_{2}}{r^2}$

Where, K is the coulombic constant = 9 x 10^9 Nm^2/C^2

By substituting the values

$F_{e}=\frac{9\times 10^{9}\times 1.6\times 10^{-19}\1.6\times 10^{-19}}{\left ( 0.053 \times 10^{-9} \right )^2}$

Fe = 8.2 x 10^-8 N

(b) The gravitational force between the electron and proton is given by

$F_{g}=\frac{Gm_{e}m_{p}}{r^{2}}$

$F_{g}=\frac{6.67\times 10^{-11}\times 9.1\times 10^{-31}\1.67\times 10^{-27}}{\left ( 0.053 \times 10^{-9} \right )^2}$

Fg = 3.6 x 10^-47 N

$\frac{F_{e}}{F_{g}}=\frac{8.2\times10^{-8}}{3.6\times 10^{-47}}$

$\frac{F_{e}}{F_{g}}=2.27\times 10^{39}$

5 0

3 years ago

Convert 1 mm to meters using scientific notation. Include units in your answer.

irinina [24]

Answer: The answer in scientific notation with the unit included is (1 × 10^-3m.)

Explanation:

In the field of physics, when working with too large or too small numbers, such can be expressed with the use of scientific notation. This helps to eliminate huge or ambiguous numbers with significant units. It is written is such a way that the first number is greater than or equal to 1 and less than 10 which is then multiplied by a factor of 10.

Units are symbols that are used to represent a measurement For example the unit of meters is (m).

Converting 1mm to m:

1000millimeters = 1meter

1 millimetre = X

Making X the subject of formula,

X = 1 ×1 /1000

X = 0.001m

Therefore expressing X in scientific notation is

1 × 10^-3meter (m)

7 0

3 years ago

A 0.200-kilogram ball A is traveling at a velocity of 2 meters/second. It hits a 1-kilogram stationary ball B. Which statement i