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dalvyx [7]
2 years ago
10

Donna drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Donna drove

home, there was no traffic and the trip only took 4 hours. If her average rate was 45 miles per hour faster on the trip home, how far away does Donna live from the mountains?
Physics
1 answer:
Dennis_Churaev [7]2 years ago
8 0

Answer:

d=360 miles

Donna lives 360 miles from the mountains.

Explanation:

Conceptual analysis

We apply the formula to calculate uniform moving distance[

d=v*t   Formula (1)

d: distance in miles

t: time in hours

v: speed in miles/hour

Development of problem

The distance Donna traveled to the mountains is equal to the distance back home, equal to d,then,we pose the kinematic equations for d, applying formula 1:

travel data to the mountains: t₁= 8 hours ,  v=v₁

d= v₁*t₁=8*v₁ Equation (1)

data back home : t₂=4hours ,  v=v₂=v₁+45

d=v₂*t₂=(v₁+45)*4=4v₁+180 Equation (2)

Equation (1)=Equation (2)

8*v₁=4v₁+180

8*v₁-4v₁=180

4v₁=180

v₁=180÷4=45 miles/hour

we replace v₁=45 miles/hour in equation (1)

d=8hour*45miles/hour

d=360 miles

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Answer:

1. The density of the cube is 1.03 g/mL.

2. Dish soap

Explanation:

1. Determination of the density of the cube.

From the question given above, the following data were obtained:

Mass (m) of cube = 21.7 g

Volume (V) of cube = 21 mL

Density (D) of cube =?

The density of a substance is simply defined as the mass of the substance per unit volume of the substance. Thus, density can be expressed mathematically as:

Density (D) = mass (m) / volume (V)

D = m / V

With the above formula, we can obtain the density of the cube as follow:

Mass (m) of cube = 21.7 g

Volume (V) of cube = 21 mL

Density (D) of cube =?

D = m / V

D = 21.7 / 21

D = 1.03 g/mL

Thus, the density of the cube is 1.03 g/mL.

2. Determination of the layer of density the cube will settle in.

From the question given above,

Subtance >>>>>>>> Density

Vegetable oil >>>>> 0.91 g/mL

Grape juice >>>>>> 0.97 m/L

Water >>>>>>>>>>> 1 g/mL

Dish soap >>>>>>>> 1.03 g/mL

Maple syrup >>>>>> 1.37 g/mL

Comparing the density of the cube (i.e 1.03 g/mL) with those in the table able, we can conclude that the cube will settle in the DISH SOAP layer since they both have the same density.

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This question involves the concepts of density, volume, and mass.

The approximate diameter of a magnesium atom is "3.55 x 10⁻¹⁰ m".

<h3>STEP 1 (FINDING MASS OF INDIVIDUAL ATOM)</h3>

It is given that:

Mass of one mole = 24 grams

Mass of 6 x 10²³ atoms = 24 grams

Mass of 1 atom = \frac{24\ grams}{6\ x\ 10^{23}\ atoms} = 4 x 10⁻²³ grams

<h3>STEP 2 (FINDING VOLUME OF A SINGLE ATOM)</h3>

\rho = \frac{m}{V}\\\\V=\frac{m}{\rho}

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Therefore,

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<h3>STEP 3 (FINDING DIAMETER OF ATOM)</h3>

The atom is in a spherical shape. Hence, its Volume can be given as follows:

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d = 0.355 x 10⁻⁷ cm = 3.55 x 10⁻¹⁰ m

Learn more about density here:

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