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2 years ago

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For tax and accounting purposes, corporations depreciate the value of equipment each year. One method used is called "linear dep

reciation," where the value decreases over time in a linear manner. Suppose that two years after purchase, an industrial milling machine is worth $820,000, and five years after purchase, the machine is worth $430,000. Find a formula for the machine value V.

1 answer:

Sladkaya [172]2 years ago

7 0

Answer:

$V=-130000x+1080000$

Explanation:

<u>Linear Dependence </u>

Some variables are known or assumed to have linear dependence which means the graph of the ordered pairs (x,V) is a straight line.

If we know two points of the line, we can come up with the exact equation and therefore make predictions for other values of x

The linear depreciation gives us these points (2,820000) and (5,430000)

The general equation of the line is

$V=mx+b$

Where V is the machine value and x is the number of years after purchase. We need to find the values of m and b.

Replacing the first point

$820000=m(2)+b$

$2m+b=820000$

Replacing the second point

$5m+b=430000$

Subtracting them

$-3m=390000$

$m=-130000$

Replacing in any of the equations, say, the first one

$2(-130000)+b=820000$

Solving for b

$b=820000+260000$

$b=1080000$

The formula for the machine value V is

$\boxed{V=-130000x+1080000}$

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<u>Answer</u>:

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<u>Explanation</u>:

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2 years ago

A particular cylindrical bucket has a height of 36.0 cm, and the radius of its circular cross-section is 15 cm. The bucket is em

Sergeeva-Olga [200]

Answer:

a. 0.000002 m

b. 0.00000182 m

Explanation:

36 cm = 0.36 m

15 cm = 0.15 m

a) We can start by calculating the air-water pressure of the bucket submerged 20m below the water surface:

$P = \ro g h = 1000 * 10 * 20 = 200000 Pa$

Suppose air is ideal gas, then if the temperature stays the same, the product of its pressure and volume stays the same

$P_1V_1 = P_2V_2$

Where P1 = 1.105 Pa is the atmospheric pressure, V_1 is the air volume in the bucket on the suface:

$V_1 = Ah$

As the pressure increases, the air inside the bucket shrinks. But the crossection area stays constant, so only h, the height of air, decreases:

$P_1Ah_1 = P_2Ah_2$

$h_2 = h_1\frac{P_1}{P_2} = 0.36\frac{1.105}{200000} = 0.000002 m$

b) If the temperatures changes, we can still reuse the ideal gas equation above:

$\frac{P_1Ah_1}{T_1} = \frac{P_2Ah_2}{T_2}$

$h_2 = h_1\frac{P_1T_2}{P_2T_1} = 0.36\frac{1.105 * 275}{200000*300} =0.00000182 m$

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2 years ago

ery large accelerations can injure the body, especially if they last for a considerable length of time. One model used to gauge

IgorC [24]

Answer:

2.98 second

Explanation:

The severity index is defined by :

$S=a^{5/2}t$

a is dimensionless constant that equals the number of multiples of g

Conditions are given as :

Initial velocity, u = 0

Acceleration, a = 34 m/s²

Final velocity, v = 16.4 km/h = 4.56 m/s

We can find t from the above data as follows :

$t=\dfrac{v-u}{a}\\\\t=\dfrac{4.56-0}{34}\\\\t=0.134\ s$

As a is the acceleration that is multiple of g.

So,

$a=\dfrac{34}{9.8}=3.46$

So,

Severity index,

$S=a^{5/2}t\\\\S=(3.46)^{5/2}\times 0.134\\\\S=2.98\ s$

Hence, the severity index for the collision is 2.98 seconds.

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2 years ago

If the volume of an object is reported as 5.0 ft3 what is the volume in cubic meters

12345 [234]

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2 years ago

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Nana76 [90]

Answer:

28.1 mph

Explanation:

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$F=\mu mg = m \frac{v^2}{r}$ (1)

where

$\mu$ is the coefficient of friction

m is the mass of the car

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v is the maximum speed of the car

r is the radius of the trajectory

On the snowy day,

$\mu=0.50\\v = 20 mph = 8.9 m/s$

So the radius of the curve is

$r=\frac{v^2}{\mu g}=\frac{(8.9)^2}{(0.50)(9.8)}=16.1 m$

Now we can use this value and re-arrange again the eq. (1) to find the maximum speed of the car on a sunny day, when $\mu=1.0$ . We find:

$v=\sqrt{\mu g r}=\sqrt{(1.0)(9.8)(8.9)}=12.6 m/s=28.1 mph$

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2 years ago

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