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rusak2 [61]
3 years ago
14

In 2010, National Textile installed a new textile machine in one of its factories at a cost of $200,000. The machine is deprecia

ted linearly over 10 years with a scrap value of $10,000.
(a) Find an expression for the textile machine's book value in the t th year of use
(0 ≤ t ≤ 10).
Mathematics
1 answer:
Inessa05 [86]3 years ago
3 0

Answer:

V(t)=-19,000t+200,000

Step-by-step explanation:

Let V(t) be the value of machine after t years and t represents the number of years after 2010.

We are given the value in the beginning as 200,000. We are also given scrap value (value at the end of period) as 10,000.

So we need to find a linear function with points (0, 200000) and (10,10000)

Let us find slope of our line using our given points.

m=\frac{10,000-200,000}{10-0}

m=\frac{-190,000}{10}

m=-19,000

Since we know that the slope-intercept form of equation is in form: y=mx+b, where,

m = Slope of line,  

b = The y-intercept or initial value.

We can see that initial value of machine is $200,000, so substituting m=-19,000 and b = 200,000, we will get our equation as:

V(t)=-19,000t+200,000

Therefore, the equation V(t)=-19,000t+200,000 represents the the textile machine's book value in the th year of use.



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<h3>Answer:  1.25 gallons</h3>

==================================

Explanation:

They currently have ten gallon jugs that contain 10% water, so this means 0.10*10 = 1 gallon of the jug is water and the other 10-1 = 9 gallons is paint. This is assuming the cans are just paint and water.

The ratio of paint to water is 90:10 which reduces to 9:1

Often it helps to reduce as much as possible, but it's actually more handy in this case to keep it at 90:10 so you can see the two parts add back up to 100%

--------------

Let x be the amount of water we add. This amount is in gallons.

We start off with 1 gallon of water and it bumps up to 1+x gallons of water.

The overall amount of 10 gallons also bumps up to 10+x gallons.

We want a ratio of 80:20 this time, so we want 20 parts water and 80 parts paint. In other words, we want 20/(20+80) = 20/100 = 20% water

Divide (1+x) over (10+x) to get (1+x)/(10+x). This represents the fraction of water. We want this fraction to be equal to 0.20, which is the 20% water amount. It is also equal to 20/100.

--------------

(1+x)/(10+x) = 20/100

100(1+x) = 20(10+x) ... cross multiply

100+100x = 200+20x ... distribute

100x-20x = 200-100

80x = 100

x = 100/80 ... divide both sides by 80

x = 1.25

You need to add 1.25 gallons of water

--------------

If you add 1.25 gallons of water, then,

amount of water = 1+x = 1+1.25 = 2.25

amount of paint&water = 10+x = 10+1.25 = 11.25

So you'll have 2.25 gallons of water out of 11.25 gallons of water&paint mix

2.25/11.25 = 0.2 = 20% water

This confirms our answer.

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Extra info:

1.25 gallons = 1 gallon + 1/4 gallon

1.25 gallons = 1 gallon + 1 quart

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Answer:

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Here we are given that M+5n=p

We are asked to solve this equation for M. In order to do that we will follow these steps.

Subtracting 5n from both sides we get

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See attachment

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<em />

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<em />

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