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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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C). Nonrigid transformation.

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Transformation in mathematics is defined as the alteration or variation in the shape of an object without altering the lengths by using a flip, turn, slide, or resizing.

The transformation 'Hexagon ABCDEF → hexagon A'B'C'D'E'F'' would best be described as the 'non-rigid' and 'stretch' transformation. Non-rigid because it alters the shape or size of the figure both vertically as well as horizontally. It would be considered a stretch transformation as it is resized by a pull from both the vertical and horizontal angles. Thus, <u>options C and F</u> are the correct answers.

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Step-by-step explanation:

<u>Given</u>: {x+(1/x)}³ = 3

<u>Asked</u>: x³ + (1/x³) = ?

<u>Solution:</u>

<u>Method</u><u> </u><u>1:</u>

We have, {x+(1/x)}³ = 3

Comparing the expression with (a+b)³, we get

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Using identity (a+b)³ = a³+b³+3ab(a+b), we get

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Our answer came incorrect.

Let's try..

<u>Method</u><u> </u><u>2</u><u>:</u>

We have,

[x+(1/x)]³ = 3

On taking cube root both sides then

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We know that

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⇛x³+(1/x)³ = [x+(1/x)]³ - 3(x)(1/x)[x+(1/x)]

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⇛x³ + (1/x³) = 3- ³√81 (or )

⇛x³ + (1/x³) = 3(1-³√3)

Therefore, x³ + (1/x³) = 3(1 - cube root of 3)

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