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RSB [31]
4 years ago
14

Jorge bought 3 DVDs, each for the same price, and a set of earphones for a price of $10. The total cost before tax was $49. What

was the cost of one DVD?
Mathematics
1 answer:
Ilia_Sergeevich [38]4 years ago
8 0

Answer:

The cost of each DVDs is $ 13   .

Step-by-step explanation:

Given as :

The cost of earphones = $ 10

The number of DVDs bought = 3

The total cost of both items before tax = $ 49

Let The cost of each DVDs = $ x

So, According to question

The cost of earphones + The cost of 3 DVDs  = $ 49

Or, $ 10 + 3 × x = $ 49

Or,  3 × x = $ 49 - $ 10

Or,  3 × x = $ 39

∴  x = \frac{39}{3}

I.e x = $ 13

Hence The cost of each DVDs is $ 13   . Answer

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Parameterize the paths

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  • from (2, 0, 0) to (2, 4, 1) by \vec r_2(t)=2\,\vec\imath+4t\,\vec\jmath+t\,\vec k with 0\le t\le1,
  • from (2, 4, 1) to (0, 4, 1) by \vec r_3(t)=(2-t)\,\vec\imath+4\,\vec\jmath+\vec k with 0\le t\le2, and
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The work done by \vec F over each segment (call them C_1,\ldots,C_4) is

\displaystyle\int_{C_1}\vec F\cdot\mathrm d\vec r_1=\int_0^2\vec0\cdot\vec\imath\,\mathrm dt=0

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\displaystyle\int_{C_3}\vec F\cdot\mathrm d\vec r_3=\int_0^2(\vec\imath+(24-12t)\,\vec\jmath+32\,\vec k)\cdot(-\vec\imath)\,\mathrm dr=-\int_0^2\mathrm dt=-2

\displaystyle\int_{C_4}\vec F\cdot\mathrm d\vec r_4=\int_0^1((1-t)^2\,\vec\imath+2(4-4t)^2\,\vec k)\cdot(-4\,\vec\jmath-\vec k)\,\mathrm dt=-2\int_0^1(4-4t)^2\,\mathrm dt=-\frac{32}3

Then the total work done by \vec F over the particle's path is 46.

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