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3 years ago

justin has 3x+12 songs jim has 5x-4 songs if they both have the same number of songs how many songs do they each have?

2 answers:

7 0

$*\\Justin's\ songs-\ \ 3x+12\\
Jim's\ songs-\ \ 5x-4\\\\The\ same\ amount\ so:\\
3x+12=5x-4\ \ \ |Subtract\ 3x\\
12=2x-4\ \ \ |Add\ 4\\
16=2x\ \ |Divide\ by\ 2\\
x=8\\\\3x+12=3*8+12=24+12=36\\5x-4=5*8-4=40-4=36\\\\
Justin\ has\ 36\ sons\ and\ Jim\ has\ also\ 36\ songs.$

Marina CMI [18]3 years ago

5 0

According to the quesiton;

3x + 12 = 5x -4
12 + 4 = 5x - 3x
16 = 2x
16 / 2 = x
8 = x
x = 8

Now, substituting the value of "x" in one of the equation, we get,
3x + 12
= 3 (8) + 12
= 24 + 12
= 36

5x- 4 = 36 ...........because according to the question, 3x + 12 = 5x - 4

So, each of them have 36 songs

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It looks like you're given

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F (0) = 5

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The first is done for you, F (0) = 5.

For the remaining b, you can solve for F(x) exactly by using the fundamental theorem of calculus:

$F(x)=F(0)+\displaystyle\int_0^x F'(t)\,\mathrm dt$

$F(x)=5+\displaystyle\int_0^x(3t^2+7)\,\mathrm dt$

$F(x)=5+(t^3+7t)\bigg|_0^x$

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Then F (0.1) = 5.701, F (0.2) = 6.408, F (0.5) = 8.625, and F (2.0) = 27.

On the other hand, if you're expected to approximate F at the given b, you can use the linear approximation to F(x) around x = 0, which is

F(x) ≈ L(x) = F (0) + F' (0) (x - 0) = 5 + 7x

Then F (0) = 5, F (0.1) ≈ 5.7, F (0.2) ≈ 6.4, F (0.5) ≈ 8.5, and F (2.0) ≈ 19. Notice how the error gets larger the further away b gets from 0.

A better numerical method would be Euler's method. Given F'(x), we iteratively use the linear approximation at successive points to get closer approximations to the actual values of F(x).

Let y(x) = F(x). Starting with x₀ = 0 and y₀ = F(x₀) = 5, we have

x₁ = x₀ + 0.1 = 0.1

y₁ = y₀ + F'(x₀) (x₁ - x₀) = 5 + 7 (0.1 - 0) → F (0.1) ≈ 5.7

x₂ = x₁ + 0.1 = 0.2

y₂ = y₁ + F'(x₁) (x₂ - x₁) = 5.7 + 7.03 (0.2 - 0.1) → F (0.2) ≈ 6.403

x₃ = x₂ + 0.3 = 0.5

y₃ = y₂ + F'(x₂) (x₃ - x₂) = 6.403 + 7.12 (0.5 - 0.2) → F (0.5) ≈ 8.539

x₄ = x₃ + 1.5 = 2.0

y₄ = y₃ + F'(x₃) (x₄ - x₃) = 8.539 + 7.75 (2.0 - 0.5) → F (2.0) ≈ 20.164

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