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3 years ago

M is directly proportional to r cubed when r = 4, m = 160. Find the value of r when m = 540

Mathematics

1 answer:

Anarel [89]3 years ago

5 0

Answer:

r = 6

Step-by-step explanation:

Given that M is directly proportional to r³ then the equation relating them is

M = kr³ ← k is the constant of proportionality

To find k use the condition r = 4 when M = 160

k = $\frac{M}{r^3}$ = $\frac{160}{64}$ = 2.5, so

M = 2.5r³ ← equation of proportionality

When M = 540, then

540 = 2.5 r³ ( divide both sides by 2.5 )

216 = r³ ( take the cube root of both sides )

r = $\sqrt[3]{216}$ = 6

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ss7ja [257]

Solution :

Given

$f(x)=x^3-x-1, x_1=1$

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Let the initial approximation is $x_1 =1$

So by Newton's method, we get

$x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)},n=1,2,...$

$x_2=x_1-\frac{f(x_1)}{f'(x_1)}=1-\frac{1^3-1-1}{3(1)^2-1}=1.5$

$x_3=1.5-\frac{(1.5)^3-1.5-1}{3(1.5)^2-1}=1.34782608$

$x_4=1.34782608-\frac{(1.34782608)^3-1.34782608-1}{3(1.34782608)^2-1}=1.32520039$

$x_5=1.32520039-\frac{(1.32520039)^3-1.32520039-1}{3(1.32520039)^2-1}=1.32471817$

$x_6=1.32471817-\frac{(1.32471817)^3-1.32471817-1}{3(1.32471817)^2-1}=1.32471795$

$x_5 \approx x_6$ are identical up to eight decimal places.

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3 years ago

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mylen [45]

Answer:

Step-by-step explanation:

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3 years ago

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2 years ago

Based on 2017 sales, the six top-selling compact cars are the Honda Civic, Toyota Corolla, Nissan Sentra, Hyundai Elantra, Chevr

fgiga [73]

Answer:

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CONCLUSION: THERE IS DIFFERENCE IN MARKET SHARES

Step-by-step explanation:

H0 : there is no difference in market shares

H1: there is difference in market shares

Chisquare (X²) = (observed - Expected)²/ expected

Honda Civic - 0.20 * 400 = 80 : (98-80)^2 /80 = 4.05

Toyota Corolla - 0.17 * 400 = 68 : (72-68)²/68 = 0.235

Nissan Sentra - 0.12 * 400 = 48 : (54-48)²/48 = 0.75

Hyundai Elantra - 0.10 *400 = 40 : (44-40)²/40 = 0.4

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Reject H0 ; if Pvalue < α

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0.105 - 0.10 = 0.005

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3 years ago

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Firlakuza [10]

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