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2 years ago

Please help!!!

Mathematics

1 answer:

Fudgin [204]2 years ago

3 0

Answer:

Part 1) 12, 31, 9, 20, 36, 5, 22

Sort the data:

5, 9, 12, 20, 22, 31, 36

Median: 20

First Quartile: 9

Third Quartile: 31

IQR: 31 - 9 = 22

and

Part 2) 63, 68, 58, 77, 50, 49, 63, 73

Sort the data:

49, 50, 58, 63, 63, 68, 73, 77

Median: (63÷63)/2 = 63

First Quartile: (50+58)/2 = 54

Third Quartile: (68+73)/2 = 70.5

IQR: 70.5 - 54 = 16.5

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At what point does the curve have maximum curvature? Y = 4ex (x, y) = what happens to the curvature as x → ∞? Κ(x) approaches as

MAXImum [283]

<u>Answer-</u>

At $x= \frac{1}{2304e^4-16e^2}$ the curve has maximum curvature.

<u>Solution-</u>

The formula for curvature =

$K(x)=\frac{{y}''}{(1+({y}')^2)^{\frac{3}{2}}}$

Here,

$y=4e^{x}$

Then,

${y}' = 4e^{x} \ and \ {y}''=4e^{x}$

Putting the values,

$K(x)=\frac{{4e^{x}}}{(1+(4e^{x})^2)^{\frac{3}{2}}} = \frac{{4e^{x}}}{(1+16e^{2x})^{\frac{3}{2}}}$

Now, in order to get the max curvature value, we have to calculate the first derivative of this function and then to get where its value is max, we have to equate it to 0.

${k}'(x) = \frac{(1+16e^{2x})^{\frac{3}{2} } (4e^{x})-(4e^{x})(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})}{(1+16e^{2x} )^{2}}$

Now, equating this to 0

$(1+16e^{2x})^{\frac{3}{2} } (4e^{x})-(4e^{x})(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x}) =0$

$\Rightarrow (1+16e^{2x})^{\frac{3}{2}}-(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})$

$\Rightarrow (1+16e^{2x})^{\frac{3}{2}}=(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})$

$\Rightarrow (1+16e^{2x})^{\frac{1}{2}}=48e^{2x}$

$\Rightarrow (1+16e^{2x})}=48^2e^{2x}=2304e^{2x}$

$\Rightarrow 2304e^{2x}-16e^{2x}-1=0$

Solving this eq,

we get $x= \frac{1}{2304e^4-16e^2}$

∴ At $x= \frac{1}{2304e^4-16e^2}$ the curvature is maximum.

6 0

2 years ago

Please help, no links or i will report

ch4aika [34]

Answer:

i believe 1/5

Step-by-step explanation:

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2 years ago

Read 2 more answers

If (5^2)p = 5^12, what is the value of p?

mr Goodwill [35]

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2 years ago

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Answer:

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Step-by-step explanation:

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