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2 years ago

Help this due today

Mathematics

1 answer:

Romashka [77]2 years ago

8 0

Answer:

the answer is b because a squared plus b squared is c squared

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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]

Answer-

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

Solution-

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

A Youth chorus of 30 members. There are 14 boys in the chorus. What is the ratio of boys to girls in the simplest form?

Bingel [31]

Answer:

C PLEASE GIVE BRAINLIEST

Step-by-step explanation:

30 - 14 = 16girls

ratio is : 14/16 = 7/8

5 0

2 years ago

A square is inscribed in the circle. A point in the figure is selected at random. Find the probability that the point will be in

Snezhnost [94]

Ok
Probability (the point will be on unshaded part) = area of unshaded part / area of the circle.

= pi r^2 - s^2
-------------- where r = radius of circle and s = length of the side of the square.
pi r^2

4 0

3 years ago

I NEED HELP!!! ASAP!

iren2701 [21]

I think the correct answer is B.

7 0

2 years ago

Which inequality represents this sentence?

babymother [125]

Answer:

n ≥ 65

Step-by-step explanation:

A number is at least 65. It means the number n can be 65 or greater.

Its translation is:

n ≥ 65

The answer options don't have this included.

3 0

2 years ago

Read 2 more answers