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lidiya [134]
3 years ago
13

How many 1/8 inch cubes fill the rectangular prism?

Mathematics
1 answer:
zepelin [54]3 years ago
5 0
You are correct it's 36 9/16
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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
3 years ago
Help me correct this plz
adelina 88 [10]
The answer will be D) 75

To find this it’s easiest to find how many animals there are per percent. So to find this you simply have to divide 30 (the number of cats) by 40 (the percent that makes up) to find the number of animals per percent.

30/40

.75

Then you multiply this by 100 to find how many animals there are total.

.75(100)

75

5 0
3 years ago
Read 2 more answers
C=2pir; r=4.6 find c
ratelena [41]

C = 2 * pi(3.14) * 4.6


C ~ 28.903

3 0
3 years ago
WILL GIVE BRAINLIEST
Luda [366]
1A
2C
3A
Give me brainliest
6 0
3 years ago
The end of a pendulum with a length of 21 cm travels an arc length of 24 cm. How many degrees does the pendulum swing?
Tanya [424]

It is given in the question that the end of a pendulum with a length of 21 cm travels an arc length of 24 cm.

So here radius is 21 cm and the arc length is 24 cm .

Now we use the arc length formula , which is

s = r* \theta

Where s is the arc length and r is the radius.

Substituting these values, we will get

24 = 21 \theta&#10;\\&#10;\theta = \frac{24}{21}&#10;\\&#10;\theta = 1.143 radians

And now we need to convert radian to degree, and for that we have to multiply by \frac{180}{ \pi}

That is

1.143 * \frac{180}{ \pi} =65.48 degree

4 0
3 years ago
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