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4 years ago

5

A cube shaped terrarium has a volume of 27/64 cubic feet. what is the length of its sides?

1 answer:

wariber [46]4 years ago

6 0

Bearing in mind that a cube is just a rectangular prism with all sides of the same length.

check the picture below.

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A common inhabitant of human intestines is the bacterium Escherichia coli, named after the German pediatrician Theodor Escherich

Bess [88]

Answer:

a). k = 2.0794

b). $A_{t}=A_{0}(2^{3t} )$

c). 13107200 cells

d). rate of growth after 6 hours = 27255112

e). 4.76 hours

Step-by-step explanation:

From the formula of bacterial population,

$A_{t}=A_{0}e^{kt}$

Where $A_{t}$ = Bacterial population after time t

$A_{0}$ = Initial population

k = relative growth factor

t = duration or time

a). For $A_{t}=2\times 50=100$ cells

and $A_{0}=50$ cells

Time t = 20 minutes = $\frac{1}{3}$ hours

Now we plug in these values in the formula,

100 = $50(e^{\frac{k}{3}})$

$e^{\frac{k}{3}}=2$

By taking natural log on both the sides of the equation,

$\frac{k}{3}(lne)=ln(2)$

k = 3ln(2) = 2.0794

b). To get the expression we will plug in the value of k in the formula.

$A_{t}=A_{0}e^{kt}$

Since k = 3ln(2)

$A_{t}=A_{0}e^{3t(ln2)}$

Let y = $e^{3t(ln2)}$

By taking natural log on both the sides of the equation,

lny = $ln(e^{3t(ln2)} )$

lny = 3t(ln2)ln(e)

ln(y) = 3t(ln2)

ln(y) = $ln(2)^{3t}$

y = $2^{3t}$

Now our expression will be $A_{t}=A_{0}(2^{3t} )$

c). Number of cells after t = 6 hours

$A_{6}=50(2^{3\times 6} )$

$A_{6}=50(2^{18})$

$A_{6}=50\times (262144)=13107200$

d). We can get the rate of growth by finding derivative of the expression

$\frac{d}{dt}(A_{t})=\frac{d}{dt}[A_{0}(e^{kt}})]$

= $A_{0}[ke^{kt}]$

Now $\frac{d}{dt}(A_{6})=k.A_{6}$

= 2.0794×13107200

= 27255112

e) From the given formula,

$A_{t}=A_{0}(2^{3t} )$

$1000000=50(2^{3t} )$

$2^{3t}=20000$

3t(ln2) = ln(20000)

t = $\frac{ln(20000)}{3(ln2)}$

t = $\frac{9.90349}{2.07944}=4.76$ hours

3 0

3 years ago

Solve and graph -12 <= x - 6 <= -2

Levart [38]

Answer:

4780373 ykitttuyyu

Step-by-step explanation:

brugegentug yktgdcm vylkg

6 0

3 years ago

The area of a circle is 9π in². What is the circumference, in inches? Express your answer in terms of \piπ

dangina [55]

Answer:

$6\pi$ in

Step-by-step explanation:

The formula to find the area of a circle: $\pi r^{2}$ , where $r$ is the radius.

The formula to find the circumference (perimeter) of a circle: $2\pi r$ , where $r$ is the radius.

1) To find the circumference of the circle, we need to find the radius ( $r$ ) first. Since the area of the circle is given to us, we need to equate this to the formula to find the area of a circle.

$9\pi =\pi r^2$

Cancel the $\pi$ by bringing it to the other side.

$9 =\pi r^2$ ÷ $\pi$

$9 = r^2\\\sqrt{9} = r\\3 = r$

2) Find the circumference of the circle by using the formula, $2\pi r$ .

= $2*\pi *3$

= $6\pi$ in

3 0

3 years ago

I’LL GIVE BRAINLIEST!

astraxan [27]

Answer:

what grade are you

Step-by-step explanation:

5 0

3 years ago

The inverse of the function f(x) = x + 10 is shown.

Vadim26 [7]

we have

$f(x) = \frac{1}{2}x + 10$

Step $1$

Let

y=f(x)

$y = \frac{1}{2}x + 10$

Exchange the variable x for y and variable y for x

$x = \frac{1}{2}y + 10$

Clear variable y

Multiply by $2$ both sides

$2x = y + 20$

$y = 2x-20$

Let

$f(x)^{-1} =y$

$f(x)^{-1}=2x-20$

therefore

the answer is

the inverse of the function is $f(x)^{-1}=2x-20$

the missing value is $20$

5 0

3 years ago

Read 2 more answers