Ask question

Ask question

All categories

3 years ago

9

Cobalt-60 has an annual decay rate of about 13%.

2 answers:

Nesterboy [21]3 years ago

4 0

<h2>Answer:</h2>

Option: C is the correct answer.

C. 18.51 g

<h2>Step-by-step explanation:</h2>

The situation of this problem can be modeled with the help of the exponential decay function :

i.e. any component if it has a initial amount as a units and is decaying at a rate of r% then the amount after t years is given by:

$n(t)=a(1-\dfrac{r}{100})^t$

Here we have:

r=13%

and a=300 g

and t=20 years

Hence, we have

$n(20)=300\cdot (1-\dfrac{13}{100})^{20}\\\\i.e.\\\\n(20)=300\cdot (1-0.13)^{20}\\\\i.e.\\\\n(20)=300\cdot (0.87)^{20}\\\\n(20)=300\cdot 0.061714\\\\i.e.\\\\n(20)=18.5142\ g$

The amount that will be left after 20 years is: 18.51 g

melomori [17]3 years ago

3 0

The answer will be c

You might be interested in

Is the spinner shown a fair spinner?Explain why or why not.

enyata [817]

Answer:

a

Step-by-step explanation:

4 0

3 years ago

A punch glass is in the shape of a hemisphere with a radius of 5 cm. If the punch is being poured into the glass so that the cha

Galina-37 [17]

Answer:

28.27 cm/s

Step-by-step explanation:

Though Process:

The punch glass (call it bowl to have a shape in mind) is in the shape of a hemisphere
the radius $r=5cm$
Punch is being poured into the bowl
The height at which the punch is increasing in the bowl is $\frac{dh}{dt} = 1.5$
the exposed area is a circle, (since the bowl is a hemisphere)
the radius of this circle can be written as $'a'$

what is being asked is the rate of change of the exposed area when the height $h = 2 cm$
the rate of change of exposed area can be written as $\frac{dA}{dt}$ .
since the exposed area is changing with respect to the height of punch. We can use the chain rule: $\frac{dA}{dt} = \frac{dA}{dh} . \frac{dh}{dt}$

and since $A = \pi a^2$ the chain rule above can simplified to $\frac{da}{dt} = \frac{da}{dh} . \frac{dh}{dt}$ -- we can call this Eq(1)

Solution:

the area of the exposed circle is

$A =\pi a^2$

the rate of change of this area can be, (using chain rule)

$\frac{dA}{dt} = 2 \pi a \frac{da}{dt}$ we can call this Eq(2)

what we are really concerned about is how $a$ changes as the punch is being poured into the bowl i.e $\frac{da}{dh}$

So we need another formula: Using the property of hemispheres and pythagoras theorem, we can use:

$r = \frac{a^2 + h^2}{2h}$

and rearrage the formula so that a is the subject:

$a^2 = 2rh - h^2$

now we can derivate a with respect to h to get $\frac{da}{dh}$

$2a \frac{da}{dh} = 2r - 2h$

simplify

$\frac{da}{dh} = \frac{r-h}{a}$

we can put this in Eq(1) in place of $\frac{da}{dh}$

$\frac{da}{dt} = \frac{r-h}{a} . \frac{dh}{dt}$

and since we know $\frac{dh}{dt} = 1.5$

$\frac{da}{dt} = \frac{(r-h)(1.5)}{a}$

and now we use substitute this $\frac{da}{dt}$ . in Eq(2)

$\frac{dA}{dt} = 2 \pi a \frac{(r-h)(1.5)}{a}$

simplify,

$\frac{dA}{dt} = 3 \pi (r-h)$

This is the rate of change of area, this is being asked in the quesiton!

Finally, we can put our known values:

$r = 5cm$

$h = 2cm$ from the question

$\frac{dA}{dt} = 3 \pi (5-2)$

$\frac{dA}{dt} = 9 \pi cm/s// or//\frac{dA}{dt} = 28.27 cm/s$

5 0

3 years ago

Solve the equation using square roots.<br> 2(x + 1)2 - 7 = 25<br> solution: x=

denpristay [2]

x=7

I'm sorry if I'm wrong

8 0

3 years ago

f is a differentiable function on the interval [0, 1] and g(x) = f(4x). The table below gives values of f '(x). What is the valu

polet [3.4K]

The table is attached in the figure.

g(x) = f(4x) ⇒⇒⇒ differentiating both sides with respect to x

∴ g'(x) = $\frac{d}{dx} [f(x)] * \frac{d}{dx} [4x]=4*f'(x)$ ⇒⇒⇒⇒⇒⇒ chain role

To find g '(0.1)

Substitute with x = 0.1

from table:

f'(0.1) = 1 ⇒ from the table

∴ g'(0.1) = 4 * [ f'(0.1) ] = 4 * 1 = 4

5 0

3 years ago

Help me with number 2 I need help fast with the right answer with showing work

Anvisha [2.4K]

Volume of a cylinder is defined as:

v = volume

r = radius

h = height.

V = $\pi$ (r^2)h

In this problem,

v = 1,356.48 in^3

r = 6 in

h = ?

Plug our numbers into the volume formula above.

1,356.48 in^3 = $\pi$ (6^2)h

Divide both sides by $\pi$ (6^2) to isolate variable h

12.0 = h

The height of the cylinder is 12.0 inches

4 0

3 years ago