Ask question

Ask question

All categories

2 years ago

8

Doctors can use radioactive chemicals to treat some forms of cancer. The half life of a certain chemical is 7 days. A patient re

ceives a treatment of 20 millicuries of the chemical. (A millicurie is a unit of radioactivity.) How much of the chemical remains in the patient 14 days later? The amount remaining after 14 days is ____ millicuries.

1 answer:

RoseWind [281]2 years ago

6 0

Answer:

5 millicuries

Step-by-step explanation:

Half life is 7 days which means it will be at 10 millicuries if we half that again for another 7 days then it will be 5.

You might be interested in

If the values in the table below model a proportional relationship, what is the equation for the function?

Jet001 [13]

Given:

The table represents a proportional relationship.

To find:

The equation of the function.

Solution:

If y is directly proportional to x, then

$y\propto x$

$y=kx$ ...(i)

where, k is the constant of proportionality.

From the given table it is clear that the function passes through (2,1). So, the equation must be satisfied by the point (2,1).

Putting x=2 and y=1 in (i), we get

$1=k(2)$

$\dfrac{1}{2}=k$

Putting $k=\dfrac{1}{2}$ , we get

$y=\dfrac{1}{2}x$

Therefore, the correct option is A.

6 0

3 years ago

The angle of elevation from me to the top of a hill is 51 degrees. The angle of elevation from me to the top of a tree is 57 deg

julia-pushkina [17]

Answer:

Approximately $101\; \rm ft$ (assuming that the height of the base of the hill is the same as that of the observer.)

Step-by-step explanation:

Refer to the diagram attached.

Let $\rm O$ denote the observer.
Let $\rm A$ denote the top of the tree.
Let $\rm R$ denote the base of the tree.
Let $\rm B$ denote the point where line $\rm AR$ (a vertical line) and the horizontal line going through $\rm O$ meets. $\angle \rm B\hat{A}R = 90^\circ$ .

Angles:

Angle of elevation of the base of the tree as it appears to the observer: $\angle \rm B\hat{O}R = 51^\circ$ .
Angle of elevation of the top of the tree as it appears to the observer: $\angle \rm B\hat{O}A = 57^\circ$ .

Let the length of segment $\rm BR$ (vertical distance between the base of the tree and the base of the hill) be $x\; \rm ft$ .

The question is asking for the length of segment $\rm AB$ . Notice that the length of this segment is $\mathrm{AB} = (x + 20)\; \rm ft$ .

The length of segment $\rm OB$ could be represented in two ways:

In right triangle $\rm \triangle OBR$ as the side adjacent to $\angle \rm B\hat{O}R = 51^\circ$ .
In right triangle $\rm \triangle OBA$ as the side adjacent to $\angle \rm B\hat{O}A = 57^\circ$ .

For example, in right triangle $\rm \triangle OBR$ , the length of the side opposite to $\angle \rm B\hat{O}R = 51^\circ$ is segment $\rm BR$ . The length of that segment is $x\; \rm ft$ .

$\begin{aligned}\tan{\left(\angle\mathrm{B\hat{O}R}\right)} = \frac{\,\rm {BR}\,}{\,\rm {OB}\,} \; \genfrac{}{}{0em}{}{\leftarrow \text{opposite}}{\leftarrow \text{adjacent}}\end{aligned}$ .

Rearrange to find an expression for the length of $\rm OB$ (in $\rm ft$ ) in terms of $x$ :

$\begin{aligned}\mathrm{OB} &= \frac{\mathrm{BR}}{\tan{\left(\angle\mathrm{B\hat{O}R}\right)}} \\ &= \frac{x}{\tan\left(51^\circ\right)}\approx 0.810\, x\end{aligned}$ .

Similarly, in right triangle $\rm \triangle OBA$ :

$\begin{aligned}\mathrm{OB} &= \frac{\mathrm{AB}}{\tan{\left(\angle\mathrm{B\hat{O}A}\right)}} \\ &= \frac{x + 20}{\tan\left(57^\circ\right)}\approx 0.649\, (x + 20)\end{aligned}$ .

Equate the right-hand side of these two equations:

$0.810\, x \approx 0.649\, (x + 20)$ .

Solve for $x$ :

$x \approx 81\; \rm ft$ .

Hence, the height of the top of this tree relative to the base of the hill would be $(x + 20)\; {\rm ft}\approx 101\; \rm ft$ .

6 0

3 years ago

What is the volume of a right circular cylinder with a radius of 5 cm and a height of 12 cm?

dexar [7]

Answer:

Answer C

Step-by-step explanation:

Formula

Volume = pi * r^2 * h

Givens

r = 5 cm
h = 12 cm

Solution

V = pi * 5^2 * 12
V = pi * 25 * 12
V = 300 pi

Answer = C

8 0

3 years ago

In which pair of numbers is the first number a multiple of the second number?

Sedaia [141]

Answer:

27,9

Step-by-step explanation:

9x3=27

5 0

3 years ago

Convert 0.00049 to scientific notation.

SOVA2 [1]

It's 10 - 4

moving decimal over to the right makes a negative exponent.

7 0

3 years ago

Read 2 more answers