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3 years ago

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The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass

. Starting with 220 grams of a radioactive isotope, how much will be left after 5 half-lives?

1 answer:

Setler [38]3 years ago

7 0

Answer:

$\boxed{6.875 \text{\: grams}}$

Step-by-step explanation:

Half-lives are how long it takes for half of a substance to decay. If you start with a certain amount and it decays for a certain amount of half-lives, you are dividing by $2^{x}$ , where <em>x</em> is equal to the amount of half-lives.

In order to solve this question, simply divide the starting value by 2 raised to the value of half-lives.

$\large\boxed{\frac{220}{2^{5}}=6.875\text{\: grams}}$

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Which set of coefficients of the terms in the Expansion of the binomial (x+y)^3 is correct?

lora16 [44]

A is correct.

Why? After opening the brackets we can see the equation as $x^{3} + 3x^{2}y + 3y^{2}x + y^{3}$

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3 years ago

A farmer has 300 ft of fence to enclose 2 adjacent rectangular pens bordering his barn. Find the maximum area he can close.

Margarita [4]

Answer:

Width of 37.5 feet and length of 50 feet will maximize the area.

Step-by-step explanation:

Let w represent width and l represent length of the pen.

We have been given that a farmer has 300 ft of fence to enclose 2 adjacent rectangular pens bordering his barn. We are asked to find the dimensions that will maximize the area.

We can see from the attachment that the perimeter of the pens would be $4w+3l$ .

We can set our given information in an equation $4w+3l=300$ .

The area of the two pens would be $A=2l\cdot w$ .

From perimeter equation, we will get:

$w=\frac{300-3l}{4}$

Substituting this value in area equation, we will get:

$A=2l\cdot (\frac{300-3l}{4})$

Since we need to maximize area, so we need to find derivative of area function as:

$A=\frac{600l-6l^2}{4}$

Bring out the constant:

$A=\frac{1}{4}*\frac{d}{dl}(600l-6l^2)$

$A=\frac{1}{4}*(600-12l)$

$A=150-3l$

Now, we will set our derivative equal to 0 as:

$150-3l=0$

$150=3l$

$\frac{150}{3}=\frac{3l}{3}$

$50=l$

Now, we will substitute $l=50$ in equation $w=\frac{300-3l}{4}$ to solve for width as:

$w=\frac{300-3(50)}{4}$

$w=\frac{300-150}{4}$

$w=\frac{150}{4}$

$w=37.5$

Therefore, width of 37.5 feet and length of 50 feet will maximize the area.

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3 years ago

Solve the folllowing quadratic equation by using the square root property.(2x-3)^2=100

Pani-rosa [81]

To solve:
find the square root of both sides

2x-3=±10

Answers:
x=-7/2
x=13/2

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3 years ago

The area of the following rectangle is 6O and^4 square meters and its length is 30 and meters

blsea [12.9K]

Answer:35

Step-by-step explanation: uhhhhh google

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3 years ago

Andrew is elder to Brian by 2 years. Andrew's father Frank is twiceas old as Andrew, and Brian is twice as old as his sister Sar

babunello [35]

Let "x" represent the age of Brian.

Andrew is elder than Brian by 2 years, we can symbolize his age as "x+2"

Frank is twice as old as Andrew, we can symbolize his age as "2(x+2)"

Sarah has half the age of Brian's, we can symbolize her age as "x/2"

Frank ans Sarah's ages differ by 40 years, we can symbolize this as:

$2(x+2)-\frac{x}{2}=40$

Solve the term is parenthesis

$\begin{gathered} 2x+4-\frac{1}{2}x=40 \\ 2x-\frac{1}{2}x+4=40 \\ \frac{3}{2}x=40-4 \\ \frac{3}{2}x=36 \\ x=24 \end{gathered}$

x=24 years

Andrew's age is

$x+2=24+2=26$

Andrew is 26 years old

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1 year ago