This solution to this problem is predicated on the fact that the circumference is just: $2\pir$ . A straight line going through the center of the garden would actually be the diameter, which is well known to be two times the radius of the circle, so we can say that the circumference is just:

$d\pi$

So, solving for both the radius and the diameter gives us:

$d\pi=8xy^2\pi\\ d=8xy^2\\ \\ 2\pi r=8xy^2\pi\\ r=4xy^2$

So, the length of thes traight path that goes through the center of the guardain is just $8xy^2$ , and we can use the radius for the next part of the problem.

The area of a circle is $\pi r^2$ , which means we can just plug in the radius and find our area:

$A=\pi r^2 \implies \\ A=\pi (4xy^2)^2\implies \\ A= 16\pi x^2y^4$

So, we have found our area( $16 \pi x^2 y^4$ ) and the problem is done.

6 0

2 years ago

The "sum" of two numbers is: A the result when both numbers are added together B the result when the first number is subtracted

Irina-Kira [14]

Answer:

A the result when both numbers are added together

5 0

2 years ago

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A user’s password to access a computer system consists of 3 letters followed by 2 digits. How many different passwords are possi

Vesnalui [34]

Answer:

26*26*26 = 17576 ways to select 3 letters

10*10= 100 ways to select 2 numbers

So then the total number of ways are:

$26^3 *10^2 = 1757600$ possible ways

Step-by-step explanation:

For this case we assume that we have 26 letters from A to Z and 10 numbers from 0 to 9 .

And we want to calculate the number of possible passwords possible if the password consists of 3 letters followed by 2 digits.

And for this case we can use the multiplication principle of combinatories, since we don't have any restriction about the letters of the numbers we can have repetition of letters or numbers.

For the number of possible letters:

26*26*26 = 17576 ways to select 3 letters

10*10= 100 ways to select 2 numbers

So then the total number of ways are:

$26^3 *10^2 = 1757600$ possible ways

7 0

2 years ago

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Table show step by step how do you simplify the algebraic expression 3(x-5)+4x. <br>Justify step 4

ale4655 [162]

<h3>Answer: Commutative Property (choice C)</h3>

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Explanation:

Here are all of the justifications for each step

Step 1. None needed. This is the original expression
Step 2. Distributive property
Step 3. Multiply (the 3 and 5 multiply to 15)
Step 4. Commutative property. Specifically, this is the commutative property of addition which allows us to add any two numbers in any order we want. In this case, the -15 and 4x terms swap places.
Step 5. Associative property. The parenthesis group the first two terms away from the third term.
Step 6. Combine like terms. Both 3x and 4x have an x only so they are like terms that combine to 7x. You can think of it as 3+4 = 7, then you just tack an x onto everything to get 3x+4x = 7x.

6 0

2 years ago