All categories

3 years ago

Give the greatest common divisor of $6^3$ and $3^6$.

Mathematics

2 answers:

zysi [14]3 years ago

8 0

Answer:

Step-by-step explanation:

Greatest common divisor is the largest positive integer that divides each integer in the given problem

6³ = (2* 3)³ = 2³ * 3³

3⁶ = 3³ * 3³

Greatest common divisor = 3³ = 3* 3* 3 = 27

Lady bird [3.3K]3 years ago

3 0

Answer:

Step-by-step explanation:

Since 3^6 is only divisible by 3 and powers of 3(including 1) the gcd of 3^6 and 6^3 mus be a power of 3 hence we need to find the highest powers of 3 that divide 6^3 and that divide 3^6, which are respectively 3^3 and 3^6, hence, taking the smaller one (since we want it to divide both), our answer is 3^3=27.

You might be interested in

Generate an equivalent expression using prime factorization for each number.

Mice21 [21]

Answer:

Step-by-step explanation:

Is ur answer !!

5 0

2 years ago

What are the coordinates of the pre-image of N' if it was reflected across the y-axis, and N' has coordinates (3, -1)? Please ex

borishaifa [10]

The answer would be (3,-1) because it is reflected

6 0

3 years ago

Vincent needs 30 inches of wood to make 1 shelf how many feet of wood dose Vincent need to make 6 shelves

babymother [125]

Answer:

Step-by-step explanation:

We can assume each shelve takes the same amount of wood to make. So if 30 inches are needed for one shelve, 30*6 inches of wood will be needed for 6 shelves. 30*6=180, so 180 inches of wood is needed to make 6 shelves. However, the question asks for the final answer to be in feet. There are 12 inches in a foot so we can divide by 12 to find the amount of feet needed to make 6 shelves. 180/12=15. Therefore, 15 feet are needed to make 6 shelves.

7 0

3 years ago

$5,000 is deposited today into a bank account. The account earns 7.5% per annum compounded half yearly for the first 6 years, th

kvv77 [185]

Answer:

The account balance six months from today is $5,187.5.

Step-by-step explanation:

This is a compound interest problem

The compound interest formula is given by:

$A = P(1 + \frac{r}{n})^{nt}$

In which A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

In this problem, we have that

The total amount formula changes after 6 years, at which point each of the principal(initial money), interest rate, and n changes.

This item asks only the balance six months from today, so we use the information given for the first 6 years.

A is the account balance, the value we hope to find.

The loan is of $5,000. So $P = 5,000$

The account earns 7.5% per annum compounded half yearly, so $r = 0.075, n = 2$ .

We want to find the account balance in 6 months. However, t is measured in years. So $t = \frac{6}{12} = 0.5$

Solving the equation:

$A = P(1 + \frac{r}{n})^{nt}$

$A = 5,000(1 + \frac{0.075}{2})^{1}$

$A = 5,187.5$

The account balance six months from today is $5,187.5.

8 0

3 years ago

An airplane has an air speed of 520 mph with a heading of 215 degrees. Find the plane's ground speed and course if it encounters

a_sh-v [17]

<span>Assuming east is positive x, north is positive y, break down the airplane's velocity into a vector in the x-y plane.
The plane is traveling 340 mph at a bearing of 210 degrees or (340cos(210), 340 sin(210)).
The wind is blowing from the west (to the east) at 50 mph or (50,0).
The actual ground speed would be the vector sum of those two (340 cos(210)+50, 340 sin(210)) or (-294.4+50,-170) or (-244.4,-170).
The magnitude of that velocity vector is

For direction

Since this angle is measured from the (-y) axis, we add 180 to get the actual heading.
The plane is traveling at 297.8 mph at a heading of 214.8 degrees. </span>

5 0

3 years ago

Read 2 more answers