You've told us the volume of the carton.
That doesn't tell us the dimensions.
If the unit cubes have to exactly fit the dimensions,
then all we know is that the dimensions are integers,
and their product is 1,000.
The carton could be
1 by 1 by 1,000
1 by 2 by 500
1 by 4 by 250
1 by 5 by 200
1 by 8 by 125
1 by 10 by 100
1 by 20 by 50
1 by 25 by 40
2 by 2 by 250
2 by 5 by 100
2 by 10 by 50
.
.
and several other possible sets.
Answer:
81π
Step-by-step explanation:
-The sum of central angles in a circle add up to 360°.
-Let x be the area of the circle.
-Given the area of a 120° is 27π, the circles area can be calculated as:
Hence, the area of the circle is 81π
Answer:
First odd number = 13
Second odd number = 15
Step-by-step explanation:
Let
First odd number = 2x + 1
Second odd number = 2x + 3
According to given conditions:
32 + 2x + 1= 3 (2x + 3)
33 + 2x = 6x + 9
Taking terms with x to left and constants to right
2x - 6x = 9 - 33 (sign of transferred terms will be changed)
-4x = -24
Dividing both sides by -4
x = -24/-4
x =6
So,
First odd number = 2x + 1 = 2*6 + 1 = 12 + 1 =13
Second odd number = 2x + 3= 2*6 +3= 12 + 3 = 15
I hope it will help you!
Answer:
![\left[\begin{array}{ccc}3&-1&\\-1&1/2\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%26-1%26%5C%5C-1%261%2F2%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
The matrix system for the linear equations: x + 2y = 8, 2x + 6y = 9
![\left[\begin{array}{ccc}1&2&\\2&6\\\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}8\\9\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%262%26%5C%5C2%266%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%5C%5C9%5Cend%7Barray%7D%5Cright%5D)
To get the coefficient of x and y, the inverse of the first matrix (let the first matrix be A) must be known.
= (1 / determinant of A) x Adjoint of A
the determinant of A = (1 x 6) - (2 x 2) = 6 - 4 = 2
Adjoint of A = ![\left[\begin{array}{ccc}6&-2&\\-2&1\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D6%26-2%26%5C%5C-2%261%5C%5C%5Cend%7Barray%7D%5Cright%5D)
= ![\frac{1}{2} \left[\begin{array}{ccc}6&-2\\-2&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D6%26-2%5C%5C-2%261%5Cend%7Barray%7D%5Cright%5D)
=
