I am assuming the both cylinders have the same measure of radius. They only differ in height.
Larger Cylinder = 343 ft³
Smaller Cylinder = 125 ft³ ; height = 5 ft.
We can use proportion for this problem; a:b = c:d where ad = bc
5 ft :125 ft³ = x : 343ft³
5 ft * 343 ft³ = 125 ft³ * x
1715 ft⁴ = 125 ft³ * x
1715 ft⁴ ÷ 125 ft³ = x
13.72 ft = x height of the larger cylinder.
Cone S = 768pi cm³
Cone T = 6144pi cm³ ; height = 24 cm
24 cm : 6144 cm³ = x : 768 cm³
24 cm * 768 cm³ = 6144 cm³ * x
18,432 cm⁴ = 6144 cm³ * x
18,432 cm⁴ ÷ 6,144 cm³ = x
3 cm = x height of Cone S.
Answer:
Element wise subtraction.
Step-by-step explanation:
Matrix Subtraction is done element wise.
Therefore, D = ![\[ \left[ {\begin{array}{ccc} 3 & 1 & 0 \\ -1 & 2 & 4 \\9 & 7 & -2 \end{array} } \right]\]](https://tex.z-dn.net/?f=%5C%5B%20%20%5Cleft%5B%20%7B%5Cbegin%7Barray%7D%7Bccc%7D%20%20%203%20%26%201%20%26%200%20%5C%5C%20%20%20-1%20%26%202%20%26%204%20%5C%5C9%20%26%207%20%26%20-2%20%20%5Cend%7Barray%7D%20%7D%20%5Cright%5D%5C%5D)
- ![\[ \left[ {\begin{array}{ccc} 5 & 2 & -4\\ 1 & 12 & 3 \\ 11 & 3 & -2 \end{array} } \right]\]](https://tex.z-dn.net/?f=%5C%5B%20%20%5Cleft%5B%20%7B%5Cbegin%7Barray%7D%7Bccc%7D%20%20%205%20%26%202%20%26%20-4%5C%5C%20%20%201%20%26%2012%20%26%203%20%5C%5C%2011%20%26%203%20%26%20-2%20%20%5Cend%7Barray%7D%20%7D%20%5Cright%5D%5C%5D)
This becomes:
![\[ D = \left[ {\begin{array}{ccc} -2 & -1 & 4 \\ -2 & -10 & 1 \\ -2 & 4 & 0 \end{array} } \right]\]](https://tex.z-dn.net/?f=%5C%5B%20%20%20D%20%3D%20%20%5Cleft%5B%20%7B%5Cbegin%7Barray%7D%7Bccc%7D%20%20%20-2%20%26%20-1%20%26%204%20%5C%5C%20%20%20%20-2%20%26%20-10%20%26%201%20%5C%5C%20%20%20%20-2%20%26%204%20%26%200%20%20%5Cend%7Barray%7D%20%7D%20%5Cright%5D%5C%5D)
Now, 
Answer:
Step-by-step explanation:
The properties of addition and multiplication allow you to rearrange and/or regroup the components of a sum or a product. That is the point of this exercise.
(2·8)·7 = 2·(8·7) . . . . parentheses have moved: associative property
2 + 7 + 8 = 8 + 2 + 7 . . . . order is rearranged: commutative property
5·3·12 = 12·5·3 . . . . . order is rearranged: commutative property
(3 +5) +12 = 3 +(5 +12) . . . . parentheses have moved: associative property
_____
<em>Additional comment</em>
Whenever you're in doubt about the equivalence of numerical expressions, you can use your calculator to evaluate them. They will give the same result if they are equivalent. (You need a good scientific or graphing calculator that uses parentheses for this. Some seriously good calculators are available as low-cost phone apps.)
The Google search box also serves as input to the Google calculator. You can use an asterisk (*) for multiplication.
