Answer:
The volume of the prism is <u>320 15/16 inches³</u>.
Step-by-step explanation:
Given:
The length of the base of a rectangular prism is 9 7/8.
The width of the prism is 8 1/8.
And the height is 4 inches.
Now, to find the volume of the prism.
(Length) <em> l = 9 7/8 = 79/8 inches.</em>
(Width) <em> w = 8 1/8 = 65/8 inches</em>.
(Height) <em>h = 4 inches</em>.
So, by putting the formula to get the volume:
Volume = w×h×l.


<em>Volume = 320 15/16 inches³.</em>
Therefore, the volume of the prism is 320 15/16 inches³.
Answer:
There are 7 cups of soup left in the pot
Step-by-step explanation:
Firstly, we need to know the number of cups of soup made.
Since 1 quarts = 4 cups, the number of cups her 4 quarts is would be 4 * 4 = 16 cups
Now she served 1.5( 1 1/2 = 1.5) to 6 people, her total servings is thus 6 * 1.5 = 9 cups
What is remaining is thus 16 cups - 9 cups = 7 cups
Recall the angle sum identities:
cos(a + b) = cos(a) cos(b) - sin(a) sin(b)
cos(a - b) = cos(a) cos(b) + sin(a) sin(b)
sin(a + b) = sin(a) cos(b) + sin(b) cos(a)
sin(a - b) = sin(a) cos(b) - sin(b) cos(a)
Notice that adding the first two together, and subtract the last from the third, we get two more identities:
cos(a + b) + cos(a - b) = 2 cos(a) cos(b)
sin(a + b) + sin(a - b) = 2 sin(b) cos(a)
Let a = 4x and b = x. Then
cos(5x) + cos(3x) = 2 cos(4x) cos(x)
sin(5x) - sin(3x) = 2 sin(x) cos(4x)
Now,

as required.
Assets = Liabilities + Capital
Liabilities = Assets - Capital
Liabilities = 50,000 - 35000
Liabilities = 15,000