Area of the canvas: 96 = 2 · W² + 2 · W L,
where W is the width and L is the length of a back and a top side. Two square sides have area W².
2 W L = 96 - 2 W² /:2
W L = 48 - W²
L = ( 48 - W² ) / W.
The inside volume of the shelter:
V = L · W · W = L · W²
V = W² · ( 48 - W² ) / W ;
V = 48 W - W³
We have to find the derivative:
V ` = 48 - 3 W²
48 - 3 W² = 0 ( for V max. )
3 W² = 48
W² = 48 : 3
W² = 16; W = √16; W = 4 ft.
L = ( 48 - 16 ) / 4 = 32 / 4 = 8 ft.
Answer: The length of the shelter for which the volume inside is maximized is 8 ft.
<span><em>Partial product </em>multiplication is the process of multiplying the numbers partially (respectively to ones, tens and hundreds) and adding them together in the end. For example, in order to find the product of 3 8 × 6 we should write that,
1) 3 8
× 6
___
4 8
2) 3 8
× 6
_____
4 8
1 8 0
3) 3 8
× 6
______
+ 4 8
1 8 0
______
2 2 8
<em>Regrouping </em>is the multiplication process when we add the partial products to the next tens and hundreds and so on without writing them down. For example, in order to find the product of 3 8 × 6 with the help of regrouping, we write that
4
3 8
× 6
___
228
, where the number 4 above 8 shows the tens of 4 (40), which is going to be added to the tens of the product of 30 times 6. The two processes are the same in a way that you are getting the same result. In the end, it is a multiplication process. The processes differ because of the methods we apply. In partial product multiplication, we break down the number in its ones, tens, hundreds steps and then calculate. However, in regrouping process we consider those steps without breaking them down. </span>
Answer:
2000 eels
Step-by-step explanation:
Let us represent the total estimate of the eels = x
She returns the 50 eels to the lake.
The next day Hannah catches 400 eels, of these 400 eels, 10 are ringed.
To solve the above question, we have the following:
50/x = 10/400
Cross Multiply
10x = 50 × 400
x = 50 × 400/10
x = 2000 eels
Therefore, the total estimate of the eels in the lake = 2000 eels
Answer:
Step-by-step explanation:
Trend line passes through the points (6,12) and (4,16).
Find the slope of the line:
Write the equation of the line in the form 
where the slope 
This line passes through the point (6,12), then its coordinates satisfy the equation:
Answer:
3x - y = 12 and x + 2y = - 10
Step-by-step explanation:
The first straight line passes through the points (2,-6) and (4,0).
Therefore, the equation of the straight line from two point form
⇒ y = 3(x - 4) = 3x - 12
⇒ 3x - y = 12 .......... (1)
Again, the second straight line passes through the points (2,-6) and (0,-5).
Therefore, the equation of this straight line will be
⇒ - 2(y + 5) = x
⇒ x + 2y = - 10 ......... (1)
Therefore, (1) and (2) are the system of equations. (Answer)
