Answer:
1/2
Step-by-step explanation:
The interior of the square is the region D = { (x,y) : 0 ≤ x,y ≤1 }. We call L(x,y) = 7y²x, M(x,y) = 8x²y. Since C is positively oriented, Green Theorem states that
Lets calculate the partial derivates of M and L, Mx and Ly. They can be computed by taking the derivate of the respective value, treating the other variable as a constant.
- Mx(x,y) = d/dx 8x²y = 16xy
- Ly(x,y) = d/dy 7y²x = 14xy
Thus, Mx(x,y) - Ly(x,y) = 2xy, and therefore, the line ntegral is equal to the double integral
We can compute the double integral by applying the Barrow's Rule, a primitive of 2xy under the variable x is x²y, thus the double integral can be computed as follows
We conclude that the line integral is 1/2
Answer:
Answer: the vase contains 1017.36 inches³ of soil.
Step-by-step explanation:
We would apply thee formula for determining the volume of a cylinder which is expressed as
Volume = πr²h
Where
h represents the height of the cylinder
r represents the radius of the cylinder.
π is a constant whose value is 3.14
From the information given
Diameter = 12 inches
Radius = diameter /2 = 12/2
Radius = 6 inches
Height = 12 inches
Therefore,
Volume of the cylindrical vase =
3.14 × 6² × 12 = 1356.48 inches³
If the vase is filled 3/4 full of soil, then the volume of soil in the vase is
3/4 × 1356.48 = 1017.36 inches³
Answer:
it is easy use the formula of triangle which is 1/2(base × height) and base is the side where the height touches and height means the perpendicular line.
And in some cases there may be the use of pythagoras theorem
Answer: The first one
Step-by-step explanation:
In order to make the offer attractive such that it would earn £25,000 for Ian Vector, Paddington Games would have to sell 460 games.
The game can be sold for £25,000 or for £2,000 and then a fee of £50 for every game sold.
In order for the amount to be the same, the amount from games sold will have to equal the difference between the £25,000 and the £2,000.
Difference is:
= 25,000 - 2,000
= £23,000
The <u>number of games to be sold</u> is:
= Difference / Amount per game
= 23,000 / 50
= 460 games
In conclusion, 460 games need to be sold to make the offer attractive.
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