Answer:
the answer is bc of my knowledge XD XD XD hahaha
Step-by-step explanation:
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Answer:
The value of x is 12 feet
Step-by-step explanation:
The shape in question is a composite shape. We can see that x is both the base of the triangle and the breadth of the rectangle.
To get the area of the shape, we will have to add the area of the rectangle to the area of the triangle.
Area of rectangle = length X breadth
Area of triangle = 1/2 base X height.
However, to calculate the area of the triangle, we need to find its height first.
The next step is to get the height of the triangle. Observing the shape properly, we can see that we can get the height by subtracting the length of the rectangle from the overall length of the shape.
Height of triangle = 16 ft - 10 ft = 6 ft
recall area = 156 square feet.
We now have most of our missing dimensions
We can now set up an equation as follows:

Therefore the value of x is 12 feet
Solution :
a). The level curves of the function :

are actually the curves

where k is a positive constant.
The equation is equivalent to


which is a family of ellipses.
We sketch the level curves for K =1,2,3 and 4.
If the shark always swim in the direction of maximum increase of blood concentration, its direction at any point would coincide with the gradient vector.
Then we know the shark's path is perpendicular to the level curves it intersects.
b). We have :

and
points in the direction of most rapid increase in concentration, which means
is tangent to the most rapid increase curve.
is a parametrization of the most
, then
is a tangent to the curve.
So then we have that 

∴ 
Using separation of variables,



⇒ y = kx^2 for some constant k
but we know that 


∴ The path of the shark will follow is along the parabola


-19 + (-12) = 7
Remove Parentheses
( -a ) = -a
= 19 - 12
Subtract The Numbers
19-12 = 7
For this case we propose a system of equations:
x: Represents the amount of small popcorn tubs
y: Represents the amount of large popcorn tubs
According to the data we have to:
(Spending all the money in your wallet)
(Buying 7 popcorn tubs)
From the second equation we have:

Substituting in the first equation:

Thus, Katie can buy 3 large tubs of popcorn.
So:

In addition, you can buy 4 small tubs of popcorn.
Answer:
3 large popcorn tubs.
4 small popcorn tubs.