Answer:
critical point of the given function f(x,y) = x²+y²+2xy is from line y = -x is the critical point of the function f(x0,y0) = 0
and it local minimum.
Step-by-step explanation:
Let the given function be;
f(x,y) = x²+y²+2xy
From above function, we can locate relative minima, maxima and the saddle point
f(x,y) = x²+y²+2xy = (x+y)²
df/dx = 2x+2y = 0 ---- (1)
df/dy =2y+2x = 0 ---- (2)
From eqn 1 and 2 above,
The arbitrary point (x0,y0) from line y = -x is the critical point of the function f(x0,y0) = 0
Then, from f(x,y) >= 0 for arbitrary (x,y) € R^n, the arbitrary point from the line x = -y is local minima of the function f.
A rectangular prism is defined by three lengths.
We can find out how many unit cubes would be in a prism by multiplying these three lengths together--that's how we find our <em>volume</em>.
Similarly, we can come up with different ways to multiply together three different numbers and make 18.
Each combination would be a new rectangular prism, with one catch:
Order doesn't matter. A prism with lengths 2, 2, and 3 is the same as one with lengths 2, 3, and 2, so don't make that mistake.
To find each combination, keep splitting 18 in different ways.
If one of the ways we split it can also be split, we need to write out that, too.
Here are the possible combinations:
18 × 1 × 1, obviously
9 × 2 × 1. splitting off 2
6 × 3 × 1. splitting off 3
4 × 6 × 1. our next biggest we can take out is 6, which can also be split...
4 × 3 × 2. there's the split of 6 into 2 and 3
<em>(3 × 6 × 1 is a repeat.)</em>
3 × 3 × 2 is new, though
<em>(2 × 9 × 1 is a repeat...)
</em><em>(2 × 3 × 3 is a repeat...)
</em>(aaaand 1 × 1 × 18 is a repeat. let's count up our combinations.)
<em>
</em>
There are 6 possible ways to multiply numbers together and get 18...
So 6 possible rectangular prisms.
Answer:
y = 11.54°
Step-by-step explanation:
Reference angle = y°
Opposite side length = 4
Hypotenuse = 20
Apply trigonometric function SOH:
y = 11.536959° ≈ 11.54° (nearest hundredth)
Answer:
27477
Step-by-step explanation:
Subtract 38700 from 29% = 27477.
We assume all money is spent on new lighting. Since they currently have $160 and need $400 we can subtract what they currently have from what they need.
$400-$160 = $240
Since we know the price of the ticket and now know they need $240 we can divide our $240 with the price of each ticket ($3)
$240/$3 = 80
So the drama club has to sell 80 more tickets in order to afford new lighting
