Which inequality represents the values of that ensure triangle exists? a triangle with these side lengths: AC = 18 units, BC = 6
1 answer:
You might be interested in
Answer:
The maximum value= 36
Minimum value = - 36
Step-by-step explanation:
Given that
f(x, y, z) = 8 x + 8 y + 4 z
h(x,y,z)=4 x² + 4 y² + 4 z² - 36
From Lagrange multipliers
Δf = λ Δh
Δf = < 8 ,8 , 4>
Δh = < 8 x ,8 y , 8 z>
Δf = λ Δh
So
< 8 ,8 , 4> = < 8 λ x ,8 λ y , 8 λ z>
8 = 8 λ x -------------1
8 = 8 λ y ---- ------2
4 = 8 λ z ----------------3
From equation 1 ,2 and 3
Now by putting the value of x,y and z in the following equation
4 x² + 4 y² + 4 z² = 36
So the value of λ is
When λ = 1/2
x = 1 / λ , y=1 / λ , z= 1 /2 λ
x= 2 , y = 2 , z=1
So
f(x, y, z) = 8 x + 8 y + 4 z
f(2, 2, 1) = 8 x 2 + 8 x 2 + 4 x 1
f(2, 2, 1) =36
When λ = - 1/2
x = 1 / λ , y=1 / λ , z= 1 /2 λ
x= - 2 , y = - 2 , z= - 1
So
f(x, y, z) = 8 x + 8 y + 4 z
f(-2, -2, -1) = 8 x (-2) + 8 x (-2) + 4 x (-1)
f(-2, -2, -1) = - 36
The maximum value= 36
Minimum value = - 36
Answer:
Step-by-step explanation:
You know that:
- 2/5 of the spice mixture was oregano.
- 1/3 of the spice mixture was basil.
Then, to find the fraction of the total amount of spice mixture that was oregano and basil, you must add both fractions, as following:
- Find the least common multiply of the denominators:
- Divide the LCM by each original denominator and multiply the result by each numerator.
- Make the addition.
Then, the result is: