Answer:
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Step-by-step explanation:
Answer:
The length of third side is: 6.3
Step-by-step explanation:
Given triangle is a right triangle where
Base = ?
Perpendicular = 5
Hypotenuse = 8
Let x be the base
As it is a right-angled triangle, Pythagoras theorem can be used to find the third side
Putting the known values
Taking square root on both sides
Rounding off to the nearest 10th
Base = 6.3
Hence,
The length of third side is: 6.3
Answer:
The relationship ⇒ <u>25x + 40y = 12,250</u>
Step-by-step explanation:
The number of student memberships = x
The number of adult memberships = y
The monthly membership fee for a student = $25
The monthly membership fee for an adult = $40
The total fee = 25x + 40y
Al's Athletic Club receives $12,250 in membership fees for the month of January.
So, the relationship between x and y is:
<u>25x + 40y = 12,250</u>
The points on the intersection of the ellipsoid with the plane that are respectively closest and furthest from the origin are
(2–√,−2–√,2−22–√)
(−2–√,2–√,2+22–√)
Using Lagrange multipliers we attempt to find the extrema of f(x,y,z)=x2+y2+z2 given that g(x,y,z)=x−y+z−2=0 and that h(x,y,z)=x2+y2−4=0.
Given,
∇f=⟨2x,2y,2z⟩
∇g=⟨1,−1,1⟩
∇h=⟨2x,2y,0⟩
Extrema satisfy the condition that ∇f=μ∇g+λ∇h for some λ,μ∈R.
This is to say,
2x=2λx+μ
2y=2λy−μ
2z=μ
If λ=1 then μ=0 and so z=0, the g constraint tells us that x=y+2, and the h constraint tells us that y2+(y+2)2=4, meaning that either y=0 or y=2. This provides us with two crucial points in addition to the g constraint:
(2,0,0)
(0,−2,0)
Now assume λ≠1, and so
x=μ2−2λ
y=−μ2−2λ=−x
Since x=−y, we have that x=±2–√, y=∓2–√. Using the g constraint, our two critical points are
(2–√,−2–√,2−22–√)
(−2–√,2–√,2+22–√)
And then it's east to determine which is the max and which is the min out of these four critical points.
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The solution of the expression is 
.
Given that
Equation; 
We have to simplify the equation.
According to the question
To simplify the equation follow all the steps given below.
Equation; 
Then,
Hence, the required expression is .
To know more about Expression click the link given below.
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