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natta225
3 months ago
8

Mateo made the model below to represent the number of miles he swims in the

Mathematics
1 answer:
Inessa [12.5K]3 months ago
6 0

Answer:

In the model, Mateo's swimming frequency per week is illustrated by the...4 rectangles...

Each time Mateo swims at the pool, the distance he covers in miles is shown as the...2 shaded sections out of 3 in 1 rectangle.

The expression...8/12 x 2/3 can be used to calculate the overall distance that Mateo swims in a week, resulting in...4/9 miles.

Step-by-step explanation:

I completed the quiz on i-ready:)

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Find the dimensions of the closed rectangular box with maximum volume that can be inscribed in the unit sphere.
Inessa [12570]

Answer:

Wyjaśnienie krok po kroku:

Załóżmy, że prostokąt ma wierzchołki (x,y,z) w dodatnim oktancie.  Prostokątny pudełko musi być symetryczne względem wszystkich trzech osi.

Wtedy jego boki to

2x,2y,2z

Objętość = 8xyz

Maksymalizuj objętość przy założeniu

x^2+y^2+z^2 =1

tj. g(x,y,z) = x^2+y^2+z^2 -1=0

Użyj mnożników Lagrange'a, mamy

∇f(x,y,z)=λ∇g(x,y,z)przy maksimum

∇f(x,y,z)=λ∇g(x,y,z) =(8yz,8xz,8xy)\\∇g(x,y,z)=(2x,2y,2z)

8yz=2λx8xz=2λy8xy=2λz

Dzieląc otrzymujemy

\frac{y}{x} =\frac{x}{y} \\x^2=y^2

Podobnie y^2=z^2

Zatem otrzymujemy 3x^2 =1\\x = \frac{1}{\sqrt{3} }

Stąd wymiary to

(2x,2y,2z)

<pzatem wymiary="" to="">

\frac{2}{\sqrt{3} },\frac{2}{\sqrt{3} },\frac{2}{\sqrt{3} } )

</pzatem>
3 0
3 months ago
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