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strojnjashka
2 months ago
6

A triangle on a coordinate plane is translated according to the rule T-8,4(x, y). Which is another way to write this rule?

Mathematics
1 answer:
Inessa [12.5K]2 months ago
8 0

Response:

C

Detailed explanation:

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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
2 months ago
A new car is purchased for 17300 dollars. The value of the car depreciates at 9.25% per year. What will the value of the car be,
lawyer [12517]

Answer: 13

I made an error on the question, and it provided the right answer. Thank me later.

4 0
2 months ago
mr. Martin is giving a math test next period. The test, which is worth 100 points, has 29 problems. Each problem is worth either
tester [12383]

The first equation is x + y = 29, and the second is 5x + 2y = 100.

8 0
2 months ago
Read 2 more answers
Suppose flaws (cracks, chips, specks, etc.) occur on the surface of glass with density of 3 per square meter. What is the probab
zzz [12365]

Answer:

0.047

Detailed breakdown:

Using a Poisson distribution with a mean m, for an area of 0.5 square meters = 1.5

The formula to determine the probability is given by

P[k] = (e^-m * m^k) k!

Thus, we can calculate

P[4] = [(e^-1.5) * (1.5^4)] ÷ 4 * 3 * 2 * 1

= (0.2231301601 * 5.0625) ÷ 24

= (1.12944375) ÷ 24

≈ 0.04706

≈ 0.047

Therefore, the final result is 0.047

8 0
2 months ago
6. Triangle ABC is rotated 90 degrees counterclockwise and then translated 3 units up to form
PIT_PIT [12445]
Given: Triangle ABC is rotated 90 degrees counterclockwise and then translated vertically by 3 units to form triangle A'B'C'. To determine: The transformation rule necessary to map each point (x,y) on Triangle ABC to its equivalent point on Triangle A'B'C'. Solution: For a figure that undergoes a 90-degree counterclockwise rotation, the transformation will be defined as: To translate a figure upward by 3 units, the appropriate transformation will be applied afterwards. Hence, when triangle ABC experiences a rotation of 90 degrees counterclockwise followed by a translation of 3 units upward to create triangle A'B'C', the transformation rule will be established accordingly.
7 0
1 month ago
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