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Llana
1 month ago
12

The half-life of carbon-14, 14C, is approximately 5,730 years. A bone fragment is estimated to have originally contained 6 milli

grams of 14C. Write the exponential decay equation where A is the amount (in mg) of carbon-14 remaining in the bone fragment after t years.
Mathematics
1 answer:
tester [12.3K]1 month ago
6 0
The general equation for exponential decay characterized by a half-life (T) is expressed as N(t) = N_0(1/2)^(t/T), where N(t) signifies the amount remaining at time t, N_0 stands for the initial amount (at t=0), and T denotes the half-life of the substance. The half-life of carbon-14 is about 5,730 years. When starting with 6 mg of carbon-14, the equation for the remaining amount after t years would be established.
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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
Write 337,060 in expanded from using exponents
Leona [12618]

Answer:

We start with the number 337 060.

Expanded form refers to a way of representing a standard form number in more detail.

This number will be converted to expanded form utilizing exponents.

=> 337 060

To begin, let's break down each component.

=> 300 000 = 3 x 10^5

=> 30 000 = 3 x 10^4

=> 7 000 = 7 x 10^3

=> 60 = 6 x 10^1

=> 3 x 10^5 + 3 x 10^4 + 7 x 10^3 + 6 x 10^1 – this is the expanded form of the number using exponents.

Step-by-step explanation:

6 0
3 months ago
Which of the following does NOT have the same slope as the rest? Question options: The slope of the line passing through the poi
Svet_ta [12734]

I cannot find the provided table. It must be that one, as the other two options both reflect a slope of 2.

3 0
2 months ago
The two circles shown above have radii of 8 in. and 4 in. What is the Circumference of the both?
lawyer [12517]
The Circumference of Circle 1 measures 50.24 inches, while Circle 2 measures 25.12 inches. For calculations, Circle 1 has a radius of 8 inches and Circle 2 a radius of 4 inches. To compute circumferences, we utilize the formula for calculating circumference involving the value of π. Substituting the respective radius values into the formula produces the computed circumferences.
6 0
1 month ago
Tina is playing a computer game. She starts with 100 points, and she loses points based on the following rules: • Each time a pl
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Answer: she needs to finish 4 levels to have a point total less than 20

Step-by-step explanation:

Considering the following:

Initial score = 100 points

Losing points for passing a level = - 8 points

Losing points for catching a flower = - 3 points

Assume Tina catches 6 flowers during each level

Total levels required to have less than 20 points

Points lost per level:

Catching 6 flowers = -(6 × 3)

Passing the level = - 8

= - 18 + - 8 = - 26 points

Levels to finish to achieve less than 20 points

Let the number of levels be y

Starting points - (26 × number of levels) < 20

100 - (26y) < 20

100 - 26y < 20

-26y < 20 - 100

-26y < - 80

y > 80/26

y > 3.07

Therefore, she must finish 4 levels to have fewer than 20 points

8 0
1 month ago
Read 2 more answers
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