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2 years ago

80 points if you answer this question!

Mathematics

2 answers:

Neporo4naja [7]2 years ago

8 0

Total amount of Carbon-14
$= 12 - (0.00012 \times 5000)$
$= 12 - 0.6$
$= 10.4$
=C

Full marks answer

QveST [7]2 years ago

5 0

Carbon 14 decays at a rate of -0.00012 grams per year

after 5000 years, 5000*0.00012 = 0.6 grams are lost from decay

An artifact was found to have an original amount of Carbon-14 of 12 grams.

after 5000 years, 12-0.6 = 11.4 grams of C-14 remains.

You might be interested in

Suppose Upper F Superscript prime Baseline left-parenthesis x right-parenthesis equals 3 x Superscript 2 Baseline plus 7 and Upp

Sedaia [141]

It looks like you're given

F'(x) = 3x² + 7

and

F (0) = 5

and you're asked to find F(b) for the values of b in the list {0, 0.1, 0.2, 0.5, 2.0}.

The first is done for you, F (0) = 5.

For the remaining b, you can solve for F(x) exactly by using the fundamental theorem of calculus:

$F(x)=F(0)+\displaystyle\int_0^x F'(t)\,\mathrm dt$

$F(x)=5+\displaystyle\int_0^x(3t^2+7)\,\mathrm dt$

$F(x)=5+(t^3+7t)\bigg|_0^x$

$F(x)=5+x^3+7x$

Then F (0.1) = 5.701, F (0.2) = 6.408, F (0.5) = 8.625, and F (2.0) = 27.

On the other hand, if you're expected to approximate F at the given b, you can use the linear approximation to F(x) around x = 0, which is

F(x) ≈ L(x) = F (0) + F' (0) (x - 0) = 5 + 7x

Then F (0) = 5, F (0.1) ≈ 5.7, F (0.2) ≈ 6.4, F (0.5) ≈ 8.5, and F (2.0) ≈ 19. Notice how the error gets larger the further away b gets from 0.

A better numerical method would be Euler's method. Given F'(x), we iteratively use the linear approximation at successive points to get closer approximations to the actual values of F(x).

Let y(x) = F(x). Starting with x₀ = 0 and y₀ = F(x₀) = 5, we have

x₁ = x₀ + 0.1 = 0.1

y₁ = y₀ + F'(x₀) (x₁ - x₀) = 5 + 7 (0.1 - 0) → F (0.1) ≈ 5.7

x₂ = x₁ + 0.1 = 0.2

y₂ = y₁ + F'(x₁) (x₂ - x₁) = 5.7 + 7.03 (0.2 - 0.1) → F (0.2) ≈ 6.403

x₃ = x₂ + 0.3 = 0.5

y₃ = y₂ + F'(x₂) (x₃ - x₂) = 6.403 + 7.12 (0.5 - 0.2) → F (0.5) ≈ 8.539

x₄ = x₃ + 1.5 = 2.0

y₄ = y₃ + F'(x₃) (x₄ - x₃) = 8.539 + 7.75 (2.0 - 0.5) → F (2.0) ≈ 20.164

4 0

2 years ago

A triangle's height is 10 feet more than its base. If the area of the triangle is 100 square feet, use factoring to find its dim

stiks02 [169]

The base length of the triangle is 10 ft. and the height of the triangle is 20ft.

Step-by-step explanation:

Height = base + 10

Area = 100 square ft

Area of a triangle= (1/2) (b) (h)

100 = (1/2) (b) (b + 10)

200 = b(b) + 10b

b(b) + 10b - 200 = 0

b(b) + 20b - 10b - 200 = 0

b ( b + 20) -10(b + 20) = 0

(b-10) (b+20) =0

b = 10 (or) b = -20

Here b is the length and cannot be negative.

So, b = 10ft

h = b + 10

h = 10 + 10

h = 20 ft.

The base length of the triangle is 10 ft. and the height of the triangle is 20ft.

6 0

3 years ago

a web designer charges a $200 fee plus $50 per hour to build a website. which equation represents the total cost, y, to a custom

dezoksy [38]

Y = 50x + 200 <=== ur equation

6 0

3 years ago

Read 2 more answers

I need sum help please and thanks :)

Leona [35]

Answer:

6/16n is your answer I think

4 0

3 years ago

4.) A bag contains 10 red marbles and 5 blue marbles. You randomly select 3 marbles from the bag. What is

sesenic [268]

Answer:

a) 1/27

b) 2/91

Step-by-step explanation:

A bag contains 10 red marbles and 5 blue marbles (15 marbles in total). You randomly select 3 marbles from the bag.

a) You replace each marble before selecting the next one.

The probability of selecting one blue marble is

$\dfrac{5}{15}=\dfrac{1}{3},$

then the probability that all 3 marbles are blue is

$\dfrac{1}{3}\times \dfrac{1}{3}\times \dfrac{1}{3}=\dfrac{1}{27}$

b) You do not replace each marble before selecting the next one. Each time the number of blue marbles decreases by 1 and the total number of marbles decreases by 1 too. So the probability that all 3 marbles are blue is

$\dfrac{5}{15}\times \dfrac{4}{14}\times \dfrac{3}{13}=\dfrac{2}{91}$

7 0

2 years ago