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Assoli18 [71]
3 years ago
10

......................................

Mathematics
1 answer:
MrRa [10]3 years ago
7 0

Answer:

D

Step-by-step explanation:

The centroid of a triangle is the intersection of the three medians of the triangle (each median connecting a vertex with the midpoint of the opposite side).

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It is known that the mass, m(t), of a radio-active substance decreases as it decays, and that the equation governing this is m′(
Murljashka [212]

Answer:

m(t) = m₀ e⁻⁰•⁰¹⁵ᵗ

Half-Life = 46.21 years.

Step-by-step explanation:

Radioactive reactions always follow a first order reaction dynamic

Let the initial mass of radioactive substance be m₀ and the mass at any time be m

(dm/dt) = -Km (Minus sign because it's a rate of reduction)

The question provides K = 0.015 from the given differential equation

(dm/dt) = -0.015m

(dm/m) = -0.015dt

 ∫ (dm/m) = -0.015 ∫ dt 

Solving the two sides as definite integrals by integrating the left hand side from m₀ to m and the Right hand side from 0 to t.

We obtain

In (m/m₀) = -0.015t

(m/m₀) = (e^(-0.015t))

m = m₀ e^(-0.015t)) = m₀ e⁻⁰•⁰¹⁵ᵗ

m(t) = m₀ e⁻⁰•⁰¹⁵ᵗ

At half life, m(t) = (m₀/2), t = T(1/2)

(m₀/2) = = m₀ e⁻⁰•⁰¹⁵ᵗ

e⁻⁰•⁰¹⁵ᵗ = (1/2)

In e⁻⁰•⁰¹⁵ᵗ = In (1/2)

-0.015t = - In 2

t = (In 2)/0.015

t = (0.693/0.015)

t = 46.21 years

Half life = T(1/2) = t = 46.21 years.

Hope this Helps!!!

7 0
3 years ago
Evaluate the expression for x = 5, y = 3, and z=14 . <br><br> 5x−6y+20z/4yz
Arlecino [84]

Answer:

4

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Last month, the daily balance in Joana's credit card account was $1,000 for 9 days, $750 for 10 days, $850 for 4 days, and $900
FrozenT [24]

Answer:

<em />Average = \$873<em />

<em />

Step-by-step explanation:

Given

$1000 for 9 days

$750 for 10 days

$850 for 4 days

$900 for other days

Required

Compute the daily average

First, we need to compute the number of days her balance is $900

Assuming the billing cycle is 30 days;

Number\ of\ days = 30 - (9 + 10 + 4)

Number\ of\ days = 30 - 23

Number\ of\ days = 7

The Average is then calculates using:

Average = \frac{\sum fx}{x}

Average = \frac{1000 * 9 + 750 * 10 + 850 * 4 + 900 * 7}{9 + 10 + 4+ 7}

Average = \frac{26200}{30}

Average = 873.333333333

<em />Average = \$873<em> --- Approximated</em>

3 0
3 years ago
Connor is going to see a movie and is taking his 4 kids. Each movie ticket costs $13 and there are an assortment of snacks avail
EleoNora [17]

If Connor buys 3 snacks at 3 dollars each for himself and his 3 children, the net cost (including movie tickets) would be 88 dollars.

If he buys x amount of snacks, his cost will be determined by C=52+3x or C=52+3*x (both are equivalent, but not everyone knows every way to represent multiplication)

Step-by-step explanation:

To find the cost of the snacks:

Cost = Price*NumberOfSnacks, or C=p*n, or C=pn

To find the unit cost of the snack, find the price, the p value, which is 3 dollars.

Then, find the total number of snacks that will be bought. Since each person receives an equal number of snacks, 3 per person, and there are 4 people (himself and his 3 children), we can multiply 3*4 to find the n value, which is now known to be 12.

C=3*12=36. Add to the 13 dollar per person charge for tickets (52 dollars for 4 people), and you get 88 dollars.

To find the cost if he buys x amount of snacks for himself and his 3 children (assumed to be "everyone"), all costs but the n value are to be the same, creating this equation:

C=52+3x

In this context, 52 is the cost of movie tickets, 3 is the cost of the snacks, and x is the total number of snacks bought. C represents total cost.

5 0
3 years ago
Find her number and explain
Andreas93 [3]
It should be 11. hope this helps :)
8 0
3 years ago
Read 2 more answers
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