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2 years ago

Z(0,-5) Go left 5, up right, and down 3.

Mathematics

1 answer:

Alex73 [517]2 years ago

7 0

Answer:

(-4,-7)

Step-by-step explanation:

plz mark brainliest

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Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had decreased by 3%. If the rate of deca

Hitman42 [59]

Answer:

The half-life of the radioactive substance is 135.9 hours.

Step-by-step explanation:

The rate of decay is proportional to the amount of the substance present at time t

This means that the amount of the substance can be modeled by the following differential equation:

$\frac{dQ}{dt} = -rt$

Which has the following solution:

$Q(t) = Q(0)e^{-rt}$

In which Q(t) is the amount after t hours, Q(0) is the initial amount and r is the decay rate.

After 6 hours the mass had decreased by 3%.

This means that $Q(6) = (1-0.03)Q(0) = 0.97Q(0)$ . We use this to find r.

$Q(t) = Q(0)e^{-rt}$

$0.97Q(0) = Q(0)e^{-6r}$

$e^{-6r} = 0.97$

$\ln{e^{-6r}} = \ln{0.97}$

$-6r = \ln{0.97}$

$r = -\frac{\ln{0.97}}{6}$

$r = 0.0051$

$Q(t) = Q(0)e^{-0.0051t}$

Determine the half-life of the radioactive substance.

This is t for which Q(t) = 0.5Q(0). So

$Q(t) = Q(0)e^{-0.0051t}$

$0.5Q(0) = Q(0)e^{-0.0051t}$

$e^{-0.0051t} = 0.5$

$\ln{e^{-0.0051t}} = \ln{0.5}$

$-0.0051t = \ln{0.5}$

$t = -\frac{\ln{0.5}}{0.0051}$

$t = 135.9$

The half-life of the radioactive substance is 135.9 hours.

6 0

3 years ago

How many 11-player soccer teams can be formed from 16 total players?

Contact [7]

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▹ Answer

▹ Step-by-Step Explanation

16 ÷ 11 = 1 R 5

1 team can only be formed since you have 16 players. You would need 22 players to form another team, since each team has 11 players.

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

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5 0

3 years ago

A rock climber climbs an average of 12.6 feet per minute. How many feet will the climber climb in 30 minutes? Write an equation

alexandr1967 [171]

Answer:

378

Step-by-step explanation:

12.6 X 30= 378

6 0

4 years ago

Can someone explain what dilatation is in math?

Helen [10]

Answer:

A dilation that creates a smaller image is called a reduction. A dilation stretches or shrinks the original figure. A description of a dilation includes the scale factor (or ratio) and the center of the dilation. The center of dilation is a fixed point in the plane.

5 0

3 years ago

Thank you guys :) will give branliest to the ones that help

Dafna11 [192]

It’s a reflection across the x-axis

6 0

3 years ago