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2 years ago

Element X decays radioactively with a half life of 10 minutes. If there are 510 grams

Mathematics

1 answer:

pishuonlain [190]2 years ago

7 0

Answer:

46 minutes

Step-by-step explanation:

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Find the distance traveled by a particle with position (x, y) as t varies in the given time interval. x = 5 sin2 t, y = 5 cos2 t

rodikova [14]

$\begin{cases}x(t)=5\sin2t\\y(t)=5\cos2t\end{cases}\implies\begin{cases}\frac{\mathrm dx}{\mathrm dt}=10\cos2t\\\frac{\mathrm dy}{\mathrm dt}=-10\sin2t\end{cases}$

The distance traveled by the particle is given by the definite integral

$\displaystyle\int_C\mathrm dS=\int_0^{3\pi}\sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt$

where $C$ is the path of the particle. The distance is then

$\displaystyle\int_0^{3\pi}\sqrt{100\cos^22t+100\sin^22t}\,\mathrm dt=10\int_0^{3\pi}\mathrm dt=30\pi$

6 0

2 years ago

Roscoe rides his bike at least 10 miles but not more than 30 miles. He rides at an average rate of 10.5 miles per hour. The amou

zheka24 [161]

Actually, the domain is the possible set of input values of a function that will make the function fit the specific criteria. In this case, the input value is m, where m is the number of miles that is travelled. The criteria is to travel at least 10 miles but not more than 30 miles, therefore the domain should be:

All real numbers from 10 to 30, inclusive

(should be real numbers not integer since any fractional number is included in the domain)

I cannot figure out why the choices are far from the answer.

3 0

3 years ago

Can a triangle have two obtuse angles? please Justify your answer.

Scrat [10]

Answer:

No, a triangle cannot have 2 obtuse angles. The definition of an obtuse angle is an angle with a measure that is greater than 90°.

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

200 labourers need 50 days to construct a road of 4 km long. How many labourers are needed to construct 8 km long in 80 days

patriot [66]

Answer:

250

Step-by-step explanation:

Number of labourers * Number of days worked = Total number of working days

Total number of working days to construct a 4km long road: $200*50=10000$

Total mumber of working days to construct a 8km long road: $10000*2=20000$

Labourers: 20000 ÷ 80 = 250.

250 labourers are required.

7 0

3 years ago

Ray MN and ray ML are two sides of an angle. What is a name of this angle?

Setler [38]

It is (c) NML
Because MN and ML is the vertex and the point meeting is M which is the angle.
The M is the angle because the common letter of both vertex is the letter M

7 0

2 years ago