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2 years ago

Find the missing side. 17 m 15 m

Mathematics

1 answer:

Sonja [21]2 years ago

6 0

Is there a image supposed to be attached?

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A breeder reactor converts uranium-238 into an isotope of plutonium-239 at a rate proportional to the amount of uranium-238 pres

topjm [15]

Let $U(t)$ denote the amount of uranium-238 in the reactor at time $t$ . As conversion to plutonium-239 occurs, the amount of uranium will decrease, so the conversion rate is negative. Because the rate is proportional to the current amount of uranium, we have

$\dfrac{\mathrm dU}{\mathrm dt}=-kU$

where $k>0$ is constant. Separating variables and integrating both sides gives

$\dfrac{\mathrm dU}U=-k\,\mathrm dt\implies\ln|U|=-kt+C\implies U=Ce^{-kt}$

Suppose we start some amount $u$ . This means that at time $t=0$ we have $U(0)=u$ , so that

$u=Ce^{-0k}\implies C=u\implies U=ue^{-kt}$

We're given that after 10 years, 99.97% of the original amount of uranium remains. This means (if $t$ is taken to be in years) for some starting amount $u$ ,

$0.9997u=ue^{-10k}\implies k=-\dfrac{\ln(0.9997)}{10}$

The half-life is the time $t_{1/2}$ it takes for the starting amount $u$ to decay to half, $0.5u$ :

$0.5u=ue^{-kt_{1/2}}\implies t_{1/2}=-\dfrac{\ln(0.5)}k=\dfrac{10\ln2}{\ln(0.9997)}$

or about 23,101 years. Notice that it doesn't matter what the actual starting amount is, the half-life is independent of that.

7 0

2 years ago

I will give branliest

Evgesh-ka [11]

Step-by-step explanation:

Height of ladder = 12ft .

Here perpendicular is height to which it reaches .

When angle is 30⁰ :-

=> sin 30⁰ = H/12

=> ½ = H/12

=> H = 12/2

=> H = 6m ( ans )

When Angle is 45⁰ :-

=> sin45⁰ = H/12

=> 1/√2 = H/12

=> H = 6*√2*√2/√2

=> H = 6√2 m ( ans )

When angle is 60⁰ :-

=> sin60⁰ = H/12

=> √3/2 = H/12

=> H = 12 *√3/2

=> H = 6√3 ( ans )

hope it helped !

6 0

3 years ago

Can someone please help

Natasha_Volkova [10]

Answer:

-6 degrees F

Step-by-step explanation:

We start with -8F as the temperature. It fell 10 degrees to 2F, then fell 8 degrees to -6F.

8 0

2 years ago

Read 2 more answers

Mage has $36 to spend on movie tickets. Each movie ticket costs $4.50. How many tickets can he buy?

Stels [109]

Answer:

x = 8 tickets

Step-by-step explanation:

Given that,

Mage has $36 to spend on movie tickets.

Each movie ticket costs $4.50.

Let he bought x tickets. ATQ,

4.50x = 36

$x=\dfrac{36}{4.5}\\\\=8$

So, he can buy 8 tickets.

4 0

2 years ago

Find the difference of 128.04 - 8.287.

riadik2000 [5.3K]

Answer:

119.753000

.....

4 0

2 years ago