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4 years ago

Find the greatest possible error for the measurement 0.991 g. A. 0.001 g B. 0.1 g C. 0.005 g D. 0.0005 g

1 answer:

8 0

The answer is D.

0.991 could have been rounded to the nearest thousandth, so the greatest possible error must be five ten thousandths, or 0.0005, since we always round up if the number is 5 or more or round down if the number is less than 5.

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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

3 years ago

How do I calculate this? Is there a formula?

alex41 [277]

<u>Answer:</u>

Height of cables = 23.75 meters

<u>Step-by-step explanation:</u>

We are given that the road is suspended from twin towers whose cables are parabolic in shape.

For this situation, imagine a graph where the x-axis represent the road surface and the point (0,0) represents the point that is on the road surface midway between the two towers.

Then draw a parabola having vertex at (0,0) and curving upwards on either side of the vertex at a distance of $x = 600$ or $x = -600$ , and y at 95.

We know that the equation of a parabola is in the form $y=ax^2$ and here it passes through the point $(600, 95)$ .

$y=ax^2$

$95=a \times 600^2$

$a=\frac{95}{360000}$

$a=\frac{19}{72000}$

So new equation for parabola would be $y=\frac{19x^2}{72000}$ .

Now we have to find the height $(y)$ of the cable when $x= 300$ .

$y=\frac{19 (300)^2}{72000}$

y = 23.75 meters

8 0

4 years ago

Read 2 more answers

If dinner costs 31 British pounds, then how much is that in U.S. Dollars?

kaheart [24]

Answer:

If dinner cost 31 British pounds than $38.78 would be the cost in U.S. dollars.

I hope this helps!

8 0

3 years ago

Read 2 more answers

I'll give brainliest if you show your work. Plz answer quickly.

makvit [3.9K]

I'm pretty sure the answer is 2.9 because It's closer to 3 than 2

8 0

3 years ago

Read 2 more answers

Using an applet, we found that the theory-based test results in a t-statistic of -7.25 and p-value less than 0.0001. State your

11111nata11111 [884]

Answer:

b. We have very strong evidence that the long-run average guess of the population size of Milwaukee, Wisconsin is smaller with the anchor of Green Bay than with the anchor of Chicago.

Step-by-step explanation:

Smaller p-value indicates a strong evidence in favor of the alternative hypothesis which means we can reject the null hypothesis. In the given scenario the p-value is 0.0001 which is very small. There is sufficient evidence for the rejection of null hypothesis.

7 0

3 years ago