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3 years ago

6

How do a graph y=5/3x-9

1 answer:

zaharov [31]3 years ago

8 0

Step-by-step explanation:

y int is -9. to graph slope think a our rise/run. change in y / change in x. move 5 units up per 3 units right. it's a positive slope to the graph is increasing towards the right

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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

A magician is filling his underwater escape tank with water. It is being filled by two water hoses. Hose 1 can fill the tank in

Westkost [7]

Answer:

4 hours

Step-by-step explanation:

4 0

2 years ago

lab scale known to have a standard deviation of 0.001gram, speimen weghtted 8 times. average weiht is 4.1602 gram. what is 99% c

gtnhenbr [62]

Answer:

$99\% CI=4.1602 \pm 0.0009$

Step-by-step explanation:

From the question we are told that:

Sample size $n=8$

Mean $\=x=4.1602$

Standard deviation $\sigma=0.001gram$

Generally 99\% confidence from table is mathematically given by

$99\% CI=4.1602 \pm *2.576*\frac{0.001}{\sqrt{{8}}}$

$P(-z$

$Z_{\alpha/2}=2.576$

Generally the equation for 99\% confidence level (CI) is mathematically given by

$99\% CI=\=x \pm Z_{\alpha/2*\frac{\sigma}{\sqrt{{n}}}$

$99\% CI=4.1602 \pm 0.0009$

5 0

2 years ago

0.007 divided by 10 equivalent to 0.07

allochka39001 [22]

Does 0.007/10=0.07

true or false?

Answer:

NO if you wanted to get 0.07 you would have to multiply not divide.

Step-by-step explanation:

0.007/10=0.0007

8 0

2 years ago

F(x)=1/2×+6 plz helpppppppppp

FromTheMoon [43]

Answer:

The solution set can be given as:

$\{x|x\ \epsilon\ R,x\neq -3\}$

Step-by-step explanation:

Given function:

$f(x)=\frac{1}{2x+6}$

To find the domain of the function in set notation.

Solution:

For the function $f(x)$ to exist the denominator must be ≠ 0

We have the denominator $(2x+6)$ which cannot be = 0.

Thus, we can find the domain of the function using the above relation.

The function $f(x)$ will not exist when:

$2x+6=0$

Solving for $x$

Subtracting both sides by 6.

$2x+6-6=0-6$

$2x=-6$

Dividing both sides by 2.

$\frac{2x}{2}=\frac{-6}{2}$

∴ $x=-3$

Thus, the function will not exist at $x=-3$ . This means it has all real number solutions except -3.

The solution set can be given as:

$\{x|x\ \epsilon\ R,x\neq -3\}$

3 0

3 years ago