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3 years ago

The speed - time graph of a car is given here. Using the data in the graph calculate the total distance covered by the car.

Mathematics

1 answer:

Ad libitum [116K]3 years ago

8 0

Answer:The Total distance covered by the car is 875m

In the given scenario, it is the area under the speed curve, the straight line. Area = 625 + 250 = 875m.

Step-by-step explanation:

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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

I need to solve 6 2/3-21/6

lora16 [44]

Step-by-step explanation:

62/3-21

62/18=0.290

290/6

Divide it

4 0

3 years ago

A culture of bacteria has an initial population of 41000 bacteria and doubles every 5 hours. Using the formula P_t = P_0\cdot 2^

vodomira [7]

Answer:

285541

Step-by-step explanation:

According To The Question,

Given, A culture of bacteria has an initial population of 41000 bacteria and doubles in every 5 hours & $P_{t} = P_{i}*(2)^{\frac{d}{t} }$ .

Now, for the population of bacteria in the culture after 14 hours is $P_{t}$ . We have Initial Population( $P_{i}$ )=41000 , d=14 & t=5 .

Put These Value in Above Formula, We get

$P_{t} = 41000*(2)^{\frac{14}{5} }$

$P_{t} = 41000*2^{2.8}$

$P_{t} = 41000*(6.9644)$

$P_{t} =$ 285540.5847 ≈ 285541

3 0

3 years ago

Read the proposition and the implication shown below. "If the lights are off, there is no one inside." Which statement is a cont

charle [14.2K]

The contrapositive switches the hypothesis and the conclusion and negates both in this form:
Statement: If A, then B
Contrapositive: If not B, then not A.

In this case, the statement is:
<span> "If the lights are off, there is no one inside."
Contrapositive:
If there is someone inside, the lights are on. </span>

4 0

3 years ago

There are three small rounds of cheddar cheese in Grace’s refrigerator. She wants to bring a small wedge of cheese in her lunch

Travka [436]

Answer:

The one-fourth of one round of cheddar cheese

Step-by-step explanation:

Because if we cut every round in 4 equal pieces, 4x3=12, we will have 12 equal pieces of cheddar cheese.

6 0

3 years ago