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sdas [7]
1 year ago
9

15. USE EFFICIENT METHODS Without

Mathematics
1 answer:
-Dominant- [34]1 year ago
8 0

Answer:

5^-7, 5^0, 5^4

Step-by-step explanation:

Any time a number has a negative exponent that means that the resulting number will be a fraction (ex. 2^-2=\frac{1}{4}). Therefore this number is the smallest number.

Anytime a number has an exponent of 0, it will always equal 1

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- Inessa ran 3 laps in 10 minutes. How long
Anni [7]

Answer: 16 minutes and 40 seconds

Step-by-step explanation:

1.) Divide 10 minutes by 3 laps in order to find out how long it takes her to run a single lap. (it ends up being 3 minutes and 20 seconds per lap)

2.) Multiply this number by 5, you get 16 minutes and 40 seconds.

NOTE: remember that you’re using intervals of 60 (seconds in a minute) rather than intervals of 100.

8 0
2 years ago
A tank contains 30 lb of salt dissolved in 500 gallons of water. A brine solution is pumped into the tank at a rate of 5 gal/min
Dmitry [639]

At any time t (min), the volume of solution in the tank is

500\,\mathrm{gal}+\left(5\dfrac{\rm gal}{\rm min}-5\dfrac{\rm gal}{\rm min}\right)t=500\,\mathrm{gal}

If A(t) is the amount of salt in the tank at any time t, then the solution has a concentration of \dfrac{A(t)}{500}\dfrac{\rm lb}{\rm gal}.

The net rate of change of the amount of salt in the solution, A'(t), is the difference between the amount flowing in and the amount getting pumped out:

A'(t)=\left(5\dfrac{\rm gal}{\rm min}\right)\left(\left(2+\sin\dfrac t4\right)\dfrac{\rm lb}{\rm gal}\right)-\left(5\dfrac{\rm gal}{\rm min}\right)\left(\dfrac{A(t)}{50}\dfrac{\rm lb}{\rm gal}\right)

Dropping the units and simplifying, we get the linear ODE

A'=10+5\sin\dfrac t4-\dfrac A{10}

10A'+A=100+50\sin\dfrac t4

Multiplying both sides by e^{10t} allows us to identify the left side as a derivative of a product:

10e^{10t}A'+e^{10t}A=\left(100+50\sin\dfrac t4\right)e^{10t}

\left(e^{10}tA\right)'=\left(100+50\sin\dfrac t4\right)e^{10t}

e^{10t}A=\displaystyle\int\left(100+50\sin\dfrac t4\right)e^{10t}\,\mathrm dt

Integrate and divide both sides by e^{10t} to get

A(t)=10-\dfrac{200}{1601}\cos\dfrac t4+\dfrac{8000}{1601}\sin\dfrac t4+Ce^{-10t}

The tanks starts off with 30 lb of salt, so A(0)=30 and we can solve for C to get a particular solution of

A(t)=10-\dfrac{200}{1601}\cos\dfrac t4+\dfrac{8000}{1601}\sin\dfrac t4+\dfrac{32,220}{1601}e^{-10t}

6 0
3 years ago
How do u write 2.45 in words
Genrish500 [490]
It would likely just be written as "two point four five", or "two and forty-five hundredths".
8 0
2 years ago
Read 2 more answers
A football team gains 18 yards in one play and then loses 12 yards in the next. What is the team's total yardage?
Sav [38]
The teams total yardage is 6 yards
5 0
3 years ago
Read 2 more answers
Exprees 24,36 as sum of two odd prime number​
swat32

Answer:

see explanation

Step-by-step explanation:

The set of the first few prime numbers are

2,  3,  7,  11,  13,  17,  19,  23 ...............

Considering the odd primes, then

24 = 7 + 17

36 = 13 + 23

8 0
3 years ago
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