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Vera_Pavlovna [14]
3 years ago
6

Write the expressions as an equivalent power with a negative exponent. 1/49 and 27/125

Mathematics
1 answer:
hoa [83]3 years ago
7 0
n^{-x}=\frac1{n^x}

\textcircled1\ \frac1{49}=\frac1{7^2}=\boxed{7^{-2}}

\textcircled2\ \frac{27}{125}=\frac{3^3}{5^3}=(\frac35)^3=\frac1{(\frac{5}{3})^3}=\boxed{\left(\frac53\right)^{-3}}


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The answer is always A
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We take a milk carton from the refrigerator and put it on the table at room temperature. We assume that the temperature of the c
Kisachek [45]
We can solve this problem using separation of variables.

Then apply the initial conditions

EXPLANATION

We were given the first order differential equation

\frac{dT}{dt}=k(T-a)

We now separate the time and the temperature variables as follows,

\frac{dT}{T-a}=kdt

Integrating both sides of the differential equation, we obtain;

ln(T-a)=kt +c

This natural logarithmic equation can be rewritten as;

T-a=e^{kt +c}

Applying the laws of exponents, we obtain,

T-a=e^{kt}\times e^{c}

T-a=e^{c}e^{kt}

We were given the initial conditions,

T(0)=4

Let us apply this condition to obtain;

4-20=e^{c}e^{k(0)}

-16=e^{c}

Now our equation, becomes

T-a=-16e^{kt}

or

T=a-16e^{kt}

When we substitute a=20,
we obtain,

T=20-16e^{kt}

b) We were also given that,

T(5)=8

Let us apply this condition again to find k.

8=20-16e^{5k}

This implied

-12=-16e^{5k}

\frac{-12}{-16}=e^{5k}

\frac{3}{4}=e^{5k}

We take logarithm to base e of both sides,

ln(\frac{3}{4})=5k

This implies that,

\frac{ln(\frac{3}{4})}{5}=k


k=-0.2877

After 15 minutes, the temperature will be,


T=20-16e^{-0.2877\times 15}

T=20-0.21376


T=19.786

After 15 minutes, the temperature is approximately 20°C


6 0
3 years ago
Juli went mining and found a large metal bar that weighed 20 kilos. After doing some analysis of the
masha68 [24]

Answer:

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12 kilos of it is copper.

Step-by-step explanation:

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T^T

8 0
2 years ago
What number is 118% of 80?
Tamiku [17]

Answer:

94.4

Step-by-step explanation:

1.18 is 118%

1.18 times 80 is 94.4

8 0
3 years ago
Read 2 more answers
Please help asap!!!!
Leya [2.2K]

Answer:

z = 25

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10z = 250

z = 25

6 0
2 years ago
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