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3 years ago

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

1 answer:

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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If you know that two legs of a right triangle are 7 and 16 units long, what is the triangle's area? If necessary, round your ans

gizmo_the_mogwai [7]

The answer is always A

5 0

2 years ago

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:

8 kilos of it is gold, since 2/5 in decimal form is 0.40

12 kilos of it is copper.

Step-by-step explanation:

Multiply 20 times 0.40, you get 8, so 8 kilos of it is gold, while 12 kilos is copper.

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

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3 years ago

Read 2 more answers

Please help asap!!!!

Leya [2.2K]

Answer:

z = 25

Step-by-step explanation:

adjacent angles in a rhombus are supplementary

3z - 15 + 7z - 55 = 180

10z - 70 = 180

10z = 250

z = 25

6 0

2 years ago