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3 years ago

If m + 4n=2n + 8m; what is the ratio of n to m

Mathematics

2 answers:

Dmitrij [34]3 years ago

8 0

Combine like terms to get 2n = 7m

MrRissso [65]3 years ago

8 0

To answer the ratio, massage this equation around to find ' n/m ' .
Let's subtract 'm' from each side:
4n = 2n + 7m
Subtract '2n' from each side:
2n = 7m
Divide each side by 'm' :2 (n/m) = 7
Divide each side by 2 :
n/m = 7/2 . . . . . there's your ratio. That's choice-'e'.

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The product of 12 and k is 84.<br><br> Solve for k.

Mrac [35]

Answer:

The product of 12 and k is 84

According to the given problem, the equation is

$\boxed{12k = 84} \\ k = \frac{84}{12} \\ \boxed{k = 7}$

<u>k = 7</u> is the right answer.

5 0

2 years ago

The amount A of the radioactive element radium in a sample decays at a rate proportional to the amount of radium present. Given

slavikrds [6]

Answer:

a) $\frac{dm}{dt} = -k\cdot m$ , b) $m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }$ , c) $m(t) = 10\cdot e^{-\frac{t}{2438.155} }$ , d) $m(300) \approx 8.842\,g$

Step-by-step explanation:

a) Let assume an initial mass m decaying at a constant rate k throughout time, the differential equation is:

$\frac{dm}{dt} = -k\cdot m$

b) The general solution is found after separating variables and integrating each sides:

$m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }$

Where $\tau$ is the time constant and $k = \frac{1}{\tau}$

c) The time constant is:

$\tau = \frac{1690\,yr}{\ln 2}$

$\tau = 2438.155\,yr$

The particular solution of the differential equation is:

$m(t) = 10\cdot e^{-\frac{t}{2438.155} }$

d) The amount of radium after 300 years is:

$m(300) \approx 8.842\,g$

4 0

3 years ago

Read 2 more answers

How many odd integers are there between 101 and 999 have distinct digits?

guapka [62]

Every number will have only 3 digits. In the ones place, there are 5 choices. For every choice of digit made in the ones place, there are 8 possible choices for the hundreds place (you can choose from 1-9, omitting whatever is used in the ones place), and there are 8 possible choices for the tens place (you can choose from 0-9, omitting whatever has already been used elsewhere).

So there are $7\cdot8\cdot8=320$ such numbers.

8 0

3 years ago

Two angles are complementary. One of the angles is twice the other.

sergiy2304 [10]

Two complementary angles must add to 90 degrees, and if you divide 90 into thirds (two parts for the larger angle, one for the smaller), then you get 30 degrees.

If the smaller angle is 30 degrees, then the larger is two times that, which is 60. 60 + 30 = 90, so the larger angle is equal to 60 degrees.

5 0

3 years ago

Read 2 more answers

Based on the information below, what are the values of x and y of the solution to the system of equations used to create the inf

Alborosie

Answer:

Option D) is correct

That is x=2 , y=-5

Step-by-step explanation:

Given that the $|A|=\left| \begin{array}{cc}4&-6\\ 8&-2\end{array}\right|, \left|A_x\right|=\left|\begin{array}{cc}38&-6\\ 28&-2\end{array}\right|, \left|A_y\right|=\left|\begin{array}{cc}4&38\\ 8&26\end{array}\right|$