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GaryK [48]
3 years ago
9

Find two numbers whose sum is 49. If the greater is 4 more than 8 times the smaller. Solve

Mathematics
2 answers:
weeeeeb [17]3 years ago
8 0


I got
44
and
5
Explanation:
Call the numbers
x
and
y
, you get:
x
+
y
=
49

x
=
8
y
+
4

substitute the second equation into the first:
8
y
+
4
+
y
=
49

9
y
=
45

y
=
45
9
=
5

so that:
x
=
8
⋅
5
+
4
=
44
Mila [183]3 years ago
5 0

Answer:

5 and 44

Step-by-step explanation:

smaller number: x

greater number: 8x + 4

x + 8x + 4 = 49

9x + 4 = 49

9x = 45

x = 5

smaller number: 5

greater number: ?

8(5) + 4 = 40 + 4 = 44

5 + 44 = 49

Hope that helps.

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The population of a certain community is known to increase at a rate proportional to the number of people present at time t. If
attashe74 [19]

Answer:

t=7.85 years

Step-by-step explanation:

We can write this rate as an ordinary differential equation.

\frac{dP}{dt}=aP

Where a is proportional constant, P the population variable, and t the time.

\frac{dP}{P}=adt

Integrating each side of the equation.

\int \frac{dP}{P}=\int adt

ln(P)=at+c

P=e^{at+c}

P=e^{c}e^{at}=Ce^{at}

To find C we need to use the initial condiction, it means evaluae P at t=0.

P_{0}=Ce^{0}=C

P=P_{0}e^{at}

Now, we use the sentence  the population has doubled in 5 years.

2P_{0}=P_{0}e^{a5}

We can find "a" in this condition.

2=e^{a5}

ln(2)=a5

a=\frac{ln(2)}{5}

a=0.14

Finally, let's find how long will it take to triple.

3P_{0}=P_{0}e^{0.14t}

3=e^{0.14t}

t=\frac{ln(3)}{0.14}

t=7.85 years

I hope it helps you!

4 0
2 years ago
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