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3 years ago

Nine times a number is one more than ten times the number.

1 answer:

3 0

I will rewrite the wording and write out the equation as it goes so there is better understanding. Once I do that, I will solve it for you.
Nine times a number (9n) is (=) one more than ten times the number (10n + 1).
Now that we've rewritten it, let's only write what we have in parenthesis.
9n = 10n + 1.
Now that we have our equation, let's solve!
9n = 10n + 1
Subtract 10n from both sides.
-1n = 1
Divide both sides by -1.
n = -1
I hope this 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

3 years ago

Rod is paid an overtime rate of $25 per hour after he earns his basic wage of $600 per week. Write an equation in slope- interce

SpyIntel [72]

P = 25h + 600.

This is because even if he works no overtime, he still gets his 600.

5 0

4 years ago

Ahat contains pieces of paper marked with the numbers 1 through 16. Is the

Anika [276]

Answer:as likely as not

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

What’s is the surface area of this

Marysya12 [62]

2.8 multiplied by 2.8 to find the surface area of the base which is 7.84
4*1/2*2.8*5.5 to find the surface area of all four triangular faces which is 30.8
Plus them together 7.84 plus 30.8 which is 38.64

6 0

3 years ago

X-3y=2 what is the slope

Brums [2.3K]

1/3 is the slope.
x-3y=2
-3y=-x+2
y=(1/3)x+2/3

3 0

4 years ago