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Diano4ka-milaya [45]

3 years ago

13

Please help me with only one question. 20 points

1 answer:

Ostrovityanka [42]3 years ago

3 0

Answer:

141.3 cubic inches

Step-by-step explanation:

The volume of a cylinder is found using the volume formula $V=\pi r^2h$ .

The radius is half the diameter 6 which is 3.

Substitute h=5 and r = 3.

$V = \pi r^2h\\V = \pi (3^2)(5)\\V=\pi *9*5\\V = 45\pi \\V= 141.3$

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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

Faction help plz!!!!

Marizza181 [45]

Complete 2/3 x the number of plates

6 0

2 years ago

An electrician charges $40 dollars to come to your house. She also charges $55 for each hour that she works. The electricion cha

Alexxx [7]

Answer:

your question doesn't make sense if an electrician came to your house it would cost $40 then $55 dollars per hour but there is no way that you can solve that (40+(55•2)=150+55=205 which is already over $190 dollars

3 0

2 years ago

Which of these expressions is equivalent to log9 10? A) log 9 B) log 19 C) 1 log 9 D) 1 log 19

eduard

It’s definitely E. I say this because there is no correct answer.

5 0

3 years ago

You have 42 ft. of fencing (1 ft. segments) to make a rectangular garden. How much should each side be to maximize your total ar

Verizon [17]

Answer:

$Length=10.5\ ft$

$Width=10.5\ ft$

$Area=110.25\ ft^{2}$

Step-by-step explanation:

Let

x----> the length of the rectangular garden

y---> the width of the rectangular garden

we know that

The perimeter of the rectangle is equal to

$P=2(x+y)$

we have

$P=42\ ft$

so

$42=2(x+y)$

simplify

$21=(x+y)$

$y=21-x$ ------> equation A

Remember that the area of rectangle is equal to

$A=xy$ ----> equation B

substitute equation A in equation B

$A=x(21-x)$

$A=21x-x^{2}$ ----> this is a vertical parabola open downward

The vertex is a maximum

The y-coordinate of the vertex is the maximum area

The x-coordinate of the vertex is the length side of the rectangle that maximize the area

using a graphing tool

The vertex is the point $(10.5,110.25)$

see the attached figure

so

$x=10.5\ ft$

Find the value of y

$y=21-10.5=10.5\ ft$

The garden is a square

the area is equal to

$A=(10.5)(10.5)=110.25\ ft^{2}$ ----> is equal to the y-coordinate of the vertex is correct

6 0

2 years ago