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3 years ago

THE property of two rational numbers is -28/81. If one of them is -2/3, then find the other.

1 answer:

4 0

The answer is:
(-28/81)/(-2/3) = -84/(-162) = 42/81

Work
Think of this simple question:
Two number when multiplied together give 15. If one number is 5, then the other is (15/5)=3.

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Find the volume of this cylinder. Please help

algol13

Answer:

$\boxed {\boxed {\sf 384 \ ft^3}}$

Step-by-step explanation:

The volume is the space an object occupies. The volume formula for a cylinder is provided and it is:

$V= \pi r^2 h$

Where:

r= radius
h= height

The radius is the distance from the center of the circle to the edge, and it is 4 feet. The height is 8 feet. We are told to use 3 for pi.

r= 4 ft
h= 8 ft
π= 3

Substitute the values into the formula.

$V= (3)(4 \ ft)^2 (8 \ ft)$

Solve the exponent.

(4 ft)²= 4 ft * 4 ft = 16 ft²

$V= (3)(16 \ ft^2)(8 \ ft)$

Multiply the three numbers together.

$V= 48 \ ft^2 (8 \ ft)$

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The volume of the cylinder is approximately <u>384 cubic feet.</u>

8 0

3 years ago

5. Find the general solution to y'''-y''+4y'-4y = 0

CaHeK987 [17]

For any equation,

$a_ny^(n)+\dots+a_1y'+a_0y=0$

assume solution of a form, $e^{yt}$

Which leads to,

$(e^{yt})'''-(e^{yt})''+4(e^{yt})'-4e^{yt}=0$

Simplify to,

$e^{yt}(y^3-y^2+4y-4)=0$

Then find solutions,

$\underline{y_1=1}, \underline{y_2=2i}, \underline{y_3=-2i}$

For non repeated real root y, we have a form of,

$y_1=c_1e^t$

Following up,

For two non repeated complex roots $y_2\neq y_3$ where,

$y_2=a+bi$

and,

$y_3=a-bi$

the general solution has a form of,

$y=e^{at}(c_2\cos(bt)+c_3\sin(bt))$

Or in this case,

$y=e^0(c_2\cos(2t)+c_3\sin(2t))$

Now we just refine and get,

$\boxed{y=c_1e^t+c_2\cos(2t)+c_3\sin(2t)}$

Hope this helps.

r3t40

5 0

4 years ago