Answer:
3.14
Step-by-step explanation:
d=2
A= pi*r^2 = pi*(d/2)^2 = pi*(2/2)^2= pi*1 =pi =3.14
Answer:

g(t) = 0
And
The differential equation
is linear and homogeneous
Step-by-step explanation:
Given that,
The differential equation is -

![e^{t}y' + (9t - \frac{1}{t^{2} + 81 } )y = 0\\e^{t}y' + (\frac{9t(t^{2} + 81 ) - 1}{t^{2} + 81 } )y = 0\\e^{t}y' + (\frac{9t^{3} + 729t - 1}{t^{2} + 81 } )y = 0\\y' + [\frac{9t^{3} + 729t - 1}{e^{t}(t^{2} + 81) } ]y = 0](https://tex.z-dn.net/?f=e%5E%7Bt%7Dy%27%20%2B%20%289t%20-%20%5Cfrac%7B1%7D%7Bt%5E%7B2%7D%20%2B%2081%20%7D%20%29y%20%3D%200%5C%5Ce%5E%7Bt%7Dy%27%20%2B%20%28%5Cfrac%7B9t%28t%5E%7B2%7D%20%2B%2081%20%29%20-%201%7D%7Bt%5E%7B2%7D%20%2B%2081%20%7D%20%29y%20%3D%200%5C%5Ce%5E%7Bt%7Dy%27%20%2B%20%28%5Cfrac%7B9t%5E%7B3%7D%20%2B%20729t%20%20-%201%7D%7Bt%5E%7B2%7D%20%2B%2081%20%7D%20%29y%20%3D%200%5C%5Cy%27%20%2B%20%5B%5Cfrac%7B9t%5E%7B3%7D%20%2B%20729t%20%20-%201%7D%7Be%5E%7Bt%7D%28t%5E%7B2%7D%20%2B%2081%29%20%7D%20%5Dy%20%3D%200)
By comparing with y′+p(t)y=g(t), we get

g(t) = 0
And
The differential equation
is linear and homogeneous.
Answer:
Since stress is greater than ultimate strength, the wire will break.
Step-by-step explanation:
The titanium wire is experimenting an axial load. Ultimate strength equals
. The wire shall break if and only if stress is at least equal to ultimate strength. The equation for axial stress (
), measured in pascals, in the wire with circular cross-section is:
(1)
Where:
- Axial force, measured in newtons.
- Cross-section diameter, measured in meters.
Please notice that axial force is the weight of the man hanging from wire.
If we know that
and
, then the axial stress experimented by the titanium wire is:


Since stress is greater than ultimate strength, the wire will break.
I'm assuming you meant 1.5 × 10⁴. Remember, when we write in standard form, you need to use ^ to denote it's 'to the power of'. So it would be 1.5 × 10^4.
I'm also assuming you meant in decimal form, because that's already in standard form.
However, the answer is 15,000. This is because you lose one zero when multiplying a decimal with one number after it. For each number after the decimal, you take off a zero. Therefore, the end number is 15,000.
It is 10.2 centimeters so option A :)