Y''+2y'+y=2e^(-t) find the general solution of the giving nonhomogenous differential equation

Mathematics

1 answer:

Degger [83]2 years ago

3 0

The general solution of the differential equation y'' + 2y' + y = 2e^(-t) is (c1 + c2 x) e^-x

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What is the area of the sector a.) 10π cm^2b.) 16π cm^2c.) 40π cm^2d.) 64π cm^2

Natalija [7]

Answer:

C. 40π cm²

Explanation:

• The central angle of the sector = 225 degrees

• The radius of the sector = 8cm

For a sector of radius r and central angle θ, we calculate the area using the formula below:

$\text{Area}=\frac{\theta}{360\degree}\times\pi r^2$

Substituting the given values, we have:

$\begin{gathered} \text{Area}=\frac{225}{360}\times\pi\times8^2 \\ =\frac{5}{8}\times64\times\pi \\ =5\times8\times\pi \\ =40\pi cm^2 \end{gathered}$

The area of the sector is 40π cm².

3 0

10 months ago

Help ASAP!!! First to answer with a correct answer gets brain...

Llana [10]

Hey there!

First, let's multiply each side of the equation by 3 to get rid of the fraction $\frac{2}{3}$ .

9 + 2x = $\frac{6}{5}$

Next we can multiply each side of the equation by 5 to get rid of the fraction $\frac{6}{5}$ .

45 + 10x = 6

There's your answer!

Hope this helps!

6 0

3 years ago

A triangle has two sides of length 15 cm and 17 cm. Select all the values of its third side that would make it a right triangle

Natali [406]

Answer:

$\sqrt{514} cm$ , 8cm, are both options

Step-by-step explanation:

For a right triangle one can find the length of the longest side by using the Pythagorean theorem. So there are two options I can think of that if the triangle is a right triangle will work. First remember what the Pythagorean theorem is : side a^2+side b^2=hypotenuse^2

The hypotenuse is the longest side of a right triangle. So if the sides that are 15 and 17 cm are not the longest sides then the formula would be:

$15^{2} +17^2=c^2\\15^2+17^2=\sqrt{514}cm$