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2 years ago

Please help will give brainliest

Mathematics

1 answer:

Gelneren [198K]2 years ago

6 0

Answer:

Step-by-step explanation:

It is B because to find the volume you multiply all three values together, which gets you 68.448. I multiplied 9.2x3.1, which got me 28.52, and then I multiplied 28.52 by 2.4 which got me 68.448.

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Y''+y'+y=0, y(0)=1, y'(0)=0

mars1129 [50]

Answer:

$y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

Step-by-step explanation:

A second order linear , homogeneous ordinary differential equation has form $ay''+by'+cy=0$ .

Given: $y''+y'+y=0$

Let $y=e^{rt}$ be it's solution.

We get,

$\left ( r^2+r+1 \right )e^{rt}=0$

Since $e^{rt}\neq 0$ , $r^2+r+1=0$

{ we know that for equation $ax^2+bx+c=0$ , roots are of form $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ }

We get,

$y=\frac{-1\pm \sqrt{1^2-4}}{2}=\frac{-1\pm \sqrt{3}i}{2}$

For two complex roots $r_1=\alpha +i\beta \,,\,r_2=\alpha -i\beta$ , the general solution is of form $y=e^{\alpha t}\left ( c_1\cos \beta t+c_2\sin \beta t \right )$

i.e $y=e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

Applying conditions y(0)=1 on $e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$ , $c_1=1$

So, equation becomes $y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

On differentiating with respect to t, we get

$y'=\frac{-1}{2}e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )+e^{\frac{-t}{2}}\left ( \frac{-\sqrt{3}}{2} \sin \left ( \frac{\sqrt{3}t}{2} \right )+c_2\frac{\sqrt{3}}{2}\cos\left ( \frac{\sqrt{3}t}{2} \right )\right )$

Applying condition: y'(0)=0, we get $0=\frac{-1}{2}+\frac{\sqrt{3}}{2}c_2\Rightarrow c_2=\frac{1}{\sqrt{3}}$

Therefore,

$y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

3 0

3 years ago

Bianca wrote the steps for her solution to the equation 2.3 + 8(1.3x – 4.75) = 629.9. She left out the description for the last

Virty [35]

I believe dividing is always the last step.

5 0

3 years ago

Read 2 more answers

If h(x) = │5x - 17│, find h(3).

arsen [322]

Answer:

Step-by-step explanation:

5x - 17

5(3) - 17 = 15 - 17 = -2

However, there is an absolute value sign over the expression. Abs value makes negatives turn positive. So -2 becomes 2.

7 0

3 years ago

How do you solve the problem 6-3x=-2x

jolli1 [7]

6-3x=2x

In order to solve these, you first want to get all the variables on one side. So, you add 3x to both sides.

6=x

The answer is x=6

Hope this helps!

3 0

3 years ago

Read 2 more answers

HELP ME PLEASE I HAVE BEEN DOING THIS FOR TWO HOURS, I BEG OF YOU‍♀️‍♀️

BabaBlast [244]

Answer:

The first factor is itself the sum of two terms
The solution is the product of two factors

Step-by-step explanation:

The math symbols of the expression include parentheses, a plus sign, and a multiplication symbol. The order of operations tells you to do the "plus" operation inside parentheses first. The numbers involved in a "plus" operation, or sum, are called "terms." The result is their sum.

Then the second operation in the order of operations is to do the multiplication of the sum on the left of the multiplication symbol by the number to the right of the multiplication symbol. The numbers involved in multiplication are called "factors". The result of multiplication is called a "product."

Matching up this vocabulary with what you see, you realize ...

the first factor is the sum of two terms
the end result of evaluating the expression is the product of two factors

6 0

3 years ago