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2 years ago

Write this statement as a conditional statement in the form “if p, then q.”

Mathematics

1 answer:

Nezavi [6.7K]2 years ago

6 0

Answer:

if three points are all located on the same line, then, the points are collier points.

Step-by-step explanation:

the if or p statement is called the hypothesis.

the then or q statement is called the conclusion.

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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

A TV has a listed price of $690.95 before tax. If the sales tax rate is 8.75%, find the total cost of the TV with sales tax incl

PSYCHO15rus [73]

Answer:

699.7

Step-by-step explanation:

690.95 + 8.75 = 699.7

8 0

2 years ago

Help???? ill take help from anyone

kozerog [31]

Answer:-1/3

Step-by-step explanation: I really don’t know

8 0

2 years ago

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Find the value of x in each case. Give reasons to justify your solutions!

ANEK [815]

Answer:

x = 11°

Step-by-step explanation:

The parallel lines suggest we look to the relationships involving angles and transversals. The angle marked 33° and ∠CAB are alternate interior angles, hence congruent:

∠CAB = 33°

5x is the measure of the external angle opposite that internal angle and angle 2x of ΔABC, so it is equal to their sum:

5x = 2x + 33°

3x = 33° . . . . . . . . . subtract 2x

x = 11° . . . . . . . . . . . divide by 3

6 0

2 years ago

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(2x2 + 2x + 3) – (x2 + 2x + 1)

Soloha48 [4]

8x+4 is the answer to your problem
hope this helps

6 0

3 years ago

Read 2 more answers