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anastassius [24]

3 years ago

7

How do three planes intersect at one point?

1 answer:

natima [27]3 years ago

7 0

Imagine a corner of a cube.
It is made of three planes interesting at a single point
The image should help.

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The use of mathematical methods to study the spread of contagious diseases goes back at least to some work by Daniel Bernoulli i

harina [27]

Answer:

a

$y(t) = y_o e^{\beta t}$

b

$x(t) = x_o e^{\frac{-\alpha y_o }{\beta }[e^{-\beta t} - 1] }$

c

$\lim_{t \to \infty} x(t) = x_oe^{\frac{-\alpha y_o}{\beta } }$

Step-by-step explanation:

From the question we are told that

$\frac{dy}{y} = -\beta dt$

Now integrating both sides

$ln y = \beta t + c$

Now taking the exponent of both sides

$y(t) = e^{\beta t + c}$

=> $y(t) = e^{\beta t} e^c$

Let $e^c = C$

So

$y(t) = C e^{\beta t}$

Now from the question we are told that

$y(0) = y_o$

Hence

$y(0) = y_o = Ce^{\beta * 0}$

=> $y_o = C$

So

$y(t) = y_o e^{\beta t}$

From the question we are told that

$\frac{dx}{dt} = -\alpha xy$

substituting for y

$\frac{dx}{dt} = - \alpha x(y_o e^{-\beta t })$

=> $\frac{dx}{x} = -\alpha y_oe^{-\beta t} dt$

Now integrating both sides

$lnx = \alpha \frac{y_o}{\beta } e^{-\beta t} + c$

Now taking the exponent of both sides

$x(t) = e^{\alpha \frac{y_o}{\beta } e^{-\beta t} + c}$

=> $x(t) = e^{\alpha \frac{y_o}{\beta } e^{-\beta t} } e^c$

Let $e^c = A$

=> $x(t) =K e^{\alpha \frac{y_o}{\beta } e^{-\beta t} }$

Now from the question we are told that

$x(0) = x_o$

So

$x(0)=x_o =K e^{\alpha \frac{y_o}{\beta } e^{-\beta * 0} }$

=> $x_o = K e^{\frac {\alpha y_o }{\beta } }$

divide both side by $(K * x_o)$

=> $K = x_o e^{\frac {\alpha y_o }{\beta } }$

So

$x(t) =x_o e^{\frac {-\alpha y_o }{\beta } } * e^{\alpha \frac{y_o}{\beta } e^{-\beta t} }$

=> $x(t)= x_o e^{\frac{-\alpha * y_o }{\beta} + \frac{\alpha y_o}{\beta } e^{-\beta t} }$

=> $x(t) = x_o e^{\frac{\alpha y_o }{\beta }[e^{-\beta t} - 1] }$

Generally as t tends to infinity , $e^{- \beta t}$ tends to zero

so

$\lim_{t \to \infty} x(t) = x_oe^{\frac{-\alpha y_o}{\beta } }$

5 0

3 years ago

Please help ! WILL GRANT BRAINLIEST

Brums [2.3K]

Answer: Substances.

Step-by-step explanation:

Battery acid,

Coke,

Vinegar,

Blood,

Beer,

Soda,

Urine,

Saliva,

Eggs.

6 0

3 years ago

I need help with my math homework

Klio2033 [76]

The answer should be J.15.

8 0

3 years ago

When Jaylen started high school, 1,430 students attended his school. On the day of his graduation, only 1,001 students attended

e-lub [12.9K]

429 students decreased

8 0

3 years ago

Read 2 more answers

Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Determine each segment length in right triangle .

Pani-rosa [81]

The segment length is 14 (square root)2

Given that Triangle ABC is right angle triangle

The vertex marked is B where side AC is the hypotenuse

The side of AC is at Vertex B is 14

The dash segment from vertex B to point D on side AC

Angle BDA is marked right angle .

Angles A and C both marked 45 degrees.

As shown in diagram

Triangle ABC is drawn according to the statement where B is vertex

The side lengths are 14

Now to find Another side length that is x

So , the equation formed is

x*cos45 = 14

x/√2 = 14

x = 14√2

Hence the length of the segment is 14√2

Learn more about Right angle triangle here brainly.com/question/64787

#SPJ1O

5 0

2 years ago