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Nookie1986 [14]

3 years ago

6

Write an equation in point slope form of the line passes through the point (9,0) and has a slope of m=-3

1 answer:

Brut [27]3 years ago

7 0

Answer:

$\huge y = - 3(x - 9)$

Step-by-step explanation:

To find an equation of a line in point slope form when given the slope and a point we use the formula

$y - y_1 = m(x - x_1)$

From the question we have the final answer as

$y - 0 = - 3(x - 9) \\ \\ \\ y = - 3(x - 9)$

Hope this helps you

You might be interested in

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

Is √1/9 greater less than or equal to 1/4

victus00 [196]

Answer:

Greater:

$\sqrt{1/9} > 1/4$

Step-by-step explanation:

$\sqrt{\frac{1}{9} } =\frac{\sqrt{1} }{\sqrt{3} } =\frac{1}{3}$

1/3 is greater than 1/4

Hope this helps

7 0

1 year ago

Can you help me please?

iren [92.7K]

Finding the volume of a cube involves multiplying with this formula.

Height * Width * Length = volume

To find what the side lengths are, we can take the cube root of 64.

∛64 = 4

Height = 4

Width = 4

Length = 4

These sides are multiplied together to get 64.

The only answer choice that makes sense is Option A.

______

Best Regards,

Wolfyy :)

6 0

3 years ago

Read 2 more answers

If the number of Conference participants decreases by 20% compared to last year, there would be 1760 participants this year. If

Basile [38]

2,640 this year
2,112 last year

the 1760 is 20% less than - so 120% of 1760 is the previous year:
1760 * 1.2 = 2112

2112 increased by 25% is a total of 125%:
2112 *1.25 = 2640

7 0

3 years ago

Read 2 more answers

Solve this system of equations by graphing. First graph the equations, and then type the solution.

stealth61 [152]

Answer:

The solution is the point (1,-4)

Step-by-step explanation:

we have

$y=-3x-1$ ----> equation A

$y=-2x-2$ ----> equation B

we know that

The solution of the system of equations by graphing is the intersection point both graphs

using a graphing tool

The intersection point is (1,-4)

see the attached figure

therefore

The solution is the point (1,-4)

5 0

3 years ago