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3 years ago

What is the slope of the line that passes through the points (-4,4) and (-6,6)

Mathematics

1 answer:

andrew-mc [135]3 years ago

4 0

The slope of the line is -1

the equation would be y = -1x

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Consider the system of differential equations dxdt=−4ydydt=−4x. Convert this system to a second order differential equation in y

koban [17]

$\dfrac{\mathrm dy}{\mathrm dt}=-4x\implies x=-\dfrac14\dfrac{\mathrm dy}{\mathrm dt}\implies\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac14\dfrac{\mathrm d^2y}{\mathrm dt^2}$

Substituting this into the other ODE gives

$-\dfrac14\dfrac{\mathrm d^2y}{\mathrm dt^2}=-4y\implies y''-16y=0$

Since $x(t)=-\dfrac14y'(t)$ , it follows that $x(0)=-\dfrac14y'(0)=4\implies y'(0)=-16$ . The ODE in $y$ has characteristic equation

$r^2-16=0$

with roots $r=\pm4$ , admitting the characteristic solution

$y_c=C_1e^{4t}+C_2e^{-4t}$

From the initial conditions we get

$y(0)=5\implies 5=C_1+C_2$

$y'(0)=16\implies-16=4C_1-4C_2$

$\implies C_1=\dfrac12,C_2=\dfrac92$

So we have

$\boxed{y(t)=\dfrac12e^{4t}+\dfrac92e^{-4t}}$

Take the derivative and multiply it by -1/4 to get the solution for $x(t)$ :

$-\dfrac14y'(t)=\boxed{x(t)=-\dfrac12e^{4t}+\dfrac92e^{-4t}}$

7 0

3 years ago

If 2x=8, then x=4<br><br> Name the property being illustrated in this expression

Kobotan [32]

2x4=8 is the expression gets the answer

4 0

3 years ago

25. An apple is launched directly upward at 64 feet per second from a platform 80 feet high. The equation for this

Viktor [21]

Answer:

a. 144 ft

b. 5 s

Step-by-step explanation:

h = -16t² + 64t + 80

a. This is a parabola, so the maximum height is at the vertex.

t = -64 / (2 × -16)

t = 2

h = -16(2)² + 64(2) + 80

h = 144

The apple reaches a maximum height of 144 ft.

b. 0 = -16t² + 64t + 80

0 = t² − 4t − 5

0 = (t + 1) (t − 5)

t = -1 or 5

t must be positive, so it takes 5 seconds to reach the ground.

3 0

3 years ago

mrs. henein is purchasing cupcakes for her homeroom class. of each cupcake costs $2.25 and she has 31 students in her homeroom c

Luda [366]

Answer:

$69.75

Step-by-step explanation:

Multiply $2.25 by 31 students

5 0

3 years ago

Read 2 more answers

Katt and sanjeev are collecting money for charity. For every £2 that kat collects, sanjeev collects £3. They collect £255 in tot

il63 [147K]

Answer: Kate = £102

Sanjeev = £153

Step-by-step explanation:

From the question, we are informed that for every £2 that kat collects, sanjeev collects £3. This csn be represented in a fraction as:

Kat = 2/5

Sanjeev = 3/5

The amount that each collects will be:

Kat = 2/5 × £255

= 2 × £51

= £102

Sanjeev = 3/5 × £255

= 3 × £51

= £153

6 0

3 years ago