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3 years ago

Find the equation of the line that is parallel to the line y=-7x+2 and passes through (-6,-3)

1 answer:

4 0

Answer: y=-7x-45

Explanation: Two parallel lines have the same slope, so that means the slope of the line would be -7. When you add that value to your equation, that would give you: y=-7x+b. Now that you have the slope, the only other value you’re missing is b. To find the value of b, you can substitute any point into the equation that’s on the line and solve for b:

-3=-7(-6)+b
-3=42+b
b=-45

Now that you have the value of b, substitute it into the final equation:

y=-7x-45

Hope this helps シ

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Solve the given DE<br><br> dx/dt=3x+2y+1<br><br> dy/dt=-2x-y+1

kirill115 [55]

We can solve for $x(t)$ first by rewriting the system of first-order ODEs as a single second-order ODE in $x(t)$ :

Taking the derivative of the first ODE gives

$\dfrac{\mathrm dx}{\mathrm dt}=3x+2y+1\implies\dfrac{\mathrm d^2x}{\mathrm dt^2}=3\dfrac{\mathrm dx}{\mathrm dt}+2\dfrac{\mathrm dy}{\mathrm dt}$

while solving for $2y$ gives

$\dfrac{\mathrm dx}{\mathrm dt}=3x+2y+1\implies2y=\dfrac{\mathrm dx}{\mathrm dt}-3x-1$

Then

$\dfrac{\mathrm d^2x}{\mathrm dt^2}=3\dfrac{\mathrm dx}{\mathrm dt}+2(-2x-y+1)$

$\dfrac{\mathrm d^2x}{\mathrm dt^2}=3\dfrac{\mathrm dx}{\mathrm dt}-4x-2y+2$

$\dfrac{\mathrm d^2x}{\mathrm dt^2}=3\dfrac{\mathrm dx}{\mathrm dt}-4x-\left(\dfrac{\mathrm dx}{\mathrm dt}-3x-1\right)+2$

$\implies\dfrac{\mathrm d^2x}{\mathrm dt^2}-2\dfrac{\mathrm dx}{\mathrm dt}+x=3$

which is linear with constant coefficients, so it's trivial to solve; the corresponding homogeneous ODE

$x''-2x'+x=0$

has characteristic equation

$r^2-2r+1=(r-1)^2=0$

with root $r=1$ (multiplicity 2), so the characteristic solution is

$x_c=C_1e^t+C_2te^t$

For the non-homogeneous ODE, assume a particular solution of the form

$x_p=a\implies{x_p}'={x_p}''=0$

Substituting these into the ODE gives

$0-2\cdot0+a=3\implies a=3$

Then the general solution for $x(t)$ is

$\boxed{x(t)=C_1e^t+C_2te^t+3}$

From here, we find

$\dfrac{\mathrm dx}{\mathrm dt}=C_1e^t+C_2(t+1)e^t$

so that

$2y=(C_1e^t+C_2(t+1)e^t)-3(C_1e^t+C_2te^t+3)-1$

$\implies\boxed{y(t)=\left(\dfrac{C_2}2-C_1\right)e^t-C_2te^t-5}$

3 0

4 years ago

What is the y-intercept of y = 5 ?

ser-zykov [4K]

The slope-intercept form is y=mx+b y = m x + b , where m is the slope and b is the y-intercept. Using the slope-intercept form, the y-intercept is 5 .

7 0

4 years ago

A triangle has side lengths 5 miles in 13 miles is it a right triangle

Debora [2.8K]

Answer:

jgfshd

Step-by-step explanation:

3 0

3 years ago

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Please help me, thank you!

dlinn [17]

Answer:

a. The first four terms are -4 , -4/3, -4/9 , -4/27

b. The series is converge

c. The series has sum to ∞ , the sum of the series is -6

Step-by-step explanation:

* Lets revise the geometric series

- Geometric series:

- There is a constant ratio between each two consecutive numbers

- Ex:

# 5 , 10 , 20 , 40 , 80 , ………………………. (×2)

# 5000 , 1000 , 200 , 40 , …………………………(÷5)

* General term (nth term) of a Geometric Progression:

- U1 = a , U2 = ar , U3 = ar2 , U4 = ar3 , U5 = ar4

- Un = ar^n-1, where a is the first term , r is the constant ratio

between each two consecutive terms and n is the position of the

number in the sequence

* In the problem

∵ The Un = -4(1/3)^n-1

∴ a = -4

∴ r = 1/3

a) To find the first four numbers use n = 1, 2 , 3 , 4

∴ U1 = a = -4

∴ U2 = -4(1/3)^(2 - 1) = -4(1/3) = -4/3

∴ U3 = -4(1/3)^(3 - 1) = -4(1/3)^2 = -4(1/9) = -4/9

∴ U4 = -4(1/3)^(4 - 1) = -4(1/3)^3 = -4(1/27) = -4/27

* The first four terms are -4 , -4/3, -4/9 , -4/27

b) If IrI < 1 then the geometric series is converge and if IrI > 1

then the geometric series is diverge

∵ r = 1/3

∴ The series is converge

c. The convergent series has sum to ∞

- The rule is: S∞ = a/(1 - r)

∴ S∞ = -4/(1 - 1/3) = -4/(2/3) = -4 × 3/2 = -6

* The sum of the series is -6

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3 years ago

I will give brainliest to whoever helps me with this question. Also, if you could please explain to me how you solved it I would

kolbaska11 [484]

I will try to help okay i will send my friends to help

6 0

3 years ago

Read 2 more answers