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2 years ago

Find the other endpoint of the line segment with the given endpoint and midpoint. Endpoint: (−8,8) Midpoint: (−7,0)

Mathematics

2 answers:

Arturiano [62]2 years ago

8 0

Answer:

The other endpoint is (-6,-8).

Step-by-step explanation:

<h3>If you follow the slope that the two points made (Endpoint: (−8,8) Midpoint: (−7,0), the slope is - $\frac{-8}{1}$ ) you follow it down like this:</h3>

I hope this helps

NikAS [45]2 years ago

3 0

Answer:

(-6, -8)

Step-by-step explanation:

Midpoint Formula: $(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )$

Simply set our variables to what we know and solve:

-7 = (-8 + x)/2

-14 = -8 + x

x = -6

0 = (8 + y)/2

0 = 8 + y

y = -8

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Find the function y1 of t which is the solution of 121y′′+110y′−24y=0 with initial conditions y1(0)=1,y′1(0)=0. y1= Note: y1 is

strojnjashka [21]

Answer:

Step-by-step explanation:

The original equation is $121y''+110y'-24y=0$ . We propose that the solution of this equations is of the form $y = Ae^{rt}$ . Then, by replacing the derivatives we get the following

$121r^2Ae^{rt}+110rAe^{rt}-24Ae^{rt}=0= Ae^{rt}(121r^2+110r-24)$

Since we want a non trival solution, it must happen that A is different from zero. Also, the exponential function is always positive, then it must happen that

$121r^2+110r-24=0$

Recall that the roots of a polynomial of the form $ax^2+bx+c$ are given by the formula

$x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}$

In our case a = 121, b = 110 and c = -24. Using the formula we get the solutions

$r_1 = -\frac{12}{11}$

$r_2 = \frac{2}{11}$

So, in this case, the general solution is $y = c_1 e^{\frac{-12t}{11}} + c_2 e^{\frac{2t}{11}}$

a) In the first case, we are given that y(0) = 1 and y'(0) = 0. By differentiating the general solution and replacing t by 0 we get the equations

$c_1 + c_2 = 1$

$c_1\frac{-12}{11} + c_2\frac{2}{11} = 0$ (or equivalently $c_2 = 6c_1$

By replacing the second equation in the first one, we get $7c_1 = 1$ which implies that $c_1 = \frac{1}{7}, c_2 = \frac{6}{7}$ .

So $y_1 = \frac{1}{7}e^{\frac{-12t}{11}} + \frac{6}{7}e^{\frac{2t}{11}}$

b) By using y(0) =0 and y'(0)=1 we get the equations

$c_1+c_2 =0$

$c_1\frac{-12}{11} + c_2\frac{2}{11} = 1$ (or equivalently $-12c_1+2c_2 = 11$

By solving this system, the solution is $c_1 = \frac{-11}{14}, c_2 = \frac{11}{14}$

Then $y_2 = \frac{-11}{14}e^{\frac{-12t}{11}} + \frac{11}{14} e^{\frac{2t}{11}}$

The Wronskian of the solutions is calculated as the determinant of the following matrix

$\left| \begin{matrix}y_1 & y_2 \\ y_1' & y_2'\end{matrix}\right|= W(t) = y_1\cdot y_2'-y_1'y_2$

By plugging the values of $y_1$ and

We can check this by using Abel's theorem. Given a second degree differential equation of the form y''+p(x)y'+q(x)y the wronskian is given by

$e^{\int -p(x) dx}$

In this case, by dividing the equation by 121 we get that p(x) = 10/11. So the wronskian is

$e^{\int -\frac{10}{11} dx} = e^{\frac{-10x}{11}}$

Note that this function is always positive, and thus, never zero. So $y_1, y_2$ is a fundamental set of solutions.

8 0

2 years ago

5 + n2 > 8<br> A. n > 6<br> B. n>3<br> C. n>1.5<br> D. n < 26

san4es73 [151]

N•2>8
then dive both sides 2n>8
and get n>4

4 0

3 years ago

Read 2 more answers

Through: (3, 4), slope = -2

sineoko [7]

Answer:

y = -2x - 2

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Points: (3, 4)

Slope: -2

y = -2x + b

4 = -2 ( 3 ) + b

4 = -6 + b

b = -2

y = -2x - 2

8 0

2 years ago

Read 2 more answers

The picture shows the footprints of a man walking. The pace length P is the distance between the rear of two consecutive footpri

Rina8888 [55]

Bernard’s walking speed is 140 meters per minute

Bernard’s walking speed is 8.4 kilometers per hour

Step-by-step explanation:

The pace length P is the distance between the rear of two consecutive footprints

The formula, n P = 140, gives an approximate relationship between n and P where,

n = number of steps per minute
P = pace length in meters
Bernard knows his pace length is 0.80 meters
The formula applies to Bernard’s walking

We need to calculate Bernard’s walking speed in meters per minute and in kilometers per hour

∵ n = number of steps per minute

∴ n unit is number / minute

∵ P = pace length in meters

∴ P unit is meter

- That means n P unit is meters/minute

∴ n P represents the speed in meters per second

∵ The formula applies to Bernard’s walking

∵ His pace length is 0.80 meters

∵ n P = 140

∴ n(0.8) = 140

- Divide both sides by 0.8

∴ n = 175

- That means he moves 175 steps per minute

∵ The distance he walks in minute = 175 × 0.8 = 140 meters/minute

∴ His speed is 140 meters per minute

Bernard’s walking speed is 140 meters per minute

∵ 1 km = 1000 m

∵ 1 hour = 60 minutes

- Divide the meters by 1000 and the minute by 60 to change

from meters per minute to kilometers per hour

∴ His walking speed = $\frac{140}{1000}$ ÷ $\frac{1}{60}$

- Change ÷ to × and reciprocal the fraction after the division sign

∴ His walking speed = $\frac{140}{1000}$ × $\frac{60}{1}$ = 8.4 km/h

Bernard’s walking speed is 8.4 kilometers per hour

Learn more:

You can learn more about the speed in brainly.com/question/5461619

#LearnwithBrainly

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3 years ago

is searching online for airline tickets. Two weeks ago, the cost to fly from to was 210 $. Now the cost is 305$. What is the

harkovskaia [24]

Answer:

Step-by-step explanation:

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3 years ago