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Volgvan
2 years ago
15

X-2y=4 going through (1,-6)

Mathematics
2 answers:
kakasveta [241]2 years ago
4 0

Answer:

A.

y

=

−

2

x

−

3

.

Explanation:

First, rewrite the equation in slope-intercept form:

y

=

m

x

+

b

.

−

x

+

2

y

=

4

⇒

2

y

=

x

+

4

⇒

y

=

1

2

x

+

2

So the slope of the given line is

m

=

1

2

.

Lines that are perpendicular have slopes that are negative reciprocals of each other. Meaning, if a line has slope

m

, then a line perpendicular to this has slope

m

*

=

−

1

m

. That means the slope of our perpendicular line is

m

*

=

−

1

1

/

2

=

−

2

.

Knowing the new slope and a point, we can find an equation for our perpendicular line by using the slope-point equation

y

−

y

1

=

m

(

x

−

x

1

)

, or by plugging in the given

(

x

,

y

)

point (and the new slope

m

*

) into

y

=

m

x

+

b

to find

b

for the new line.

y

−

y

1

=

m

(

x

−

x

1

)

⇒

y

−

1

=

−

2

[

x

−

(

−

2

)

]

⇒

y

−

1

=

−

2

[

x

+

2

]

⇒

y

=

−

2

x

−

3

or

y

=

m

x

+

b

⇒

1

=

−

2

(

−

2

)

+

b

⇒

1

=

4

+

b

⇒

b

=

−

3

∴

y

=

m

x

+

b

becomes

y

=

−

2

x

−

3

.

Step-by-step explanation:

attashe74 [19]2 years ago
4 0

Answer:

false

Step-by-step explanation:

Okay so we plug in the values for x and y to make the equation:

1 - 2 x -6 = 4

And then we just solve the left side:

2 x -6 = -12

1 - -12 = 1 + 12 = 13

So this is false

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Answer:

a)\sqrt{144-288t+208t^2} b.) -12knots, 8 knots c) No e)4\sqrt{13}

Step-by-step explanation:

We know that the initial distance between ships A and B was 12 nautical miles. Ship A moves at 12 knots(nautical miles per hour) south. Ship B moves at 8 knots east.

a)

We know that at time t , the ship A has moved 12\dot t (n.m) and ship B has moved 8\dot t (n.m). We also know that the ship A moves closer to the line of the movement of B and that ship B moves further on its line.

Using Pythagorean theorem, we can write the distance s as:

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b)

We want to find \frac{ds}{dt} for t=0 and t=1

\sqrt{144-288t+208t^2}|\frac{d}{dt}\\\\\frac{ds}{dt}=\frac{1}{2\sqrt{144-288t+208t^2}}\dot (-288+416t)\\\\\frac{ds}{dt}=\frac{208t-144}{\sqrt{144-288t+208t^2}}\\\\\frac{ds}{dt}(0)=\frac{208\dot 0-144}{\sqrt{144-288\dot 0 + 209\dot 0^2}}=-12knots\\\\\frac{ds}{dt}(1)=\frac{208\dot 1-144}{\sqrt{144-288\dot 1 + 209\dot 1^2}}=8knots

c)

We know that the visibility was 5n.m. We want to see whether the distance s was under 5 miles at any point.

Ships have seen each other = s\leq 5\\\\\sqrt{144-288t+208t^2}\leq 5\\\\144-288t+208t^2\leq 25\\\\199-288t+208t^2\leq 0

Since function f(x)=199-288x+208x^2 is quadratic, concave up and has no real roots, we know that 199-288x+208x^2>0 for every t. So, the ships haven't seen each other.

d)

Attachedis the graph of s(red) and ds/dt(blue). We can see that our results from parts b and c were correct.

e)

Function ds/dt has a horizontal asympote in the first quadrant if

                                                \lim_{t \to \infty} \frac{ds}{dt}

So, lets check this limit:

\lim_{t \to \infty} \frac{ds}{dt}=\lim_{t \to \infty} \frac{208t-144}{\sqrt{144-288t+208t^2}}\\\\=\lim_{t \to \infty} \frac{208-\frac{144}{t}}{\sqrt{\frac{144}{t^2}-\frac{288}{t}+208}}\\\\=\frac{208-0}{\sqrt{0-0+208}}\\\\=\frac{208}{\sqrt{208}}\\\\=4\sqrt{13}

Notice that:

4\sqrt{13}=\sqrt{12^2+5^2}=√(speed of ship A² + speed of ship B²)

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