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3 years ago

Katie said, "Negative numbers are integers". What was her error?

Mathematics

1 answer:

Sunny_sXe [5.5K]3 years ago

6 0

Negative numbers are integers.The set of integers include negative numbers, positive numbers, and zero

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Solving distance problems- <br> 10 points

slega [8]

Answer:

1. 54 and 9/20 km

2. 80 mm

3. 1.142 mi

4.0.83333 cm

Step-by-step explanation:

Do them all by the butterfly method.

5 0

2 years ago

Distance between two ships At noon, ship A was 12 nautical miles due north of ship B. Ship A was sailing south at 12 knots (naut

frozen [14]

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.

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:

$\sqrt{(12-12\dot t)^2 + (8\dot t)^2}\\s=\sqrt{144-288t+144t^2+64t^2}\\s=\sqrt{144-288t+208t^2}$

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

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

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.

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

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)

5 0

3 years ago

(b) In the figure below, mL VYW=48° and m VX=55º. Find m VW.

sergejj [24]

Answer: 151⁰

Ok done. Thank to me :>

7 0

2 years ago

4x+2> or equal to 14 and -21x+1>22, find all real numbers for x

astraxan [27]

$4x+2\geq 14\ and -21x+1>22 \\\\4x\geq 12 \ |:3\ and \ -21x>21 \ |:(-21)\\\\ x\geq 3 \ and \ x$
No solutions

8 0

3 years ago

Maria must choose a number between 61 and 107 that is a multiple of 5, 6, and 10. Write all the numbers that she could choose. I

RSB [31]

Multiples of 5 : 65,70,75,80,85,90,95,100,105
multiples of 6 : 66,72,78,84,90,96,102
multiples of 10 : 70,80,90,100

she could choose : 90...and thats it

4 0

3 years ago