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2 years ago

Pythagoras and True Love

Mathematics

1 answer:

Katena32 [7]2 years ago

6 0

Let us find the length of rope Jules will need using the pythagoras theorem .

Width of the moat ( let the moat be the base of this triangle ) = 14 foot

Distance from Roma's window to the boat ( let this be the side of the triangle where the right angle is present ) =20 feet

Then the length of rope needed ( hypotenuse ) =

= Let us name the triangle that is formed as △ ABC . Then ;

In △ ABC :

AB = the width of moat ( leg of triangle ) = 14 foot

BC = The distance from the window to the moat ( base ) = 20 feet

AC = Length of rope needed ( hypotenuse ) =

= AB ² + BC² = AC² ( according to the pythagoras theorem the square on the hypotenuse will be equal to the sum of the squares on the other two legs )

= 14² + 20² = AC²

= 196 + 400 = AC²

= 596 = AC²

= 24 × 24 = AC × AC

= 24 foot = AC = length of rope needed by jules .

Therefore , Jules will need a 24 foot rope so that his girlfriend can slide down and escape from her apartment .

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A buoy floating in the sea is bobbing in simple harmonic motion with period 2 seconds and amplitude 8 in. Its displacement d fro

Mrac [35]

Answer:

The equation of the displacement $d$ as a function of time $t$ is :

$d(t)=8sin(\pi t+\pi )$

Step-by-step explanation:

Generally , A simple harmonic wave is a sinusoidal function that is it can be expressed in simple $sin$ or $cos$ terms.

Thus,

$d(t) = Asin(wt+c)$

is the general form of displacement of a SHM.

where,

$d(t)$ is the displacement with respect to the mean position at any time $t$
$A$ is amplitude
$w$ is the natural frequency of oscillation ( $rads^{-1}$ )
$c$ is the phase angle which indicates the initial position of the object in SHM ( $rad$ )

given,

Time period ( $T$ ) = $2s$
$A=8$
The natural frequency ( $w$ ) and time period ( $T$ ) is :

$w=\frac{2\pi} {T}$

∴

$w$ = $\frac{2\pi }{2} = \pi$ $rads^{-1}$

∴

the equation :

⇒ $d(t)=8sin(\pi t+c)$ ------1

since $d=0$ when $t=o$ ,

⇒ $0=8sinc\\c=n\pi$ ------2

where n is an integer ;

⇒since the bouy immediately moves in the negative direction , $x$ must be negative or c must be an odd multiple of $\pi$ .

⇒ $d(t) = 8sin(\pi t+(2k+1)\pi )$ ------3

where k is also an integer ;

the least value of $k=0$ ;

thus ,

the equation is :

$d(t)=8sin(\pi t+\pi )$

7 0

2 years ago

A school theater director is planning a voluntary trip to New York City for students. He sends a poll regarding interest

PilotLPTM [1.2K]

Answer:

Sixty-eight percent is likely an overestimate for the percentage of parents interested in the trip.

Step-by-step explanation:

6 0

2 years ago

How do I find each measure? Please I need answers ASAP it's due at 1:50

Norma-Jean [14]

Answer:

Angle CAD is 44 degrees

Angle ACD is 44 degrees

Angle ACB is 136 degrees

Angle ABC is 22 degrees

Explanation:

29. Triangle ADC is an isosceles triangle because it has two equal sides.

If segments AD and DC are congruent, then segment AC is the base and the base angles of an isosceles triangle are equal.

Let x be angle CAD.

Let's go ahead x;

$\begin{gathered} 92+x+x=180\text{ (sum of angles in a triangle)} \\ 92+2x=180 \\ 2x=180-92 \\ 2x=88 \\ x=\frac{88}{2} \\ \therefore x=44^{\circ} \end{gathered}$

Therefore, measure of angle CAD is 44 degrees.

30. Measure of angle ACD is 44 degrees (Base angles of an isosceles triangle are equal)

31. Let angle ACB be y,

Let's go ahead and find measure of angle ACB;

$\begin{gathered} 44+y=180\text{ (angles on a straight line)} \\ y=180-44 \\ \therefore y=136^{\circ} \end{gathered}$

So measure of angle ACB is 136 degrees.

32. Let angle ABC be z.

Triangle ACB is also an isosceles triangle so the base angles are the same.

Let's go ahead and find z;

$\begin{gathered} 136+z+z=180_{}\text{ (sum of angles in a triangle)} \\ 138+2z=180 \\ 2z=180-136 \\ 2z=44 \\ z=\frac{44}{2} \\ \therefore z=22^{\circ} \end{gathered}$

So measure of angle ABC is 22 degrees.

3 0

8 months ago

What is the length of the side opposite the 60 degree angle?

yaroslaw [1]

All triangles equal 180 so the answer would be set up as follows:
180-60-90 (right triangle) = 30 degrees
30 degrees is the answer

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3 years ago

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