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Licemer1 [7]
3 years ago
11

A 5-meter ladder is leaning against the side of a house. The foot of the ladder is pulled away from the house at a rate of 0.4 m

/sec. Determine how fast the top of the ladder is descending when the foot of the ladder is 3 meters from the house.
Mathematics
1 answer:
Flura [38]3 years ago
3 0
<h2>The top of the ladder is descending at 0.3 m/s.</h2>

Step-by-step explanation:

By Pythagoras theorem we know that

              Hypotenuse² = Base² + Perpendicular²

                   h² = b² + p²

We have for ladder

                        h = 5 m

                        b = 3 m

                        5² = 3² + p²

                        p = 4 m

                        \frac{db}{dt}=0.4m/s\\\\\frac{dh}{dt}=0

Differentiating h² = b² + p² with respect to time

                    2h\times \frac{dh}{dt}=2b\times \frac{db}{dt}+2p\times \frac{dp}{dt}\\\\5\times 0=3\times 0.4+4\times \frac{dp}{dt}\\\\\frac{dp}{dt}=-0.3m/s

The top of the ladder is descending at 0.3 m/s.

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A trumpet has a length of 140cm. The first valve lowers the root note by two semitones (f1/f0 = 2-2/12) and the second valve low
Alexxandr [17]

Answer:

a.  17.145cm

b. 8.325cm

c. 0.846

d. 2.896

Step-by-step explanation:

It is known that frequency is inversely proportional to length.

Case 1: The player presses only the first valve.

f₁/fo = 2^{-2/12} = lo/l₁

given that lo= 140cm.

l₁ = 2^{2/12}lo = 157.145

change in length:

l₁ - lo = 157.145 - 140 = 17.145cm

Case 2: The player presses only the second valve.

f₂/fo = 2^{-1/12} = lo/l₂

l₂ = 2^{1/12}lo = 148.325cm

l₂  - lo= 148.325-140 = 8.325cm

Case 3: The player presses both the first and second valve.

Change in length is the sum of change in length when they are individually pressed.

l₃ - lo = 17.145+8.325 = 25.47cm

l₃ = 25.47cm+lo = 165.47cm

f₃/fo  = 2^{-n/12} = lo/l₃

f₃/fo = 2^{-n/12} = 140/{165.47 = 0.846

2^{-n/12} = 0.846\Rightarrow n/12 = -log(0.846)/log(2) = 0.2413

n = 0.2413*12 = 2.896

5 0
3 years ago
2(p + 1) = 18<br> what is p?
marshall27 [118]
It would be: 2(p + 1) = 18
= 2p + 2 = 18
= 2p = 18 - 2
= 2p = 16
= p = 16/2
= p = 8

In short, Your Answer would be 8

Hope this helps!
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Answer:

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Step-by-step explanation:

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mihalych1998 [28]

Answer:

C. x=20^{\circ}

Step-by-step explanation:

Angle 6 and angle with measure 45° are vertical angles (opposite angles whan two lines intersect). By Vertical Angles Theorem, vertical angles are congruent, so

m\angle 6=45^{\circ}

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