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Alex_Xolod [135]
3 years ago
10

A mechanic alters the lighthouse to make the light rotate in such a way that is reflection travels north word along the wall at

a constant rate of 100 ft./s how fast in radians per second is the beam of light rotating when the lights reflection is 100 feet north of the point on the wall that is closest to the lighthouse
Mathematics
1 answer:
Pavel [41]3 years ago
8 0

Answer:

The correct solution will be "1 Rad/sec".

Step-by-step explanation:

The given value is:

Velocity (V)

= 100 ft./sec

As we know,

Angular velocity,

⇒  \omega=\frac{V}{R}

On substituting the values, we get

⇒     =\frac{100}{100}

⇒     =1 \ Rad/sec

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Michelle found the area of a circle as 78.5 〖in〗^2. She used 3.14 for π. What is the radius of the circle? Explain how you found
SCORPION-xisa [38]

Answer:

r = 5 inches

Step-by-step explanation:

Area of circle, A=78.5\ in^2

It is required to find the radius of the circle. The area of a circle is given by the formula :

A=\pi r^2

r is radius of the circle

r=\sqrt{\dfrac{A}{\pi}} \\\\r=\sqrt{\dfrac{78.5}{3.14}} \\\\r=5\ \text{inch}

So, the radius of the circle is 5 inches.

5 0
3 years ago
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steposvetlana [31]

Answer:

See Below.

Step-by-step explanation:

In the given figure, AP = BP = PC.

And we want to prove that ∠ABC is a right angle.

Since AP = BP and BP = PC, we can create two isosceles triangles: ΔAPB and ΔCPB.

By the definition of isosceles triangles, in ΔAPB, ∠PAB and ∠PBA are equivalent. Let the measure of each of them be <em>x°</em>.

Likewise, in ΔCPB, ∠PCB and ∠PBC are equivalent.

And since AP = BP = PC, each of the angles∠PCB and ∠PBC will also be equivalent to <em>x°.</em>

<em />

And since the sum of the interior angles of a triangle total 180°, we acquire:

\angle PAB+\angle PBA+\angle PCB+\angle PBC=180

Since they are all equivalent:

4x=180

Hence:

x=45^\circ

∠ABC is the sum of ∠PBA and ∠PBC, each of which measures 45°. Hence:

\angle ABC=\angle PBA+\angle PBC=45+45=90^\circ

8 0
3 years ago
Read 2 more answers
Nitric acid (specific gravity 1.42) costs $51.95 per liter. A student spills 5.112 kg of nitric acid in the laboratory, what is
Leno4ka [110]

Answer:

The cost of wasted nitric acid is $187.02

Step-by-step explanation:

Since it is given that specific gravity of Nitric Acid is 1.42 Thus the density of nitric acid is

\rho _{acid}=S.G\times \rho _{water}\\\\\\\rho_{acid}=1.42\times 1\frac{g}{cm^3}\\\\\rho_{acid}=1.42g/cm^3

Now from the basic relation of mass volume and density we have

\rho =\frac{Mass}{Volume}\\\\\therefore Volume=\frac{Mass}{\rho }

Since the mass of the nitric acid is given to be 5.112 kg = 5112 grams

Thus the volume of nitric acid is

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Now we know that 1000 cubic centimeters euals 1 litrer

Thus the calculated volume in liters is

V_{liters}=\frac{3600}{1000}=3.6Liters

Thus the cost of acid spilled  equals

Cost=3.6\times 51.95=187.02

5 0
3 years ago
Find the slope of the line passing through the points (3,9) and 12,-5)​
astraxan [27]

Answer:

9/-24  or ~ -0.38

Step-by-step explanation:

x       y

3      9

12   -15

from 9 to -15 it will be subtracting 24

From 3 to 12 it will be adding 9

y/x = 9/-24  or -0.375 ~ -0.38

7 0
3 years ago
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