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Digiron [165]
3 years ago
14

A n-faced regular polyhedron consists of 2n edges and (2n-4) vertices. Find n .

Mathematics
1 answer:
ira [324]3 years ago
3 0

We could use Euler's polyhedron formula:

F=n\qquad\qquad\text{(Faces)}\\\\E=2n\qquad\qquad\text{(Edges)}\\\\V=2n-4\qquad\qquad\text{(Vertices)}\\\\\\V-E+F=2\\\\2n-4-2n+n=2\\\\-4+n=2\qquad|+4\\\\\boxed{n=6}



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A red car is driving along the road in the direction of the police car and is 130 feet up the road from the location of the poli
pishuonlain [190]

Complete question:

A police car is located 50 feet to the side of a straight road. A red car is driving along the road in the direction of the police car and is 130 feet up the road from the location of the police car. The police radar reads that the distance between the police car and the red car is decreasing at a rate of 75 feet per second. How fast is the red car actually traveling along the road.

Answer:

The red car is traveling along the road at 80.356 ft/s

Step-by-step explanation:

Given

Police car is 50 feet side off the road

Red car is 130 feet up the road

Distance between them is decreasing at the rate of 75 feet per sec

Let x be how far the police is off the road.

Let y be how far the red car is up the road.  

Let h be the distance between the police and the red car.

This forms a right triangle so we can use the Pythagorean theorem, to solve for h

h² = x² + y²

h² = 50² + 130²

h² = 19400

h = √19400

h = 139.284 ft

Again;

Let dx/dt be how fast the police is traveling toward the road.

Let dy/dt  be how fast the red car is traveling along the road.

Let dh/dt be how fast the distance between the police and the car is decreasing.

Recall that, h² = x² + y² (now differentiate with respect to time, t)

2h(dh/dt) = 2x(dx/dt) + 2y(dy/dt)

divide through by 2

h(dh/dt) = x(dx/dt) + y(dy/dt)

since the police car is not, dx/dt = 0

and dy/dt is the how fast is the red car actually traveling along the road

139.284(75) = 50(0) + 130(dy/dt)

10446.3 = 0 + 130(dy/dt)

dy/dt = 10446.3 / 130

dy/dt = 80.356 ft/s

Therefore, the red car is traveling along the road at 80.356 ft/s

6 0
3 years ago
168_138_123_ _ _ _ _ _ me ayudan por favor?✅​
Mazyrski [523]

paso a paso

Step-by-step explanation:

tienes que saber cuanto le quito al otro por que

el primero es 168 y el otro es 138 cubro le quito 30 y el otro

es 123 igual tienes que quitarle tal ves es sumarle primero y después 2 de restarle

espero que te sirva

5 0
2 years ago
The table gives the probabilities of which type of sandwich is likely to be the top-selling item each month in restaurants acros
spin [16.1K]
2,3,4,1, the probability is in order from greatest to least. If they asked for least to greatest then, 1,4,3,2. So use the least to greatest one.
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What is the decimal expansion of 7/2
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Answer:

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Step-by-step explanation:

you just divide ig

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The figure the Floor Plan of a balcony ,it consists of △ABC and semi-circle ,
ivanzaharov [21]

Step-by-step explanation:

(a) In right triangle ABC,

AC^2 =AB^2 +BC^2  \\  =  {12}^{2} +  {5}^{2}   \\  = 144 + 25 \\  = 169 \\  AC =  \sqrt{169}  \\  \therefore \: AC =  13\: m \\  \\ AC \: is \: the \: diameter \: of \: semicircle \\  \therefore \: r =  \frac{1}{2} \times  AC = \frac{1}{2} \times 13 = 6.5 \: m \\  Circumference \:of \:semi-circle \\ C = \pi \: r = 3.14 \times 6.5 = 20.41 \:m\:

Perimeter of Balcony = 12 + 5 + 20.41 = 37.41 m

(b) Area of balcony

=\frac{1}{2}\times 12\times 5+\frac{1}{2} \pi r^2 \\\\=\times 6\times 5+\frac{1}{2} \times 3.14\times (6.5)^2 \\\\=30+\frac{1}{2} \times 3.14\times42.25\\\\= 30+\frac{1}{2} \times 132.665\\\\= 30 + 66.3325\\\\= 96.3325 \:m^2 \\\\\approx 96. 33\:m^2

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3 years ago
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