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2 years ago

The endpoints of a regular pentagon are (-1,4) and (2,3). What is the perimeter of the Pentagon?

Mathematics

1 answer:

ryzh [129]2 years ago

4 0

the assumption being that the endpoints are two continuous points in the pentagon, Check picture below.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-1}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[2-(-1)]^2+[3-4]^2}\implies d=\sqrt{(2+1)^2+(3-4)^2} \\\\\\ d=\sqrt{9+1}\implies d=\sqrt{10}~\hfill \stackrel{\stackrel{~\hfill \stackrel{\textit{5 sides}}{}}{\textit{perimeter of the pentagon}}}{5\sqrt{10}}$

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The line AB has midpoint (2,5).<br> A has coordinates (1, 2).<br> Find the coordinates of B.

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Answer:

$X_m = \frac{A_x +B_x}{2}= \frac{1+B_x}{2}= 2$

And we can solve for $B_x$ and we got:

$1+B_x = 4$

$B_x = 3$

$Y_m = \frac{A_y +B_y}{2}= \frac{2+B_y}{2}= 5$

And we can solve for $B_x$ and we got:

$2+B_y = 10$

$B_y = 8$

So then the coordinates for B are (3,8)

Step-by-step explanation:

For this case we know that the midpoint for the segment AB is (2,5)

And we know that the coordinates of A are (1,2)

We know that for a given segment the formulas in order to find the midpoint are given by:

$X_m = \frac{A_x +B_x}{2}= \frac{1+B_x}{2}= 2$

And we can solve for $B_x$ and we got:

$1+B_x = 4$

$B_x = 3$

$Y_m = \frac{A_y +B_y}{2}= \frac{2+B_y}{2}= 5$

And we can solve for $B_x$ and we got:

$2+B_y = 10$

$B_y = 8$

So then the coordinates for B are (3,8)

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3 years ago

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Answer:

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goldenfox [79]

Answer: y=23

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3 years ago

What is the decibel level of the noise from a firecracker with intensity 10^-4 watts per square inch? Use a logarithmic model

vagabundo [1.1K]

Answer:

$\large \boxed{\text{110 db}}$

Step-by-step explanation:

The intensity β of a sound wave in decibels is given by the formula

$\beta = 10 \log \left (\dfrac{I}{I_{0}} \right)$

and I₀ = the reference intensity (10⁻¹² W/m²)

Data:

I = 10⁻⁴ W·in⁻²

Calculations:

1. Convert watts per square inch to watts per square metre

$\text{Sound level} = \dfrac{10^{-4}\text{ W}}{\text{1 in}^{2}} \times \left(\dfrac{\text{39.37 in}}{\text{1 m}}\right )^{2} = 1.5 \times 10^{-1} \text{ W$\cdot$m}^{-2}$

2. Convert the intensity to decibels.

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