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2 years ago

Which of the following angles can be trisected using only a compass and straightedge?

Mathematics

2 answers:

velikii [3]2 years ago

7 0

Answer:

The correct option is (<u>A) 90°</u>

Step-by-step explanation:

The angles can be trisected which constructive angle θ, an angle of measure 3θ can be trivially trisected.

So, the angle in option (A) is written as 3θ.

3θ=3(30°)

but rest options can't write as 3θ.

Hence, the correct option is (<u>A) 90°</u>

Butoxors [25]2 years ago

6 0

I believe it's A......

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Find the mass and center of mass of the lamina that occupies the region D and has the given density function rho. D = {(x, y) |

Bas_tet [7]

Answer:

$M=168k$

$(\bar{x},\bar{y})=(5,\frac{85}{28})$

Step-by-step explanation:

Let's begin with the mass definition in terms of density.

$M=\int\int \rho dA$

Now, we know the limits of the integrals of x and y, and also know that ρ = ky², so we will have:

$M=\int^{9}_{1}\int^{4}_{1}ky^{2} dydx$

Let's solve this integral:

$M=k\int^{9}_{1}\frac{y^{3}}{3}|^{4}_{1}dx$

$M=k\int^{9}_{1}21dx$

$M=21k\int^{9}_{1}dx=21k*x|^{9}_{1}$

So the mass will be:

$M=21k*8=168k$

Now we need to find the x-coordinate of the center of mass.

$\bar{x}=\frac{1}{M}\int\int x*\rho dydx$

$\bar{x}=\frac{1}{M}\int^{9}_{1}\int^{4}_{1}x*ky^{2} dydx$

$\bar{x}=\frac{k}{168k}\int^{9}_{1}\int^{4}_{1}x*y^{2} dydx$

$\bar{x}=\frac{1}{168}\int^{9}_{1}x*\frac{y^{3}}{3}|^{4}_{1}dx$

$\bar{x}=\frac{1}{168}\int^{9}_{1}x*21 dx$

$\bar{x}=\frac{21}{168}\frac{x^{2}}{2}|^{9}_{1}$

$\bar{x}=\frac{21}{168}*40=5$

Now we need to find the y-coordinate of the center of mass.

$\bar{y}=\frac{1}{M}\int\int y*\rho dydx$

$\bar{y}=\frac{1}{M}\int^{9}_{1}\int^{4}_{1}y*ky^{2} dydx$

$\bar{y}=\frac{k}{168k}\int^{9}_{1}\int^{4}_{1}y^{3} dydx$

$\bar{y}=\frac{1}{168}\int^{9}_{1}\frac{y^{4}}{4}|^{4}_{1}dx$

$\bar{y}=\frac{1}{168}\int^{9}_{1}\frac{255}{4}dx$

$\bar{y}=\frac{255}{672}\int^{9}_{1}dx$

$\bar{y}=\frac{255}{672}8=\frac{2040}{672}$

$\bar{y}=\frac{85}{28}$

Therefore the center of mass is:

$(\bar{x},\bar{y})=(5,\frac{85}{28})$

I hope it helps you!

3 0

2 years ago

L = loudness, in decibels (dB); I = sound intensity, in watts/m2; I0 = 10−12 watts/m2

irina [24]

The sound intensity of the Pile Driver is 39.5
or nearly 40 times the sound intensity of the jackhammer.

Given with Loudness in dB for pile driver = 112 dB
We have to convert it in terms of sound intensity.
First,
112dB/10 = 11.2

Then we'll use this as exponent of 10
(10)^(11.2) = 1.5849 * 10 ^ 11

Then use the equation of Watts per square meter to find the intensity:
I / (10^-12 W/m^2) =1.5849 * 10 ^ 11
I = sound intensity = 0.158

Then compare:

Sound intensity of Pile Driver/ Sound intensity of Jackhammer
(0.158) / (0.004)
= 39.5
or nearly 40 times the jackhammer.

3 0

2 years ago

Read 2 more answers

Which is the best description of the graph of the function f(x) = 60(One-third)x? The graph has an initial value of 20, and each

dezoksy [38]

Answer:

The graph has an initial value of 60, and each successive term is determined by multiplying by One-third.

Step-by-step explanation:

Which is the best description of the graph of the function f(x) = 60(One-third)x?

A. The graph has an initial value of 20, and each successive term is determined by subtracting One-third.

B. The graph has an initial value of 20, and each successive term is determined by multiplying by One-third.

C. The graph has an initial value of 60, and each successive term is determined by subtracting One-third.

D. The graph has an initial value of 60, and each successive term is determined by multiplying by One-third.

Given:

f(x) = 60 (1/3)^x see graph attached.

Examining the graph, we notice that

1. The graph has an initial value of 60, at point (0,60)

2. The graph decreases as x increases. Each successive term is determined by multiplying by 1/3, namely in the sequence

{(0,60), (1,20), (2, 20/3), (3, 20/9), ...}

This means the choice is D (or the fourth one).

4 0

1 year ago

Read 2 more answers

Write two expressions where the solution is 41

Marina CMI [18]

40+1=41
10×4+1=41
that is what I have so there you go

3 0

2 years ago

50 POINTS!! PLEASE ASAP. The director of a local ballet company needs to print the programs for the next performance. Janet’s Pr

Maru [420]

For this case we find the expression that represents the cost of each printing press.

x: Be the variable that represents the number of programs to print

So:

Cost 1: Janet’s Print Shop

$C (x) = 0.25x + 35$

Cost 2: The Printing Press

$C (x) = 0.15x + 50$

If we want to find the number of programs for which the costs are the same, then we equate both equations:

$0.25x + 35 = 0.15x + 50\\0.25x-0.15x = 50-35\\0.1x = 15\\x = \frac {15} {0.1}\\x = 150$

Thus, for 150 programs the cost is the same.

Answer:

For 150 programs the cost is the same.

5 0

2 years ago

Read 2 more answers