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A motion sensor has a range of 65 meters as shown. The ultrasonic waves sweeping out from the sensor span an angle of 135°.

VMariaS [17]

The approximate area that is within range of the motion sensor is 4975 square meters

<h3>How to determine the area of the range?</h3>

The figure is not given, however the area of the range can be calculated without the figure.

The given parameters are:

Angle, ⊕ = 135°

Radius, r = 65 meters

The area of the range is calculated using the following sector area

$A = \frac{\theta}{360} * \pi r^2$

This gives

$A = \frac{135}{360} * 3.14 * 65^2$

Evaluate

A = 4974.9375

Approximate

A = 4975

Hence, the approximate area that is within range of the motion sensor is 4975 square meters

Read more about sector areas at:

brainly.com/question/16736105

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4 0

2 years ago

Solve the equation for the given variable. *<br> 3(x + 4) – 2 = 10

algol13

Answer: 0

Step-by-step explanation:

3)(x)+(3)(4)+−2=10

(3x)+(12+−2)=10

3x+10=10

3x+10−10=10−10

3x=0

3x/3 = 0/3

x=0

6 0

3 years ago

X-y+z=-4<br><br> 3x+2y-z=5<br><br> -2x+3y-z=15<br><br> How do I solve this?

Lera25 [3.4K]

$1)\ \ \ x-y+z=-4\ \ \ \Rightarrow\ \ \ z=-4-x+y\\\\2)\ \ \ 3x+2y-z=5 \\.\ \ \ \ \Rightarrow\ \ 3x+2y-(-4-x+y)=5 \\.\ \ \ \ \Rightarrow\ \ 3x+2y+4+x-y=5 \\.\ \ \ \ \Rightarrow\ \ 4x+y=1\\\\3)\ \ \ -2x+3y-z=15\\.\ \ \ \ \Rightarrow\ \ -2x+3y-(-4-x+y)=15\\.\ \ \ \ \Rightarrow\ \ -2x+3y+4+x-y=15\\.\ \ \ \ \Rightarrow\ \ -x+2y=11\\--------------------\\$

$z=-4-x+y\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ and\\ \left \{ {{4x+y=1\ \ \ \ } \atop {-x+2y=11\ /\cdot4}} \right. \\\\\left \{ {{4x+y=1\ \ \ \ } \atop {-4x+8y=44}} \right. \\-------\\y+8y=1+44\\9y=45\ /:9\\y=5\\\\-x+2y=11\ \ \ \Rightarrow\ \ \ x=2y-11\ \ \ \Rightarrow\ \ \ x=2\cdot5-11=-1\\\\z=-4-x+y=-4-(-1)+5=-4+1+5=2\\\\Ans.\ x=-1\ \ \ and\ \ \ y=5\ \ \ and\ \ \ z=2$

5 0

3 years ago

How would I solve the problem:<br> e^4x=120

borishaifa [10]

Answer: x = 1.1968729357 ; or, round to: 1.2 .
____________________________________________ You would take the "ln" (that is, "natural logarithm") of EACH side of the equation:

ln (e^4x) = ln (120);
______________________
Then continue:

4x ln e = ln 120

4x = ln 120 ; (since "ln e = 1")

then divide EACH side of the equation by "4", to isolate "x" on one side of the equation; and to solve for "x" ;
___________________________________
4x / 4 = (ln 120) / 4 ;
___________________________
x = (ln 120) / 4 ;
______________________________
Using a calculator:
_________________________________________________________
x = (ln 120) / 4 = (4.78749174278) / 4 = 1.1968729357
Answer: x = 1.1968729357 ; or, round to: 1.2 .
____________________________________________

8 0

3 years ago

A group of people were asked if they had run a red light in the last year. 290 responded "yes", and 177 responded "no". Find the

GuDViN [60]

Answer:

0.621

Step-by-step explanation:

Number of people that have run a red light in the last year = 290

Number of people that have not run a red light in the last year = 177

Total number of respondents = 290 + 177

= 467

Pr(if a person is chosen at random, they have run a red light in the last year) = $\frac{number of people who has run the red light last year}{total number of respondents}$

= $\frac{290}{467}$

= 0.621

The probability that if a person is chosen at random, they have run a red light in the last year is 0.621.

6 0

3 years ago