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Verdich [7]
3 years ago
6

A central angle of a circle measures 1.5 radians. If the radius of the circle is 3 cm, what is the area of the related sector?

Mathematics
1 answer:
soldi70 [24.7K]3 years ago
7 0

Answer:

Option B. 6.75\ cm^{2}

Step-by-step explanation:

we know that

The area of a circle is equal to

A=\pi r^{2}

we have

r=3\ cm

substitute

A=\pi (3^{2})=9 \pi\ cm^{2}

Remember that

2\pi radians subtends the complete circle of area 9 \pi\ cm^{2}

so

by proportion

Find the area of the related sector for a central angle of 1.5 radians

Let

x------> the area of the related sector

\frac{9 \pi}{2\pi}\frac{cm^{2}}{radians} =\frac{x}{1.5}\frac{cm^{2}}{radians}\\ \\x=9*1.5/2\\ \\x= 6.75\ cm^{2}

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Biologists have found that the number of chirps some types of cricket make per minute depends upon the temperature this relation
Alex Ar [27]

Answer: Crickets make 172 chirps/min at 80 degrees Fahrenheit

Step-by-step explanation:

Step 1

Using the point slope formulae for Linear functions , we have that

y - y1 = m(x - x1)

where x  and y are two points  representing the  temperature and chirps /min respectively

And  

m= slope

Step 2 : Finding the slope , m

where x1=60

           y1=92

           x2= 75

           y2=152

m= (y2-y1)/ (x2-x1)

= (152- 92)/(75-60)

=60/15 =4

Bringing down the point/slope formula and imputing the known values to find our equation to show the relationship cricket make per minute and  the temperature

y - y1 = m(x - x1)

y - 92= 4(x - 60)

y - 92 = 4x -240

y = 4x - 240 + 92

y = 4x - 148

Step 3

To find the number of chirps be per minute (y) if the temperature is 80 degrees Fahrenheit( x)

y = 4(80) - 160

y = 320 - 148

y = 172 chirps/min at 80 degrees Fahrenheit

6 0
3 years ago
(4x + 3)(4x - 3)<br> Help pls
tekilochka [14]

Answer:

16x^2-9

Step-by-step explanation:

\left(4x+3\right)\left(4x-3\right)

We´ll <u>Apply Difference Two Squares Formula:</u>

  • \left(a+b\right)\left(a-b\right)=a^2-b^2

\longmapsto \left(4x+3\right)\left(4x-3\right)

\longmapsto \left(4x\right)^2-3^2

<u>Apply exponent rule</u>:

  • \left(a\times \:b\right)^n=a^nb^n

\longmapsto 4^2x^2-3^2

\longmapsto 16x^2-9

_________________________

6 0
3 years ago
Read 2 more answers
Confused and need help
vodka [1.7K]

First, reflect the triangle across x

Then translate the triangle 1 unit to the right and 9 units down

8 0
3 years ago
Solve the problem. Make sure your answer is in simplest form. 3/16 x 4/21 = ?
Irina18 [472]

Answer:

\frac{1}{28}

Step-by-step explanation:

The result is given by means of some algebraic handling:

\frac{3}{16}\times \frac{4}{21}

\frac{12}{336} - Multiplication of rationals.

\frac{6}{168} - Dividing each term by 2.

\frac{3}{84} - Dividing each term by 2.

\frac{1}{28} - Dividing each term by 3.

8 0
3 years ago
The marked price of an article is Rs 2,800 which is 40 % above the cost price. If it
mixer [17]

Answer:

mp=2800

mp=cp+40%ofcp=cp+40/100×cp=1.4cp

2800=1.4çp

cp=2800/1.4=2000

discount=20%

profit%=?

Step-by-step explanation:

sp=mp-discount%of mp=2800-20/100×2800=2240

profit=sp-cp=2240-2000=240

profit%=profit/cp×100%=240/2000×100%=12%

7 0
3 years ago
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