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krek1111 [17]
2 years ago
7

What is the area of a sector with measure of arc equal to 90Á and radius equal to 1 foot? 0.25pi sq. ft. 0.5pi sq. ft. pi sq. ft

Mathematics
2 answers:
Semmy [17]2 years ago
5 0
<span>Given a circle with radius r = 8 and a sector with subtended angle measuring 45°, find the area of the sector and the arc length.

They've given me the radius and the central angle, so I can just plug into the formulas. For convenience, I'll first convert "45°" to the corresponding radian value of π/4:
 
A = ((pi/4)/2)(8^2) = (pi/8)(8^2) = 8pi, s = (pi/4)(8) = 2pi

area A = 8π, arc-length s = 2π
Given a sector with radius r = 3 and a corresponding arc length of 5π, find the area of the sector.

 
For this exercise, they've given me the radius and arc length. From this, I can work backwards to find the subtended angle.
Then I can plug-n-chug to find the sector area.
 5pi = (theta)(3), (theta) = (5/3)pi So the central angle is (5/3)π.
Then the area of the sector is:
 A = ((5/3)pi / 2)*(3^2) = ((5/6)pi)*(9) = (15/2)pi A = (15 pi) / 2

</span><span>90/360 = 0.25 pi sq ft</span>
Elis [28]2 years ago
3 0
The area of any sector of a circle can be calculated by multiplying the area of the circle and the angle in degrees over 360. It is expressed as:

Area of a sector = πr²(n/360)

We calculate as follows:


Area of a sector = πr²(n/360)

Area of a sector = π(1²)(90/360)

Area of a sector = 0.25π ft² -----> OPTION 1
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Determine the equation of the inverse of y=1/4x^3-2
dedylja [7]

<u>Answer</u>


y⁻¹ = ∛(4x+8)



<u>Explanation</u>

y=(1/4)x³ - 2.

To find the inverse of this equation, you first make x the subject of the formular.

y=(1/4)x³ - 2

Multiply both sides by 4;

4y = x³ - 8

Add 8 on both sides of the equation;

4y + 8 = x³

x³ = 4y + 8

Apply the cube root on both sides to get the value of x;

x = ∛(4y+8)


The inverse of y=(1/4)x³ - 2 is;

y⁻¹ = ∛(4x+8)


7 0
3 years ago
Find the sum of the first 8 terms in the sequence 2 8 32 128
Zigmanuir [339]

the sequence is in multiples of 4 (2*4=8, 8*4=32, 32*4=128)

so 128*4=512, 512*4=2048, 2048*4=8192 & 8192*4=32768

2+8+32+128+512+2048+8192+32768=43690 

4 0
3 years ago
The sum of the two decimals is 1 the product of these decimals is 0.25 the quotient of these two decimals is 1 what are the two
ExtremeBDS [4]
Since the quotient of the two decimal numbers is 1, that tells use that they are the same number.
Since the sum of the two numbers equals 1 and both numbers are the same, then the answer must be 1 divided by 2. or .5
the fractions would be 1/2 and 1/2

5 0
3 years ago
Jayden is driving on a long road trip. He currently has 11 gallons of gas in his car. Each hour that he drives, his car uses up
DENIUS [597]

Answer:

a. 8 gallons

b. (11-0.75t) gallons

Step-by-step explanation:

a. Here in this question, we are told that the total amount of fuel in the fuel tank is 11 gallons and the car consumes 0.75 gallon per hour. We are interested in knowing the amount of fuel left in the tank after driving for four hours.

We proceed as follows;

Since 0.75 gallon is consumed in an hour, the amount of fuel consumed in 4 hours would be the amount consumed in an hour * 4 hours

Mathematically, that would be 0.75 * 4 = 3 gallon

Now, the amount of fuel left is simply the difference between the initial amount of fuel in the tank minus the amount of fuel present after 4 hours.

That would be; 11 - 3 = 8 gallons

b. Like above, we want to know the amount of fuel left after t hours.

Since 0.75 is used up per hour, the amount used up in t hours would be 0.75 * t = 0.75t

Now, the amount of fuel that would be left in the tank would be the difference between what we had initially and what was used up.

Mathematically, that would be 11- 0.75t

4 0
2 years ago
Solve 5 tan x = 5√(3) for 0° ≤ x ≤ 180°.<br><br> a. 60°<br> b. 150°<br> c. 30°<br> d. 120°
ladessa [460]

Answer:

\boxed{a.\:\:\:60\degree}

Step-by-step explanation:


The given trigonometric equation is


5\tan(x)=5\sqrt{3} for 0\degree \le x\le 180\degree.


We divide through by 5 to get;


\tan(x)=\sqrt{3}


We take the inverse tangent of both sides to obtain;


x=tan^{-1}(\sqrt{3})


x=60\degree


Since the tangent ratio is positive, it means x could also be in the 3rd quadrant. But this is outside the given range.


Therefore the correct answer is A


6 0
3 years ago
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