The area bounded by the 2 parabolas is A(θ) = 1/2∫(r₂²- r₁²).dθ between limits θ = a,b...
<span>the limits are solution to 3cosθ = 1+cosθ the points of intersection of curves. </span>
<span>2cosθ = 1 => θ = ±π/3 </span>
<span>A(θ) = 1/2∫(r₂²- r₁²).dθ = 1/2∫(3cosθ)² - (1+cosθ)².dθ </span>
<span>= 1/2∫(3cosθ)².dθ - 1/2∫(1+cosθ)².dθ </span>
<span>= 9/8[2θ + sin(2θ)] - 1/8[6θ + 8sinθ +sin(2θ)] .. </span>
<span>.............where I have used ∫(cosθ)².dθ=1/4[2θ + sin(2θ)] </span>
<span>= 3θ/2 +sin(2θ) - sin(θ) </span>
<span>Area = A(π/3) - A(-π/3) </span>
<span>= 3π/6 + sin(2π/3) -sin(π/3) - (-3π/6) - sin(-2π/3) + sin(-π/3) </span>
<span>= π.</span>
Answer:
The linear function that discribes the size of the population in function of the t in years is p = 700t - 1,397,300
Step-by-step explanation:
A linear function is defined by a line, so in order to determine the linear function we can use the two points that were given to us to create a line equation and use that as our linear function. The points given to us were (2009; 9000) and (2014; 12500), in this case the year is our value of "x" and the size of the population is our value of "y". The first step is to find the slope of the line which is given by:
m = (y2 - y1)/(x2 - x1)
m = (12500 -9000)/(2014 - 2009) = 3500/5 = 700
Then we can use the slope and the first point to build the equation:
p - 9000 = 700*(t - 2009)
p = 700t - 1406300 + 9000
p = 700t - 1397300
Answer:
2:1
Step-by-step explanation:
The USA has 46 gold medals.
Russia has 24 gold medals.
Your ratio is 46:24.
Simplifying this, you get about 2:1, and that is your answer.
I hope this helped, and if this did please mark this as brainliest! Thank you, and have a good day!
bearing in mind that standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
1 beehive produces 85 lb/year
10³ beehives = 1,000 beehives produce 85x1,000 = 85,000 lb/year
