Answer:
Option A.
Step-by-step explanation:
Based on the information provided on the question
the function used to model Tony's run is:
f(x) = -250*x + 5000
This means that after x = 20 minutes, Tony will arrive to the finish line
f(20) = -250*(20) + 5000 = -5000 + 5000 = 0
The function is always decreasing, because we are dealing with a line with negative slope.
Option A.
we are given
differential equation as
we are given
Firstly, we will find y' , y'' and y'''
those are first , second and third derivative
First derivative is
Second derivative is
Third derivative is
now, we can plug these values into differential equation
and we get
now, we can factor out common terms
we can move that term on right side
now, we can factor out
now, we can set them equal
so, we will get
...............Answer
Answer:
5 blocks
Step-by-step explanation:
5 blocks for every barometer
First term is -7, so a_1 = -7
To get the next term, we add on 4. We can see this if we subtract like so
d = (2nd term) - (1st term) = (-3) - (-7) = -3+7 = 4
So d = 4 is the common difference.
Apply a_1 = -7 and d = 4 to get...
a_n = a_1 + d*(n-1)
a_n = -7 + 4*(n-1)
a_n = -7 + (n-1)*4
Answer: Choice A
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>
