Answer:
The rational zero of the polynomial are 
.
Step-by-step explanation:
Given polynomial as :
f(x) = 4 x³ - 8 x² - 19 x - 7
Now the ration zero can be find as
,
where P is the constant term
And Q is the coefficient of the highest polynomial
So, From given polynomial , P = -7 , Q = 4
Now , 
I.e = 
Or, The rational zero are
Hence The rational zero of the polynomial are . Answer
Answer:
41.89 units
Step-by-step explanation:
Area of a sector: Θ/360 * (pi)(r)^2
We are given with the expression arctan(-sqrt(3)) and asked to evaluate it. In this case, we can use a calculator or the rule of common triangles to answer this question. the value of <span>arctan(-sqrt(3)) is -60. Since negative tan is found in 2nd and 4th quadrant, the angles are 180-60 or 120 degrees and 360-60 or 300 degrees.</span>
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:
b. 6 cm
Step-by-step explanation:
Q is the midpoint of PR, so QR = PR/2 = (12 cm)/2 = 6 cm
