Answer:
416666666/100000000
Step-by-step explanation:
To write 4.16666666 as a fraction you have to write 4.16666666 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
Answer:
a) 249 = 249 or 2.49 × 10²
b) - 100 = - (10)²
c) 10 + 7169 = 7179
Step-by-step explanation:
Answer:
Step-by-step explanation:
Required to prove that:
Sin θ(Sec θ + Cosec θ)= tan θ+1
Steps:
Recall sec θ= 1/cos θ and cosec θ=1/sin θ
Substitution into the Left Hand Side gives:
Sin θ(Sec θ + Cosec θ)
= Sin θ(1/cos θ + 1/sinθ )
Expanding the Brackets
=sinθ/cos θ + sinθ/sinθ
=tanθ+1 which is the Right Hand Side as required.
Note that from trigonometry sinθ/cosθ = tan θ
The slope is rise over run
3/5
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>