Answer:
A
Step-by-step explanation:
So first you need to know the formula for the area of a segment of a circle which is... A = 0.5 × (θ - sinθ) × r²
*make sure that you do this question in RADIANS
You know that θ (the angle) is 90° which is equal to π/2 and the radius is 3, so from here you just plug in numbers to the equation.
A = 0.5 × ( π/2 - sin(π/2)) × 3²
A = 2.5685... sq units = 3 sq units
Answer:
Step-by-step explanation:
Given the surface
G(x, y, z) =2z²
Over the hemisphere
x² + y² + z² = 36. For z≥0
Using polar coordinate
x=sin Φ cos θ,
y = sin Φ sin θ,
z = cos Φ
0 ≤ Φ ≤ π/2, 0 ≤ θ ≤ 2π
Therefore
r(Φ, θ) = sin Φ cos θ i + sin Φ sin θ j + cos Φ k
Also, dS= |rθ×rΦ|= sinΦ
dS=sinΦdΦdθ
Then we want to compute the volume integral of
∫ ∫ₛ G(x, y, z) dS
G(x, y, z) =2z²
Therefore in polar forms
G(x, y, z) =2(cos Φ)²
G(x, y, z) = 2cos²Φ
Given that dS=sinΦdΦdθ
∫ ∫ₛ G(x, y, z) dS
∫ ∫ 2cos²ΦsinΦdΦdθ at 0 ≤ Φ ≤ π/2,
0 ≤ θ ≤ 2π
∫ 2cos²ΦsinΦ •θdΦ from 0 ≤ θ ≤ 2π
2∫cos²ΦsinΦ •(2π-0)dΦ
4π∫ cos²ΦsinΦ dΦ from 0 ≤ Φ ≤ π/2
Let U = cosΦ
dU/dΦ =-sinΦ
-dU/sinΦ =dΦ
4π∫ U²sinΦ(-dU/sinΦ) 0 ≤ Φ ≤ π/2
-4π∫ U² dU
-4π U³/3, then U=cosΦ
[-4πcos³Φ / 3 ] from 0 ≤ Φ ≤ π/2
[-4π cos³(π/2)/3 - [-4π cos³(0)/3]
0+4π/3
4π/3
4π/3 unit²
The two dinosaurs probably crossed paths at estimated coordinates (- 1, 2.5).
To find where the two equations actually intersect, set them equal to each other.
- 1/2x + 3 = 2x + 4
Subtract 4 from both sides, and add 1/2x to both sides to combine like terms.
2 1/2x = - 1 --> 5/2x = - 1
Multiply by 2/5 on both sides to isolate x
x = - 1(2/5)
x = - 2/5
Now plug in to either of the two equations. I used 2x + 4
- 1/2(- 2/5) + 3 = y
1/5 + 3 = y
y = 3 1/5
The actual coordinates where the dinosaurs crossed paths was (- 2/5, 3 and 1/5).
My original estimate was (- 1, 2 1/2) because based on the graph drawn above the point of interest (the intersection) appears to be below the third unit on the y-axis as well as in between the negative two unit and origin on the x-axis. My estimate was also off because the x-axis is counting by twos which does not necessarily allow for an accurate estimate strictly based on the naked eye.
Answer:
10th term of the sequence 64,16,4... = 1/4096
Step-by-step explanation:
Points to remember
nth term of GP is given by.
Tₙ = ar⁽ⁿ⁻¹⁾
Where r is the common ratio and a is the first term
<u>To find the 10th term of given GP</u>
It is given that,
64, 16, 4,......
a = 64 and 6 = 1/4 Here
T₁₀ = ar⁽ⁿ⁻¹⁾
= 64 * (1/4)⁽¹⁰⁻¹⁾ = 64 * (1/4⁹)
= 4³/4⁹ = 1/4⁶ = 1/4096
Uh oH 6+ well I guess than 6+ if this get wrong then I'm sorry
