First get the tangent vectors by differentiating r1 and r2

Evaluate at t=0

Use identity for angle between 2 vectors:

Evaluate dot product and unit vectors:

Sub into identity and solve for theta:

Answer:
Angle of intersection is about 79 degrees.
From the given ratio, we can get the percentages of the money that Plan G and the arena gets.
Plan G percentage = (2/(2 + 5)) x 100% = 28.57%
Arena percentage = (5/(2 + 5)) x 100% = 71.43%
We then multiply the amount they get by the decimal equivalent of the percentage of the arena.
Amount for arena = (£14,000) x (0.7143) = £10,000.2
Answer:
Circle requires ≈ 20 m of edging
Step-by-step explanation:
A = πR²
R = √(A/π)
C = 2πR = 2π√(A/π)
C = 2π√(30/π) = 19.41625... ≈ 20 m
square needs ≈ 22 m of edging
equilateral triangle needs ≈ 25 m of edging
Answer:
4a^2
Step-by-step explanation:

Therefore, the largest common factor is 4a^2. Hope this helps!
Assume Josh made X cupcakes; Alice made Y cupcakes; Tom made Z cupcakes.
Josh made 10 more cakes than Alice so,
X = Y + 10 ---- 1st Eqn.
Alice made 8 more than Tom so,
Y= Z+8 --- 2nd Eqn.
Total cakes = 62 so,
X+Y+Z = 62 ---- 3rd Eqn.
by solving three equations we get X= 30; Y= 20; Z=12.
So Tom made 12 cupcakes