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galina1969 [7]
3 years ago
15

Ab- 0.5b + 1/2 when a = 1 and b = 5

Mathematics
1 answer:
aniked [119]3 years ago
7 0
Since you already know the values of a and b, all you have to do is split the problem into little parts and plug everything into its spot. AB would equal 1(5) which is 5. Athens 0.5b would equal, 0.5(5) to equal 2.5. So now your equation is 5-2.5+1/2 which equals 3.
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The curves r1(t) = 4t, t2, t3 and r2(t) = sin(t), sin(5t), 2t intersect at the origin. find their angle of intersection, θ, corr
san4es73 [151]
First get the tangent vectors by differentiating r1 and r2 
r_1 '(t) = (4,2t,3t^2) \\  \\  r_2'(t) = (cos (t), 5 cos(5t), 2)
Evaluate at t=0
r_1' = (4,0,0) \\  \\ r_2' = (1,5,2)

Use identity for angle between 2 vectors:
u*v = |u| |v| cos \theta

Evaluate dot product and unit vectors:
u*v = (4,0,0)*(1,5,2) = 4 \\  \\ |u| = \sqrt{4^2 +0^2+0^2} = 4 \\  \\ |v| = \sqrt{1^2 + 5^2+2^2} = \sqrt{30}

Sub into identity and solve for theta:
4 = 4 \sqrt{30} cos \theta \\  \\ cos\theta = \frac{1}{\sqrt{30}} \\  \\ \theta = 79.48

Answer:
Angle of intersection is about 79 degrees.




5 0
3 years ago
Plan G is paid £14,000 for a concert. If the money made is split at 2:5 between Plan G and the arena. How much money did the are
77julia77 [94]
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
7 0
3 years ago
Sasha is planning to create a garden with area 30 m2. She could use a
son4ous [18]

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

5 0
3 years ago
Find the greatest common factor.<br> 42²x² + 42²x+ 40²<br> Enter the correct answer.
svlad2 [7]

Answer:

4a^2

Step-by-step explanation:

4a^2x^2+4a^2x+4a^2= \\\\4a^2(x^2+x+1)

Therefore, the largest common factor is 4a^2. Hope this helps!

3 0
3 years ago
Please help me with this question PLEASE
uysha [10]
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 
7 0
3 years ago
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