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murzikaleks [220]
3 years ago
12

The sum of two numbers is 49 and the difference between these two numbers is 9. What are these two numbers?​Shown working out pl

ease
Mathematics
1 answer:
8_murik_8 [283]3 years ago
7 0

Let numbers be x and y

ATQ

  • x+y=49---(1)

  • x-y=9---(2)

Adding both

\\ \sf\longmapsto 2x=58

\\ \sf\longmapsto x=\dfrac{58}{2}

\\ \sf\longmapsto x=29

Now putting value in eq(2)

\\ \sf\longmapsto x-y=9

\\ \sf\longmapsto 29-9=y

\\ \sf\longmapsto y=20

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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.




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