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Two lines have equations r_1=(1,-1,2)+a(-1,3,4) and r_2=(c,-4,0)+b(0,3,2). If the lines intersect find c:

If the lines intersect the position vectors r_1 and r_2 must be equal at the point of intersection, so: (1,-1,2)+a(-1,3,4)=(c,-4,0)+b(0,3,2) which gives three equations for the three components: 1-a=c, -1+3a...
AZ
Answered by Aleksandar Z. • Maths tutor
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2x-4=6, find x.

[add 4 to both sides] 2x=10 Therefore, x=5
EW
Answered by Elena W. • Maths tutor
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Explain the significance of atomic number and mass number in determining atomic properties. Which of these changes in isotopes?

Atomic Number: Number of Protons in the nucleus of the atom, also equal to the number of electrons in a neutral atom. Mass Number: Total number of "nucleons" (Protons and Neutrons) in the nucleus I...
JT
Answered by Joshua T. • Chemistry tutor
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Should you structure your argument in an essay by writing one side and then the other, or write it paragraph by paragraph?

Both of these are acceptable, but I would advise writing it paragraph by paragraph, as quite often students run out of time in the exam and that way at least you've covered both sides of the argument. It als...
SB
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solve the simultaneous equations , 5a+2b=23 & 9a-2b=19, algebraically.

find sum of both equations: 14a=42, therefore a=3, substitute 'a' into an equation: (5x3)+2b=23, therefore 2b=8, therfore b=4
RP
Answered by Rohan P. • Maths tutor
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