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Let p(x) =30x^3 - 7x^2 -7x + 2. Prove that (2x+1) is a factor of p(x).

We use the factor theorem which states that (2x+1) is a factor of p(x) if and only if the root of (2x+1)=0 is also a root of p(x). The root of 2x+1=0 is x = -1/2 (-1 from both sides and then divide both side...
HK
Answered by Henry K. • Maths tutor
9508 Views

The complex number -2sqrt(2) + 2sqrt(6)I can be expressed in the form r*exp(iTheta), where r>0 and -pi < theta <= pi. By using the form r*exp(iTheta) solve the equation z^5 = -2sqrt(2) + 2sqrt(6)i.

Using an argand diagram we can see that this (in fact all) complex numbers create a right angled triangle and using this fact we can find the modulus of this number. The modulus of this number is the 'r' in ...
TG
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Outline how Lorenz and Harlow studied attachment using animals. (6 marks)

I would suggest an exemplar answer to this question to be:Lorenz studied imprinting in goslings by dividing the eggs from a mother, hatching, and rearing them in different environments. Half were left with t...
HS
Answered by Hannah S. • Psychology tutor
24448 Views

Why is the first ionisation energy of barium larger than the first ionsiation energy of caesium?

Barium has one more proton than caesium. The outer electrons of both elements are in the same shell so they feel the same shielding effect. However, as barium has one more proton, barium's outer electrons wi...
JL
Answered by Jeremy L. • Chemistry tutor
6356 Views

Outline the circulation of blood and the physical changes of the heart during the cardiac cycle.

The cardiac cycle is split into 2 main phases: systole where the heart contracts and ejects blood out from the heart and diastole where the heart relaxes and fills with blood. The right side of the heart pum...
AM
Answered by Aishah M. • Biology tutor
3173 Views