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Prove that the square of an odd number is always 1 more than a multiple of 4.

First we consider how to represent an odd number. We know that any even number can be represented as 2k for some integer k since, by definition, all even numbers are multiples of 2. We also know that all odd...
JL
Answered by Josh L. • Maths tutor
10581 Views

We have 2 spinners: spinner A and spinner B. Spinner A can land on 2, 3, 5 or 7. Spinner B can land on 2, 3, 4, 5 or 6. Spin both. Win if one spinner lands on odd and the other lands on even. Play game twice, what is the probability of winning both games?

P(win 2 out of 2 games) = P(win first game and win second game) = P(win first game)^2. So want to find the probability of winning a game.To win, either we need A odd and B even or we need A even and B odd.P(...
HC
Answered by Henry C. • Maths tutor
8478 Views

Simplify (2x+3)^2 - (2x +3)(x-5). Give your answer in the form ax^2 +bx +c

Break this down into two parts. a. Multiply out the 1st bracket, (2x+3)^2: This goes to (2x+3)(2x+3) which is equal to 4x^2 + 9 +6x+6x . Collect the like terms to get 4x^2 +12x +9. b. Multiply out the second...
KS
Answered by Kenji S. • Maths tutor
9921 Views

A square based pyramid with corners ABCD has side length 6 cm. The distance from the centre of the square (C) to the top vertex of the pyramid (V) is 4 cm. Work out the total surface area of the pyramid.

The first thing I would do with this question is to draw it out to help visualise the shape.From this drawing you can see that the shape has 4 triangle shaped faces (let's call this triangle T1) and 1 square...
ME
Answered by Matthew E. • Maths tutor
5583 Views

A bomb of mass 34kg, at rest is detonated. The explosion splits the bomb into two pieces, one of mass 13kg, which is thrown to the left at a velocity of 28 m/s. What is the velocity of the second piece?

In a collision where no external forces act linear momentum is conserved.Convention: Right + left -0=-13x28 + 21xVV=17.33 kg m/s to the right
RC
Answered by Rory C. • Physics tutor
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