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How does freeze-thaw weathering occur?

Freeze-thaw weather occurs when water enters a small crack in a rock, which often happens during rainfall, then when temperatures fall to below 0 degrees celsius this water freezes and expands. This widen...

EG
Answered by Emily G. Geography tutor
3967 Views

Why is sin(t)^2 + cos(t)^2 = 1 true for all t?

To answer this we need to consider a circle of radius r centred at the origin, drawn in the x,y plane. We'll draw a right-angled triangle such that the hypotenuse is the radius, and say that the point whe...

MV
Answered by Matt V. Maths tutor
3126 Views

(a) Use integration by parts to find ∫ x sin(3x) dx

The question asks for integration by parts. Therefore we need to differentiate one variable and integrate the other. First we need to decide which variable is going to be which. Algebra should always be d...

GA
Answered by George A. Maths tutor
7672 Views

What's the gradient of the curve y=x^3+2x^2 at the point where x=2?

Gradient is change in y divided change in x.As the change shrinks to effectively nothing (as we want to gradient at a point, not between points), we use dy/dx (the derivative of y with respect to x), to w...

ZI
Answered by Zachary I. Maths tutor
7039 Views

Solve the simultaneous equations: y = x + 6, x^2 + 2y = 9

y = x + 3x2 + 2y = 9We want to make the squared equation have either only x's or only y's, so we substitute y = x + 3 into the equation:x2 + 2(x + 3) = 9We need to take out the brack...

HH
Answered by Hayley H. Maths tutor
3065 Views

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