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Find the length of the hypotenuse of a right-angled triangle using i) Pythagoras Theorem ii) Trigonometry. The triangle has sides of lengths 3cm and 4cm and an acute angle of 30 degrees.

Part iPythagoras Theorem states a² = b² + c² , where a is the hypotenuse.Using this the lengths can be substituted into the equation as b and c, a² = 3

Answered by Zaakir S. • Maths tutor

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Differentiate y = x^2 - 2x-3 + e^3x + 2ln(x)

The above function has several components with different rules on how to differentiate each of them. For each:(1) y = x²dy/dx = 2x This follows the general rule of differentiating polynomials: ...

Answered by Jim H. • Maths tutor

3169 Views

A curve is defined by the parametric equations x = 2t and y = 4t^2 + t. Find the gradient of the curve when t = 4

the gradient of the curve = dy/dx
and dy/dx = (dy/dt)(dt/dx)
dy/dt = 8t + 1
dx/dt = 2 therefore dt/dx = 1/2
dy/dx as above = (8t + 1) * 1/2 = (8t + 1)/2
where t = 4, dy/dx = (8*4...

Answered by Angus B. • Maths tutor

4763 Views

Nancy is driving and makes a wrong turn. The satnav indicates that her journey will take an extra 7 minutes. Nancy drives at an average speed of 60km/h to the nearest 5km/h. What's the greatest possible distance traveled in this detour in km to 2.d.p?

Start by selecting useful information in the text.time = 7 minutesspeed = 60km/h to the nearest 5km/hmaximum possible distance travelled = ? kmWe know a time and speed and want to know a distance. So we c...

Answered by Louis G. • Maths tutor

2354 Views

Solve 7x+6>1+2x

For this such question, we need to find what values x can be. We need to get all the terms containing x one side of the equation and all the other terms on the other side then isolate x. To do this, we mu...

Answered by Annie M. • Maths tutor

4835 Views