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A triangle has 3 angles of 60 degrees, (5y-40) degrees, and (2y+20) degrees. Show that the triangle is equilateral.

All the angles in a triangle add up to 180 degrees.

Therefore, 60 + (5y - 40) + (2y + 20) = 180.

This can be simplified to 7y +40 = 180.

And simplified again to 7y = 140, which then m...

AC
Answered by Alex C. Maths tutor
6052 Views

Billy wants to buy 10kg of the same oranges. Type A comes in bags of 1.25 kg and costs £1.50. Type B comes in bags of 5kg and used to cost £6.60 but are now 15% off. Which type is more worth it for Billy and how much does it cost?

For Type A: 10kg/1.25kg = 8 bags, therefore for 10kg it costs 8 x £1.50 = £12.00.

For Type B: 1 bag used to cost £6.60 but now has 15% off =>15% of £6.60 => £6.60 x 0.15 = £0.99 => So one ...

AC
Answered by Alex C. Maths tutor
4117 Views

Integrate tan (x) with respect to x.

I = ∫ Tan (x) dx= ∫ (sin(x)) / (cos(x)) dx

We see that this is close to the standard integral  F'(x) / F(x) dx Ln (F(x)) + C

MH
Answered by Matthew H. Maths tutor
11380 Views

Find the tangent to y = x^2 - 4x + 9 at the point (3,15)

First find dy/dx:

dy/dx = 4x - 4

And thus at (3,15):

dy/dx = 12 - 4 = 8 = m (as m is the gradient of a curve)

So using y - y1 = m(x - x1) where...

SH
Answered by Scott H. Maths tutor
2848 Views

Find the derivative (dy/dx) of the curve equation x^2 -y^2 +y = 1.

Most of the differentiation problems require us to apply one of the well known rules, be it product rule, quotient rule or chain rule. But those problems have one thing in common:  explicite formula for y...

AG
Answered by Adam G. Maths tutor
4399 Views

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