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There is a bag of blue, red, and white counters. 1/6 of the bag is blue counters. 1/4 of the bag is red counters. What is the smallest number of white counters that could possibly be in the bag.

6 and 4 are common factors of 24.

1/6 = 4/24, and 1/4=6/24.

4/24+6/24 =10/24 of the bag is blue and red counters. Therefore, 24/24-10/24=14/24 of the bag is white counters.

14/24 can ...

AC
Answered by Alex C. Maths tutor
5759 Views

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
6255 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
4261 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
11773 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
2973 Views

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