# Sohini Khan

A supportive and engaging tutor with an aim for success

5927Students helped
£40Per hour
Maths

Asked by Yasmin · 4 years ago

How many digits are in one billion?

It used to be in the UK that one billion is a million million, but now in the UK we use a thousand million as one billion. This means currently a thousand million = one billion = 1,000,000,000. To answer your question, there are 10 digits in one billion.

Maths

Asked by Olivia · 4 years ago

Are there tips for getting better grades ?

Repeat by voice what you are studying until you perfect remind it. Schematic of it would help

Maths

Asked by Yeeun · 4 years ago

Triangle numbers are formed from the expression: 1/2n(n+1). Prove that the ratio between two consecutive triangle numbers is always n:n+2?

So if you pick some triangle number A = 1/2n(n+1), a consecutive triangle number would be B= 1/2(n+1)(n+2). Note that B is smaller than A as it has a larger denominator so when it comes to triangle numbers in order, it goes B, then A. If we put these numbers in ascending order into a ratio, we get: 1/2(n+1)(n+2):1/2n(n+1) Now if we multiply both sides by 2n(n+1), we can get rid of the denominat... more

Maths

Asked by Yeeun · 4 years ago

If a linear sequence had a common difference of 8, what are the three consecutive terms in the sequence which add up to give a total of 126?

Since the three terms are consecutive and have a difference of 8, I can write these terms as k, k+8, k+16 The total of these should be 126: k + k+8 + k+16 = 3k+24 = 126 Solving for k, we get: 3k = 102 k = 34 So, our three terms are: 34, 42, 50 Hope that helps! ~ Sohini

Maths

Asked by Amar · 4 years ago

A solid hemisphere has a radius of x. A solid Cone has a diameter of 3x and a perpendicular height of y. the hemisphere and the cone have equal volumes. Show that y=8/9x. Use the formulas provided. Need help asap please!?

The volume of a cone is r^2(pi)h/3. The volume of a hemisphere is 2(pi)r^3/3 - this is found by dividing the volume of a sphere by 2. If the volumes of both shapes are equal, we can say: (1.5x)^2(pi)(y)/3 = 2(pi)(x^3)/3 We can get rid of the pi on both sides, and multiply both sides by 3 as well, to simplify the equation. y(1.5x)^2 = 2x^3 Expanding the left side’s brackets gives us: 2.25yx^2... more

Maths

Asked by Lucy · 4 years ago

Expressed as a product of its prime factors in index form, a number N is N=3x5squared x xcubed Express 5Nsquared as a product of prime factors in index form. Give your answer in terms of x?

If N = 3 x (5^2) x (x^3) Then 5N^2 = 5 x N x N = 5 x (3 x (5^2) x (x^3)) x (3 x (5^2) x (x^3)) = (5^5) x (3^2) x (x^6)

Maths

Asked by Faith · 4 years ago

Trigonometry - how do you find the special angles (sin 30,45,60; cos 30,45,60 and tan 30,45,60)?

The best way (without using a calculator) is by memorising the two triangles: 1. an isosceles right-angled triangle with lengths 1, 1 and 2 (hypotenuse) and angles 45°, 45° and 90° 2. a right-angled triangle with lengths 1, rt3 and 2 (hypotenuse) and angles 30°, 60° and 90° - the 30° angle should be opposite the side of length 1 as it’s the smallest angle If you memorise these two triangles, and... more

Maths

Asked by Yeeun · 4 years ago

What is the nth term rule for this quadratic sequence? 6, 10, 18, 30?

First we make some nth term that almost fits what we have. Almost, because we have to compare our nth term and the question’s nth term to fill in the blanks. So since it’s a quadratic sequence, we have to find the second difference, halve it and stick it in front of the n^2. Our first differences are: 6 (+4) 10 (+8) 18 (+12) 30 Our second differences are: 4 (+4) 8 (+4) 12 So our second differe... more

# Sohini Khan

A supportive and engaging tutor with an aim for success

5927Students helped