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3 girls and 4 boys are seated randomly on a bench. Find the probability that the girls set together and the boys sit together.

The number off total arrangements is 7!(permutation). The number of ways for which the girls and boys sit togehter is 3! 4! 2. The probability is the division of the number of way by the total possibilities,...
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Answered by Lina L. • Maths tutor
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Solve (sec (x))^2 + 2tan(x) = 0

Using the trigonometric identity: (sec(x))^2 = (tan(x))^2 + 1 we get to (tan(x))^2 + 2tan(x) + 1 = 0. We can express this result as the multiplication of 2 equal factors arriving at (tan(x) + 1)^2 = 0. This ...
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Answered by Lina L. • Maths tutor
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The points {3,3,0}, {0,6,3} and {6,6,7} all lie on the same plane. Find the Cartesian equation of the plane.

A Cartesian equation is in the form ax + by + cz = d. The a, b and c constants are given by the normal vector to the plane so we must find this first. You find the two direction vectors of the plane by subtr...
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Answered by Alejandro G. • Maths tutor
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Consider the infinite geometric sequence 25 , 5 , 1 , 0.2 , ... (a) Find the common ratio. (b) Find (i) the 10th term; (ii) an expression for the nth term. (c) Find the sum of the infinite sequence.

QUESTION (a) R = U(n+1)/U(n ) = 5/25= 0.2(b) (i) U(10) = 25 x (1/5)^9 = 0.0000128 (ii) U(n) = 25 x (1/5)^(n-1)(c) S = U(1)/(1-r) = 25/(1-(1/5))=25/(4/5))=125/4=31.25
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Answered by Carlota R. • Maths tutor
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All tickets for a concert are the same price. Amy and Dan pay £63 for some tickets. Amy pays £24.50 for 7 tickets. How many tickets does Dan buy?

We start to work with this question by underlining the most important information it provides us: All tickets for a concert are the same price . Amy and Dan pay £63 for some tickets . Amy pays £24.50 for 7 t...
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Answered by Soma F. • Maths tutor
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