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Find the indefinite integral tan(5x)tan(3x)tan(2x)

Noticing that tan(5x) = tan(3x+2x) we use the tan compound angle formula to find tan(5x) = (tan(2x)+tan(3x))/(1-tan(2x)tan(3x)) and thus tan(5x)tan(3x)tan(2x) = tan(5x)-tan(3x)-tan(2x). From then we can inte...
SO
Answered by Sean O. • Maths tutor
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Factorise (x^2 +3x-18)=0, solving for x

To factorise and solve this equation we must put it into two brackets, instead of one, each with a single x term. As the is an x^2 term we know there must be an x in each bracket Because the number term at t...
RM
Answered by Rachael M. • Maths tutor
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Solve for simultaneous equations x +5y =9 and 3x + 2y =5.

Here we have 2 unknown variables, x and y. First number the two equations, so x + 5y = 9 is (1), while 3x + 2y = 5 (2). Rearrange both equations so that they become (1) x = 9-5y and (2) x= (5-2y)/3. Next, si...
AL
Answered by Abigail L. • Maths tutor
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A child of m1=48 kg, is initially standing at rest on a skateboard. The child jumps off the skateboard moving horizontally with a speed v1=1.2 ms^-1. The skateboard moves with a speed v2=16 ms^-1 in the opposite direction. Find the mass of the skateboard.

We approach this problem using the conservation of linear momentum, which tells us that m1 x v1 = m2 x v2. We substitute the values of m1, v1 and v2, and solve for m2: 48x1.2=m2x16; m2=57.6/16=3.6 kg.
AP
Answered by Alberto P. • Maths tutor
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Washing powder is sold in two sizes: Bag 1 is 600 grams for £3.30. Bag 2 is 1500 grams and usually costs £9.60 but currently has 15% off. Which is better value?

To determine which is better value, we need to determine the price per gram of each washing powder. Bag 1: For the 600g bag, this is done by dividing the price by the number of grams: 3.30/600 = £0.0055/g or...
JL
Answered by Joe L. • Maths tutor
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