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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
8123 Views

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
7084 Views

Differentiate x^3 + y^4 = 34 using implicit differentiation

An implicity function is one that is not expressed in the form y = f(x) such as the equation in the question. Instead of rearranging the equation to make y the subject, the equation can be differentiated usi...
OM
Answered by Olavo M. • Maths tutor
2668 Views

At what points does the line y = x +1 intersect the circle x^2 + y^2 + 18x + 20y + 81 = 0.

The method we shall use is substitution. We shall replace y each term by 'x + 1' so we are able to obtain an equation in one variable. x^2 + (x+1)^2 + 18x + 20(x+1) + 81 = 0. We now expand the brackets. x^2 ...
HR
Answered by Harry R. • Maths tutor
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