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When do two simultaneous equations have a solution?

This question was put to someone during their teacher training. This is a good question to ask, it is very important in maths to know that something you intend to study does actually exist. To explain the qu...
DD
Answered by Dylan D. • Maths tutor
3554 Views

8^(3/4)*2^(x) = 16^(4/5). Work out the exact value of x.

8 = 2^3 and 16 = 2^4. Substituting these into the above equation, we get 2^(9/4)*2^(x) = 2^(16/5). Using the laws of indices, we can derive the equation (9/4) + x = (16/5). In decimal form, this is 2.25 + x ...
KS
Answered by Katherine S. • Maths tutor
6513 Views

Make x the subject of the formula 4(2x-y) = 3ax - 5

4(2x-y) = 3ax - 5Step 1 - Expand 8x - 4y = 3ax - 5Step 2 - Collect like terms 8x - 3ax = 4y - 5Step 3 - Factorise x(8-3a) = 4y - 5Step 4 - Isolate x x = (4y - 5)/(8-3a)
AS
Answered by Adam S. • Maths tutor
3730 Views

A flight travels at 750kmph for 7 hours and 18 minutes, work out the distance travelled? Then convert 750 km/h into metres per second.

To work out the distance travelled, you must multiply its average (mean) speed by the time for which it was travelling, therefore in this case, 750 x 73/10 (NB the time is 7 plus 18/60 or 3/10, not 7.18), th...
CM
Answered by Charlie M. • Maths tutor
6560 Views

Find all possible values of θ for tan θ = 2 sin θ with the range 0◦ ≤ θ ≤ 360◦

First you rearrange the equation.It is known that tanθ=sinθ/cosθ therefore if we replace tanθ with sin/cos we get:sinθ/cosθ=2sinθIf you multiply both sides by cosθ this becomes:sinθ=2sinθcosθThen if you minu...
KL
Answered by Kehinde L. • Maths tutor
10946 Views