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Johnny take 4 hours 50 minutes to drive 213 miles to Manchester. He then takes the train to Liverpool. Liverpool is 37 miles from Manchester and the train travels at 90mph. Calculate Johnny's average speed for his total journey in mph.

Total journey average speed = (total distance travelled ÷ total time taken).Total distance travelled = 213 miles + 37 miles = 250 milesTotal time taken (hours) = 4 + (50 ÷ 60) + time from Manchester to Liver...
SW
Answered by Steven W. • Maths tutor
3747 Views

What is the derivative of y = (3x-2)^1/2 ?

Use the chain rule, u = 3x-2dy/dx = dy/du du/dxdy/du = d(u^1/2)/du = 1/2 u ^-1/2power down and minus 1du/dx = 3constants =0so, dy/dx = 3 1/2 (3x-2)^-1/2= 3/2 (3x-2)^-1/2
CJ
Answered by Chloe J. • Maths tutor
10150 Views

Write 5cos(theta) – 2sin(theta) in the form Rcos(theta + alpha), where R and alpha are constants, R > 0 and 0 <=alpha < 2 π Give the exact value of R and give the value of alpha in radians to 3 decimal places.

Use the formula cos(A+B)=cosAcosB-sinAsinB, Rcos(theta+alpha)=Rcos(alpha)cos(theta)-Rsin(alpha)sin(theta)5=Rcos(alpha)2=Rsin(alpha)tan(alpha)=2/5alpha= 0.381R=sqrt(5^2+2^2)=sqrt(29)So, 5cos(theta) – 2sin(the...
JW
Answered by Joe W. • Maths tutor
12276 Views

The equation of the line L1 is y = 3x – 2 The equation of the line L2 is 3y – 9x + 5 = 0 Show that these two lines are parallel.

L1 is in the form y=mx+c where m is the gradient, 3.L2 can be rewritten as 3y=9x-5, then y=3x-(5/3) to reach y=mx+c. So, the gradient of L2 is 3.Therefore, both lines are parallel.
JW
Answered by Joe W. • Maths tutor
5278 Views

The angles of a triangle are a, 2a and 2a + 30. Work out the value of a.

The areas of a triangle add up to 180 degrees. Therefore to tackle this question you must use algebra as you know that the sum of a, 2a and 2a + 30 is 180. a + 2a + 2a + 30 = 180 All the like terms can be pu...
AG
Answered by Amy G. • Maths tutor
4698 Views