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Integrate cos^2x + cosx + sin^2x + 3 with respect to x

Step 1: simplify the question using the law cos 2 x + sin 2 x = 1 /// Step 2: add the numbers /// Step 3: integrate cosx (remember the differentiation/integration circle sin --> cos --> -sin --> -co...
AB
Answered by Amanda B. • Maths tutor
4228 Views

A 1kg mass is launched from the ground into the air at an angle of 30 degrees to the horizontal and with initial speed 25 ms^-1. Assuming negligible air resistance, how far from the starting point will the mass travel before it hits the ground?

1: Draw a diagram 2: Split the velocity into its horizontal and vertical components using trig. Vertical velocity: 25sin(30) Horizontal velocity: 25cos(30) 3: Work out forces on the mass to find vertical and...
CS
Answered by Connor S. • Maths tutor
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Differentiate the function X^4 - (20/3)X^3 + 2X^2 + 7. Find the stationary points and classify.

Differentiation => 4X 3 - 20X 2 + 4XTo find the stationary points, set this differentiation = 04x (x 2 - 5x +4)4x (x-4)(x-1)x=0, x=4, x=1 are stationary points. Find the second derivative 12X 2 -40X +4. S...
AH
Answered by Alice H. • Maths tutor
3648 Views

A ball is released on a smooth ramp at a distance of 5 metres from the ground. Calculate its speed when it reaches the bottom of the ramp.

The ramp is smooth, so the effects of friction can be ignored. Therefore, the potential energy lost by the ball is equivalent to the kinetic energy gained by the ball. The formula for kinetic energy is 1/2 *...
CB
Answered by Cameron B. • Maths tutor
5267 Views

R=1000e^-ct , it takes 5730 years for half of the substance to decay a. find the number of atoms at the start of the decay. b. calculate the number of atoms left when t=22920. c. sketch the function.

a.1000 b. R=62.5 c. Sketch
PU
Answered by Prasad U. • Maths tutor
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