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Solve the simultaneous equations 3x + y = 23 and 4x + 4y = 52

3x + y =23, 4x +4y=5212x+4y=92, 12x+12y=1568y=64y=8sub in3x+8=23, 3x=15x=5y=8x=5
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Answered by Samuel B. • Maths tutor
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A cannon at ground level is firing at a fort 200m away with 20m high walls. It aims at an angle 30 degrees above the horizontal and fires cannonballs at 50m/s. Assuming no air resistance, will the cannonballs fall short, hit the walls or enter the fort?

solving horizontally, use v=s/t, where s=200, v=25(3) 1/2 . Hence t=s/v=8/(3) 1/2 (where t is the time when the ball would reach the fort if it does not reach the ground)Solivng vertically, s=?, u=25, v is i...
Answered by • Maths tutor
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Use Integration by parts to find ∫ xsin3x dx

∫ xsin3x dx takes the form of any integral ∫ (u)(dv/dx) dx. ∫ (u)(dv/dx) dx = uv - ∫ (v)(du/dx) dx Taking u=x and dv/dx= sin3x. The equation can be re-written in the form uv - ∫ (v)(du/dx) dx. Therefore, ∫ x...
SV
Answered by Safiyyah V. • Maths tutor
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The graph of y = x^2 + 4x - 3 (Graph A) is translated by the vector (3 | 2), find the equation of the new graph (Graph B)

Minimum point of Graph A:*complete square to find(x+2)^2 - 4 - 3 = 0(x+2)^2 - 7 = 0Therefore minimum point = (-2, -7)Minimum point of Graph B:(-2+3, -7+2) = (1, -5)*reverse complete the square method(x-1)^2 ...
GB
Answered by George B. • Maths tutor
5540 Views

Find the volume of a cone with radius 13cm and with a perpendicular height of 9cm.

volume= 1/3( πr 2 )h= 1/3 (3.14x 13x 13)x9= 1592.79 cm 3 (2.d.p) = 1590 cm 3 (3.s.f) r= radius h= perpendicular height
MB
Answered by Meghan B. • Maths tutor
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