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find the integral of (2x - (3x^1/2) +1) between 9 and 4

2x become x 2 3x 1/2 becomes 2x 3/2 1 becomes x sub 9 into values for x = (81 - 54 +9) which equals 36 sub 4 into values for x = (16 - 16 + 4) which equals 4 now take away the value when you sub in 4 from wh...
AH
Answered by Amber H. • Maths tutor
3597 Views

Express 9^(3x + 1) in the form 3^y , giving y in the form ax + b, where a and b are constants.

9^ (3x + 1) We know that 3 to power of 2 equals 9. 3x3 = 3^2 = 9, = 3^ (2 * [3x + 1]) We simply the term because 2 * [3x + 1] = 6x + 2 = 3^ ( 6x + 2) This term is in the form of 3^ y, so we know that y = 6x ...
WL
Answered by William L. • Maths tutor
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A tunnel has height, h, (in metres) given by h=14-x^2 where x is the horizontal distance from the centre of the tunnel. Find the cross sectional area of the tunnel. Also find the maximum height of a truck passing through the tunnel that is 4m wide.

Firstly, solve 0=14-x^2 to find the horisontal distance to the edges of the tunnel. x1=sqrt(14), x2= -sqrt(14). Integrate h=14-x^2 between x1 and x2 28*sqrt(14) -(2(sqrt(14)^3))/3. This is the required area ...
JG
Answered by James G. • Maths tutor
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Express 3(x^2) - 12x + 5 in the form a(x - b)^2 - c.

Starting with a(x - b)^2 - c, if we expand the bracket we get: a(x^2 - 2xb + b^2) -c Since we need to end up with the coefficient on x^2 being 3 and in the expression above x^2 is only multiplied by a, this ...
LH
Answered by Lucy H. • Maths tutor
10901 Views

Write the complex number Z=1/2+sqrt(3)/2j both as a function involving cos & sin, and as a function involving an exponential.

|Z| = sqrt(1/2^2 + (sqrt(3)/2)^2) = 1 arg(Z) = arctan((sqrt(3)/2)/(1/2)) = pi/3 Z = cos(pi/3) + jsin(pi/3) Z = e^j(pi/3) Apologies for the use of sqrt(), I have no way yet of using the symbol on my laptop
SR
Answered by Sol R. • Maths tutor
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