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An ice cream cone with a base 4.5 cm in diameter and whose height is 10 cm is filled with ice cream. What is the volume of ice cream to 3 d.p.? If the density of ice cream is 1095 kg/m^3, what is the mass of ice cream in 5 cones to 3 s.f.?

Volume of cone= 1/3 Pi h r^2 r=2.25 V=1/3 Pi 10 2.25^2=53.01 cm^3=5.301x10&-5 m^3 Mass=density*volume Mass=(5.301x10^-5) 1095= 0.05805 kg Mass of 5= 0.05805 5=0.290 kg
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Answered by Bevan J. • Maths tutor
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Solve e^x-6e^-x=1

Multiply everything through by e x and rearrange so it equals zero you now have e 2x -e x -6=0 It is now similar to a quadratic equation, make the dummy substitution y=e x y=3 or -2 x= ln(3) and ln(-2) does ...
KI
Answered by Kishwar I. • Maths tutor
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1iii) Solve 7/2x^2+13/4x+1=2

In order to solve this trickier problem, the quadratic equation must be applied x=[-b +- sqrt(b^2-4ac)]/2a Apologies for messy notation, full solution will be demonstrated during interview clearly when white...
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Answered by Kishwar I. • Maths tutor
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1ii) sketch y=x^2-4x-21

A parabola shape with x intercepts at x = -3 and x = 7 and the y intercept at y = -21
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Answered by Kishwar I. • Maths tutor
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1i) solve x^2-4x-21=0

Factorise to get (x+3)(x-7)=0 So you can see that x = -3 or x =7
KI
Answered by Kishwar I. • Maths tutor
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