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The points {3,3,0}, {0,6,3} and {6,6,7} all lie on the same plane. Find the Cartesian equation of the plane.

A Cartesian equation is in the form ax + by + cz = d. The a, b and c constants are given by the normal vector to the plane so we must find this first. You find the two direction vectors of the plane by subtr...
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Answered by Alejandro G. • Maths tutor
1542 Views

How do I find the missing length using trigonometry?

First of all, label the sides in the right-angled triangle. Then, write out SOHCAHTOA, using three small triangles. Next, tick off the letters of the sides that either have a number, or the letter x, written...
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Answered by Patrick L. • Maths tutor
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Show that the derivative of tan(x) is sec^2(x), where sec(x) is defined as 1/cos(x). [Hint: think of tan(x) as a quotient of two related functions and apply the appropriate identity]

tan(x) is defined as sin(x)/cos(x) For a function which can be written as f(x) = u(x)/v(x) the quotient rule can be appliedThe quotient rule states f ' (x) = (u'v-v'u)/v^2 Applying this to the formula for ta...
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Answered by Oliver C. • Maths tutor
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Given that dy/dx = 6x*2 - 3x + 4 And y =14 when x=2. Express y in terms of x

Dy/dx = 6x 2 - 3x + 4y = 12x - 3 + c14 = 12(2) - 3 + (c)14= 24 - 3 + c14 = 21 + cc= -7y = 12x - 10
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Answered by Medi N. • Maths tutor
2730 Views

Integrate y= x^3+3x^2-4x-7 between x values 1 and 3

Firstly, integrate y with respect to dx. Increase the powers of x by 1 and then divide the coefficient of x by the new power of x. I.e.: x^3 becomes 1/4x^4. The power increases from 3 to 4 and the coefficien...
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Answered by Louis A. • Maths tutor
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