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Relative to a fixed origin O, the point A has position vector (8i+13j-2k), the point B has position vector (10i+14j-4k). A line l passes through points A and B. Find the vector equation of this line.

The vector equation of any line is composed of the addition of a point on the line and some distance in the direction of the line, in the form y=(x,y,z) +d(x_1, y_1, z_1), where (x,y,z) is any point on th...

Answered by Carlota S. • Maths tutor

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What is the indefinite integral of xlog(x)?

The integral can be split into two different functions of x which is a hint that we must use the integration by parts method. The method is defined as

Answered by William H. • Maths tutor

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Using the binomial theorem, find the coefficient of x^4*y^5 in (x-2y)^9.
The term containing x⁴y⁵ will be C(9, 5)x⁴(-2y)⁵ = (9!/(5!4!))x⁴(-2)⁵y⁵The coefficient of which will be 1...
GH
Answered by George H. • Maths tutor
3195 Views

Using the trigonometric identity for tan(A + B), prove that tan(3x)=(3tan(x)-tan^3(x))/(1-3tan^2(x))
tan(3x)=tan(2x+x), by using the identity for tan(A+B)=(tan(A)+tan(B))/(1-tan(A)tan(B)),tan(3x)=tan(2x+x)=(tan(2x)+tan(x))/(1-tan(2x)tan(x)), using it again for tan(2x),tan(3x)=tan(2x+x)=([(tan(x)+tan(x))/...
IR
Answered by Ivan R. • Maths tutor
9159 Views

a curve is defined by y=2x^2 - 10x +7. point (3, -5) lies on this curve. find the equation of the normal to this curve
equation of tangent is y - y1 = m(x-x1). differentiating y gives us the value of m. so dy/dx = 4x-10. we know x is 3. therefore, dy/dx = m = 2 but we need equation of the normal, which is y-y1=(1/m)(x-x1)...
HH
Answered by Huy H. • Maths tutor
3134 Views

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Relative to a fixed origin O, the point A has position vector (8i+13j-2k), the point B has position vector (10i+14j-4k). A line l passes through points A and B. Find the vector equation of this line.

What is the indefinite integral of xlog(x)?

Using the binomial theorem, find the coefficient of x^4*y^5 in (x-2y)^9.

Using the trigonometric identity for tan(A + B), prove that tan(3x)=(3tan(x)-tan^3(x))/(1-3tan^2(x))

a curve is defined by y=2x^2 - 10x +7. point (3, -5) lies on this curve. find the equation of the normal to this curve

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