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Find integer solutions for m - n(log3(2)) = 10(log9(6)).

From the properties of logarithms (log b a = log c a / log c b), 10log 9 6 can be rewritten as 10(log 3 6 / log 3 9). Since log 3 9 = 2, 10log 9 6 = 5log 3 6. We then bring both log terms to the same side of...
TK
Answered by Tristan K. • Maths tutor
11718 Views

PQR is a triangle with vertices P (−2, 4), Q(4, 0) and R (3, 6). Find the equation of the median through R.

(1) Find the Midpoint of PQ which is (1,2) (Halfway between the x and y coordinates)(2) dy/dx for M(1,2) -> R(3,6) = (6-2)/(3-1) = 4/2 = 2(3) y =mx + c so y = 2x + c when R(3,6) is input 6 = 2(3) + c, c =...
SH
Answered by Scott H. • Maths tutor
5045 Views

Why is ꭍ2x=x^2+C?

Differentiating x 2 gives dx 2 /dx=2x. Differentiating a constant C gives 0. d( x 2 +C)/dx=dx 2 /dx+dC/dx=2x+0=2x. Since integration is the inverse function of differentiation, integrating 2x gives x 2 +C.
LD
Answered by Larisa D. • Maths tutor
6264 Views

Find the stationary points of the curve y (x)= 1/3x^3 - 5/2x^2 + 4x and classify them.

To find the stationary points of the curve y(x), you must first differentiate the equation for y(x) in terms of x. This gives d(y(x))/dx = x^2 -5x +4. Now set this differential equal to zero and solve for x ...
DR
Answered by Danny R. • Maths tutor
6612 Views

Find the indefinite integral of x^8*ln(3x) using integration by parts

For this method we need to choose our u and dv/dx. Using the Late method (Logarithm, algebra, trigonometric, exponential), we can pick our u value which will be ln(3x). du/dx is therefore 1/x, using the chai...
JB
Answered by Joel B. • Maths tutor
6403 Views