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In the figure triangles ACB and APO are equilateral. (i) Explain why /_BAO = /_PAC B) (i) The diagram shows part of the graphs of both y=sec x and y= (4Sqr2 /Pi)x Show that (Pi/4 , Sqr 2) satisfies both of these equations. (ii) The area bounded by the curve y=secx, y= (4Sqr2 /Pi)x and the...

I am having trouble finding the Length of AX. I have included an image of the diagram. ABCD is a trapezium in which AB is parallel to DC. The diagonals intersect at X. AB=12cm, DC = 8cm and AC=10cm. ii) Hence find the length of AX. I have already proved that Triangle AXD is similar to...

I thought a question on viruses, bacteria, fungi and prions was going to come as a multiple choice so I didn't really study it. Then when in the exam it came as a...

The question asked to draw the curve first, I'll type out the whole question. B) Consider a straight line with the equation 3y=mx+6, M>0, and a curve with equation y=log(x+1) (i) By Substituting m=2, sketch 3y=2x+6 and y=log(x+1) together on the same diagram. (ii) Show that the vertical...

Bump. Could you guys please help me with this question. 3y=mx+6 and y=log(x+1) [Base e], the vertical distance from the straight line to the curve is given by mx/3 + 2 - log(x+1) [Base e]. Show that the shortest vertical distance is given the expression 3-m/3 - log(3/m) [Base e]

The graph of a parabolic function crosses the x-axis at the origin and at x=4. If the minimum value of the function is -1, determine the parabolic function. A right isosceles triangle has one vertex at the origin O and another at the point A(1,3). The base of the triangle has the equation...

The acceleration of a particle is given by: A = 8e^-2t + 3e^-t Where x is the displacement in meters and t is time in seconds. Initially its velocity is -6m/s and its displacement is 5m Show that the displacement of the particle is given by: x = 2e^-2t + 3e^-t + t

A flu for instance does not have an exact vaccine. The flu is constantly changing, a vaccine for the flu might work one time but then won't work after few months later that's because the flu is constantly evolving, the antigens are a different shape every time therefore the body needs to make a...

ABCD is a rectangle. Prove that TriangleBFC is similar to TriangleDCE.

Oh lol. I don't know how I did not see that.

Find the Area of the Shaded Region[Red].

Hey guys, I have just recently received my marks back for my second assessment task for english and my marks are appalling. Could you guys please read my essay and tell me where am I going wrong and what would you give it out of /15. Henry Lawson is an Australian writer who uses distinctively...

I have misread the question. The point P is a moving point so they wanted the area inside the parabola that is closed off by the line y=x+6. Please tell me if my working is correct. A = [Integral of -2 to 3 of (x+6)dx] - [Integral of -2 to 3 of (x^2)dx] = [x^2/2 +6x] - [x^3/3] =...

Is the Area = 1/2 * Root50 * (|p-p^2+6|)/(Root2) = Root50/2 * [(p-3)(p+2)]/Root5 = Root10[(p-3)(p+2)]/2

Woops, co-ordinates for B is (-2,4)

The Points A(3,9) and B(-2,4) lie on the parabola y=x^2. The line y=x+6 joins A and B. The Point P(p,p^2) is a variable on the parabola below the line. Find the area of the parabolic segment APB, i.e. the area below the line and above the parabola. Stacking Logs, 2 in the top row, 3 in the...

For the second line from the bottom of your working, how did you go from: 1 - log 2 To log10 - log 2?

1/root5+root2 + 3/3root2-root5 = 1(Root5 - Root2)/(Root5+Root2)(Root5-Root2) + 3(3Root2+Root5)/(3Root2-Root5)(3Root2+Root5) = (Root5-Root2)/3 + (9Root2+3Root2)/13 = ( 13(Root5-Root2) + 3(9Root2+3Root2) )/ 39 = (13Root5-13Root2+27Root2+9Root2)/39 = (13Root5+23Root2)/39

The logarithm is in base 10. The graph looks like this.

Solve logx^2 + log8x = 3 The diagram shows the graph of a certain function y=f(x). Sketch the graph of f'(x). The graph looks similar to a y=sinx graph except that its been pushed to the left a bit.