If (x-1)^3 = 8
then would x-1 = +- cube root of 8, or just + cube root of 8 and why?
Also, does anyone know how you would work out sin(11pi/4), which is sin(2.75pi), and is in quadrant 2, and the rule for quadrant 2 is pi - base, but since it's 2.75, would you do (2pi) + (pi-base)?
And how would you work out the value of the base?
How would you find the basic angle for a negative value?
For instance cos(x) = -1/2
How would you work out (x+1)^3 = -2 without a calculator?
Thanks
Last edited by boredsatan; 19 Jan 2018 at 9:30 AM.
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Bump!
Any one know how to do the above questions?
Also, does anyone know how to solve the equation sin x = 1/2 for [-pi, to 2pi]
I'm confused with the negative domain
Thanks
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Bump
Can somebody PLEASE ANSWER all my questions above?
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The sine wave has symmetry across the origin, so it's an odd function, which means that .
Basically that implies that the sine of a negative angle is the same as reversing the sign of the sine of the positive angle, i.e.
.
When we go in the positive direction, the first angle for which is .
So that means that when we go in the negative direction, the first angle for which is .
But is outside the range of , so it's not a solution to the equation.
HSC 2018 - [English Adv.] • [Maths Ext. 1] • [Maths Ext. 2] • [Chemistry] • [Software Design and Development]
Last edited by fan96; 21 Jan 2018 at 8:01 PM.
HSC 2018 - [English Adv.] • [Maths Ext. 1] • [Maths Ext. 2] • [Chemistry] • [Software Design and Development]
The equation of the image of the graph of y = sin x under a transformation of a dilation of factor 1/2 from the y-axis followed by a translation of pi/4 units in the positive direction of the x axis is:
I'm narrowed it down two 2 options, but don't know which one is correct. Can someone please explain which one is correct and why
y = sin(2x - pi/4) or y = sin2(x-pi/4)
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let f: [0, pi/2] → R, where f(x) = cos(3x) -2. The graph of f is transformed by a reflection in the x-axis followed by a dilation of factor 3 from the y-axis. How would you work out the resulting graph, super confusing so wold greatly appreciate if someone helped out
Last edited by boredsatan; 23 Jan 2018 at 8:57 PM.
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I'm not familiar with that specific terminology, but if "dilation of factor 1/2 from the y-axis" means compressing the function horizontally, then you replace with and to shift it right you would replace with , in that order.
Dilate:
Shift graph:
Reflect across x axis:
Dilate:
HSC 2018 - [English Adv.] • [Maths Ext. 1] • [Maths Ext. 2] • [Chemistry] • [Software Design and Development]
An open tank is to be made from a sheet of metal 84 cm by 40 cm by cutting congruent squares of side length x cm from each of the corners.
I've found the volume to be = (84-2x)(40-2x)(x)
State the maximal domain for V when it is considered as a function of x. Confused how to do this part
Any help would be appreciated
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A rectangle is defined by vertices N and P(x,y) on the curve with equation y = 16-x^2 and vertices M and Q on the x axis
a.i. Find the area, A of the rectangle in terms of x
ii. state the implied domain for the function defined by the rule given in part i
Can someone please help me with this?
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A metal worker is required to cut a circular cylinder from a solid sphere of radius 5 cm. Express r in terms of h, where r cm is the radius of the cylinder and h cm is the height of the cylinder. Hence show that the volume, V cm^3, of the cylinder is given by V = (1/4)(pi)(h)(100-h^2)
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n a tidal river, the time between high tides and low tides is 12 hours. The average depth of water at a point in the river is 5m. At high tide the depth is 8 m. Assume that the depth of the water, h(t) m, at this point is given by
h(t) = A sin(nt+e)+b, where t is the number of hours after noon. At noon there is a high tide.
a. find the values of A, n,b, and e
b. at what times is the depth of the water 6 m?
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Bump
Can somebody PLEASE ANSWER all my questions above?
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