Correct solutions? (1 Viewer)

[eternallyboreduser]

Would the following w/o, solutions be considered correct/valid? Thanks in advance

 

[cossine]

Would the following w/o, solutions be considered correct/valid? Thanks in advance

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15 is good. 19 is too hard to read.

 

[liamkk112]

Would the following w/o, solutions be considered correct/valid? Thanks in advance

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for 15 u could give more of a proof as follows:
by the product rule for two functions
then applying the rule again:

then we can see the pattern that you listed above being apparent

 

[eternallyboreduser]

15 is good. 19 is too hard to read.

Wdym by too hard to read? In regards to my handwriting or the way i set out my w/o?

 

[eternallyboreduser]

Bump, anyone mind checking 19b?

 

[Luukas.2]

19b goes wrong at the end.

You have shown that and the distance from to the axis of symmetry is . You are required to show that

​

but you have instead equated them to (erroneously) conclude that . One possible completion would be:

​

 

[eternallyboreduser]

19b goes wrong at the end.

You have shown that and the distance from to the axis of symmetry is . You are required to show that

​

but you have instead equated them to (erroneously) conclude that . One possible completion would be:

​

Lol i made a ratio thats a : sign not a = sign sorry for the messy handwriting

 

[Luukas.2]

Lol i made a ratio thats a : sign not a = sign sorry for the messy handwriting

Then out equal signs at the LHS of each ratio, showing that the ratio is equal to the line before... or use fractions.

And, the distance to the axis is not , it is . You have drawn a diagram is which but nothing in the question requires it, so you need the absolute value for the distance to certainly be positive.

 

[eternallyboreduser]

Then out equal signs at the LHS of each ratio, showing that the ratio is equal to the line before... or use fractions.

And, the distance to the axis is not , it is . You have drawn a diagram is which but nothing in the question requires it, so you need the absolute value for the distance to certainly be positive.

Yeah right forgot to put the abs brackets lol

 

[eternallyboreduser]

bump

 

[eternallyboreduser]

my ngo test in two days please help

 

[eternallyboreduser]

some math god pls tell me if 19b was done right or along the lines of the correct sol

 

[anonymoushehe]

some math god pls tell me if 19b was done right or along the lines of the correct sol

this is what the solutions book said

 

[eternallyboreduser]

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this is what the solutions book said

Yeah i did not understand what theyre tryna say in that at all hence why i posted it here lo

 

[Luukas.2]

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this is what the solutions book said

The coordinate for the point is as the solutions posted by @anonymoushehe state.

The coordinate for the point is , matching the solution @eternallyboreduser gave.

The coordinate for the vertex is . Thus, , noting that we don't actually know if is positive or negative.

The axis of symmetry runs through the vertex and so is making the perpendicular distance from to the axis: , as we also don't know if or .

As I noted above, @eternallyboreduser has all of this correct except for the missing absolute value signs.

The solutions posted are incorrect in stating that as the latter term is and not (assuming ), but we can say that:

​

which satisfies the question. Eternallyboreduser, as I stated above, your solution is fine except for the end part.

 

[Luukas.2]

Yeah i did not understand what theyre tryna say in that at all hence why i posted it here lo

Not surprising as the solutions are poorly expressed and contain errors. Issues that I note include:

• It is not clear that the "coordinate for the tangent" refers to the point where the tangent touches the curve and not the point that we seek, where the tangent meets the axis.
• The coordinates represent the vertex and not the axis of symmetry - which is a line, and so can't be represented by a single point - though this point is where the axis of symmetry crosses the curve.
• The point lies on the -axis vertically above / below the point and is in no sense representative of the vertex.
• However, as the axis of symmetry is vertical, the perpendicular distance from it to is horizontal, and so the required distance is from the point to . The answers do not state this value, though it is .
• Both and lie on the axis and so this distance is vertical (and so the coordinates will cancel in the distance formula, which is what the answers are trying to state), yielding , as you showed (apart from the absolute value).
• The final statement that the distances are the same is simply wrong. Having not stated the distance from the axis of symmetry, this would certainly be penalised because it implies that the perpendicular distance is , which it isn't... and the perpendicular distance squared is not a distance anyway...

Though not actually an error, the lack of a diagram is poor practice when answering a question like this.