Slope is vertical change over horizontal change. Since coordinates conveniently give both the horizontal and vertical coordinates of a points, we can use the coordinates of both points to differentiate, or find the change horizontally and the change vertically between the two points.
Answer:

Step-by-step explanation:
Given
See attachment
Required
Find x
The relationship between x, 47 and
is:

i.e.

Solving further:

Make x the subject



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<em> --- approximated</em>
I will leave out the base, b since it's the same for all these logarithms.

Implicit defferentation
remember that dy/dx y= dy/dx
so
take derivitive of both sides

solve for

minus 2x both sides

divide both sides by 2y


when is the slope equal to

solve for





find where the circle and this line intersects
substitute

for y




times both sides by


sqrt both sides, take positive and negative roots
x=+/-10
sub back




the points are (10,-24) and (-10,24)
9514 1404 393
Answer:
5/4
Step-by-step explanation:
The relationship between the sec and csc functions is ...
csc(A) = sec(A)/√(sec²(A) -1)
For the given value of sec(A), this is ...
csc(A) = (5/3)/√((5/3)² -1) = (5/3)/√(16/9) = (5/3)/(4/3)
csc(A) = 5/4
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Some calculators can tell you the answer directly.