Answer:
ln(125) ≈ 4.828314
Step-by-step explanation:
The relevant log relation is ...
log(a^b) = b·log(a)
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This means your expression is equivalent to ...
3·ln(5) = ln(5^3) = ln(125) ≈ 4.828314
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The "exact" answer is ln(125).
Answer:
z' = 2iz +11 -2i
Step-by-step explanation:
Dilation multiplies each point by the scale factor. Rotation by 90° CCW is equivalent to multiplication by i.
When the center is not the origin, the transformation is applied to the difference from the center, then the result is added to the center.
z' = 2i(z -(3+4i)) + (3+4i)
Simplifying gives ...
z' = 2iz -6i +8 +3 +4i
z' = 2iz +11 -2i
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<em>Check</em>
For example, consider the point 1 unit east of the center of dilation/rotation. That point is z = 4+4i. Applying the transformation moves this point to ...
z' = 2i(4 +4i) +11 -2i = 8i -8 +11 -2i
z' = 3 +6i . . . . . 2 units north of the center of dilation/rotation
This is where it is expected to be after dilation by a scale factor of 2 and rotation 90° CCW.
Answer:
r sin 55
Step-by-step explanation:
2nd is correct answer
The answer is x=7/2 or 3.5