How to simplify 7-|-23|+|-7|
2 answers:
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Answer: The point (-10,-20) becomes (-8,-16) & point (15,25) becomes (12,20).
Step-by-step explanation:
When a point (x,y) is dilated by a scale factor k from the origin, then the new points become
The given rule of dilation : (x,y) →(0.8x, 0.8y)
The first point is (-10,-20), so its image will be
So, the point (-10,-20) becomes (-8,-16).
The second point is (15,25), so its image will be
So, the point (15,25) becomes (12,20).
Hence, the point (-10,-20) becomes (-8,-16) & point (15,25) becomes (12,20).
Assuming you mean f(t) = g(t) × h(t), notice that
f(t) = g(t) × h(t) = cos(t) sin(t) = 1/2 sin(2t)
Then the difference quotient of f is
Recall the angle sum identity for sine:
sin(x + y) = sin(x) cos(y) + cos(x) sin(y)
Then we can write the difference quotient as
or
(As a bonus, notice that as h approaches 0, we have (cos(2h) - 1)/(2h) → 0 and sin(2h)/(2h) → 1, so we recover the derivative of f(t) as cos(2t).)