A fuel is purified by passing it through a clay pipe. Each foot of the clay pipe removes a fixed percentage of impurities in the
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Answer:
Rotation of triangle A across a point (1.5, -0.5) by 180°.
Step-by-step explanation:
Translation of a figure about a vector means translation of a figure by 3 units to the left on x-axis and 1 unit in the positive direction of the y-axis.
Rule for the translation will be,
(x, y) → [(x - 3), (y + 1)]
From the figure attached,
Vertices of the triangle A are A(1, -1), B(1, -4) and C(3, -4)
After translation new image points will be A'(-2, 0), B'(-2, -3), C'(0, -3).
After rotation of these image points 180° about the origin will be,
Rule for the rotation,
(x, y) → (-x, -y)
A'(-2, 0) → A"(2, 0)
B'(-2, -3) → B"(2, 3)
C'(0, -3) → C"(0, 3)
Therefore, A(1, -1) → A"(2, 0) is the single transformation.
Rule for this transformation which maps triangle C to A will be defined by,
Rotation of triangle A across a point (1.5, -0.5) by 180°.
Answer:
And when we apply the limit we got that:
Step-by-step explanation:
Assuming this complete problem: "The following formula for the sum of the cubes of the first n integers is proved in Appendix E. Use it to evaluate the limit . 1^3+2^3+3^3+...+n^3=[n(n+1)/2]^2"
We have the following formula in order to find the sum of cubes:
We can express this formula like this:
And using this property we need to proof that: 1^3+2^3+3^3+...+n^3=[n(n+1)/2]^2
If we operate and we take out the 1/4 as a factor we got this:
We can cancel and we got
We can reorder the terms like this:
We can do some algebra and we got:
We can solve the square and we got:
And when we apply the limit we got that: