How does the volume of a prism change if each dimension of the prism is doubled?
2 answers:
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We can find a formula for nth term of the given sequence as follows:
1, 5, 12, 22, 35
The 1st differences between terms:
4, 7, 10, 13
The 2nd differences :
3, 3, 3
Since it takes two rounds of differences to arrive at a constant difference between terms, the nth term will be a 2nd degree polynomial of the form: , where c is a constant. The coefficients a, b, and the constant c can be found.
We can form the following 3 equations with 3 unknowns a, b, c:
Solving for a, b, c, we get:
a = 3/2, b = -1/2, c = 0
Therefore, the nth term of the given sequence is:
The points of new triangle is (3,-2), (6,-3) and (2,-5).
<u>Step-by-step explanation:</u>
The given points in the triangle A(-3,7), B(9,3) and C(-7,-5).
The scale factor is and centered at point (5,-5).
The formula to dilate a point that is not centered on a origin is given by,
D(x,y)=(h+t(x-h),k+t(y-t)).
where (h,k) is the center point.
To find A',
D(-3,7)=(5-2, -5+3).
D(-3,7)=(3,-2).
To find B',
D(9,3) = (5+1,-5+2).
D(9.3)=(6,-3).
To find C',
D(-7,-5)=(5-3,-5+0).
D(-7,-5)=(2,-5).
∴ The points of new triangle is (3,-2), (6,-3) and (2,-5).
