The answer needs the volume of the original pyramid minus the small pyramid cut off.
Volume of pyramid = (area of base x height)/3
(12 x 6 x 14)/3 - (4 x 10 x 6)/3 = 256 m^3
The diagram is completely wrong so this problem is actually impossible to solve!
If you slice horizontally across a rectangular pyramid the ratios of the edges will remain constant.
The two rectangles are not the same shape! 12:6 is not the same ratio as 10:4
If the original pyramid in this question was sliced in half the top rectangle of the frustum would be 6 x 3.
In this diagram the height was reduced from 14m to 8m so the top 6m was removed.
If the base was 12 x 6 the top rectangle should be 6/14 smaller = 5.14m by 2.57m (not 10 x 4)
If you are brave you could point this out to your teacher
(4x^5-15x^3-10x^2)-(2x^5-5x^3-2x^2)
So, the first thing we will do is add like terms. But before that, lets get rid of both parenthesis. We'll just get rid of the first pair, and for the second pair, we will multiple everything in the second parenthesis by -1
4x^5-15x^3-10x^2-2x^5+5x^3+2x^2
Now, we will add like terms.
2x^5-10x^3-8x^2
Now, there's a common factor that all of these terms share; it's 2x^2. 2x^5 can be divided by 2, as well as -10x^3 and -8x^2 (these are the coefficients, number found in front of the variable.) So, we'll distribute 2
2x^2(x^3-5x-4) (we take the 2x^2 out by dividing all terms by 2x^2)
So, our answer would be
2x^2
9514 1404 393
Answer:
- real: -1, 2; complex: +i, -i
- 1, 3, 4
Step-by-step explanation:
1. The graph (red) shows the only real zeros to be -1 and 2. When the corresponding factors are divided from the function, the remaining factor is the quadratic (x^2 +1), which has only complex roots. The quadratic is graphed in green.
The linear factorization is ...
f(x) = (x +1)(x -2)(x -i)(x +i)
The roots are -1, 2, -i, +i.
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2. The graph (blue) shows the zeros are 1, 3, 4.
You observe that the sum of coefficients is zero, so x=1 is a root. Factoring that out gives the quadratic (x^2 -7x +12), which you recognize factors as
(x -3)(x -4) . . . zeros of 3 and 4
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I have attached a spreadsheet that does synthetic division. There are web sites that will do this, too. The tables shown correspond to f1(x)/(x-2) and f2(x)/(x-1). When you fill in the zero and coefficients, the built-in formulas do the rest.
Answer:
find three consecutive even integers such that the sum of the second and third is equal to the first and third is 54 more than the second
Step-by-step explanation:
