Which equation represents the sentence?
2 answers:
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First solve x³=9x
We can ignore x = -3 because it is not in the first quadrant.
<span>So our integral is going to go from x=0 to x=3.
</span>
<span>Now we can use the formula
</span><span>
</span>![\int\limits_{0}^{3}(\pi (9x)^2-\pi(x^3)^2)dx \\\int\limits_{0}^{3}(\pi (9x)^2-\pi(x^3)^2)dx \\\pi\int\limits_{0}^{3}(81x^2-x^6)dx \\2\times \int\limits_{0}^{3}[\pi(9x)^2-\pi(x^3)^2]dx \\\pi\left[81\frac{x^3}{3}-\frac{x^7}{7}\right]_{0}^{3} \\ \\\frac{2916\pi}{7}](https://tex.z-dn.net/?f=%5Cint%5Climits_%7B0%7D%5E%7B3%7D%28%5Cpi%20%289x%29%5E2-%5Cpi%28x%5E3%29%5E2%29dx%0A%5C%5C%5Cint%5Climits_%7B0%7D%5E%7B3%7D%28%5Cpi%20%289x%29%5E2-%5Cpi%28x%5E3%29%5E2%29dx%0A%5C%5C%5Cpi%5Cint%5Climits_%7B0%7D%5E%7B3%7D%2881x%5E2-x%5E6%29dx%0A%5C%5C2%5Ctimes%20%5Cint%5Climits_%7B0%7D%5E%7B3%7D%5B%5Cpi%289x%29%5E2-%5Cpi%28x%5E3%29%5E2%5Ddx%0A%5C%5C%5Cpi%5Cleft%5B81%5Cfrac%7Bx%5E3%7D%7B3%7D-%5Cfrac%7Bx%5E7%7D%7B7%7D%5Cright%5D_%7B0%7D%5E%7B3%7D%20%5C%5C%20%5C%5C%5Cfrac%7B2916%5Cpi%7D%7B7%7D)
<span>
</span>
We can ignore x = -3 because it is not in the first quadrant.
<span>So our integral is going to go from x=0 to x=3.
</span>
<span>Now we can use the formula
</span><span>
</span>
</span>
Answer:
The length and width dimensions of solid 'a' are multiplied by 2 while the height remains the same to get the representative quantity in solid, b
Step-by-step explanation:
The given parameters of solid 'a' are;
The shape of solid, a = Right, rectangular prism
Let 'l' represent the length of solid 'a', let 'w' represent the width of solid 'a' and let 'h' represent the height of solid 'a'
We have;
The length of solid, = 2·l
The width of solid, = 2·w
The height of solid, = h
Given that we have;
The length of solid, b = 2 × The length of solid, a
The width of solid, b = 2 × The width of solid, a
The height of solid, b = The height of solid, a
The dimensions of length and width of each quantity in solid 'a' will be multiplied by 2 to find the dimension of a similar quantity in solid 'b'
The change in volume from solid 'a' to solid 'b' is given as follows;
The volume of solid, 'a', Vₐ = l × w × h = l·w·h
The volume of solid, 'b', = 2·l × 2·w ×h = 4·l·w·h
= 4 × Vₐ
Therefore, the volume of each unit volume in solid 'a' is multiplied by 4 to get the volume of the image of the unit volume in solid 'b'
The cross sectional area of solid 'a', Aₐ = l × w
The cross sectional area of solid 'b', = 2·l × 2·w = 4·l·w
= 4 × Aₐ
The cross sectional area of each unit of solid 'a' is multiplied by 4 to get the image of the unit cross sectional area in solid 'b'.
Therefore;
The change in the height and width of of solid 'b' is equal to a change in twice the height and width of solid 'a' at a given height, 'h'
The relationships are;
= 2·l,
= 2·w,
= h