0.4 as a decimal,40% in percentage, and 2 (a line under 2) 5 goes under the line as fraction
Answer:
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
f(x)=x^2+2x
Let x= 4
f(4)=4^2+2*4
= 16 + 8
= 24
we know that
the volume of a solid oblique pyramid is equal to
where
B is the area of the base
h is the height of the pyramid
in this problem we have that
B is a square
where
<u>
</u>
so
substitute in the formula of volume
![V=\frac{1}{3}*x^{2}*(x+2)\\ \\V=\frac{1}{3}*[x^{3} +2x^{2}]\ cm^{3}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%2Ax%5E%7B2%7D%2A%28x%2B2%29%5C%5C%20%5C%5CV%3D%5Cfrac%7B1%7D%7B3%7D%2A%5Bx%5E%7B3%7D%20%2B2x%5E%7B2%7D%5D%5C%20cm%5E%7B3%7D)
therefore
<u>the answer is</u>
![V=\frac{1}{3}*[x^{3} +2x^{2}]\ cm^{3}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%2A%5Bx%5E%7B3%7D%20%2B2x%5E%7B2%7D%5D%5C%20cm%5E%7B3%7D)
Area of the parabolic region = Integral of [a^2 - x^2 ]dx | from - a to a =
(a^2)x - (x^3)/3 | from - a to a = (a^2)(a) - (a^3)/3 - (a^2)(-a) + (-a^3)/3 =
= 2a^3 - 2(a^3)/3 = [4/3](a^3)
Area of the triangle = [1/2]base*height = [1/2](2a)(a)^2 = <span>a^3
ratio area of the triangle / area of the parabolic region = a^3 / {[4/3](a^3)} =
Limit of </span><span><span>a^3 / {[4/3](a^3)} </span>as a -> 0 = 1 /(4/3) = 4/3
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