Calculate R8 for f (x) =10−x
over [3,5]. Here is the solution:
R8 = ∫ [3..5] (10 - x) dx
= [ (50 - 25/2 ) - ( 30 - 9/2 ) ]
= ( 75/2 – 51/2 ) = 24/2
<span>= 12</span>
Assignment: ![\bold{Simplify \ Equation: \ 7\left(3\sqrt{2}x\right)-3\left(3\sqrt{16}x\right)-3\left(3\sqrt{8}x\right)}](https://tex.z-dn.net/?f=%5Cbold%7BSimplify%20%5C%20Equation%3A%20%5C%207%5Cleft%283%5Csqrt%7B2%7Dx%5Cright%29-3%5Cleft%283%5Csqrt%7B16%7Dx%5Cright%29-3%5Cleft%283%5Csqrt%7B8%7Dx%5Cright%29%7D)
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Answer: ![\boxed{\bold{3\sqrt{2}x-36x}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cbold%7B3%5Csqrt%7B2%7Dx-36x%7D%7D)
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Explanation: ![\downarrow\downarrow\downarrow](https://tex.z-dn.net/?f=%5Cdownarrow%5Cdownarrow%5Cdownarrow)
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[ Step One ] Remove Parenthesis (a) = a
![\bold{7\cdot \:3\sqrt{2}x-3\cdot \:3\sqrt{16}x-3\cdot \:3\sqrt{8}x}](https://tex.z-dn.net/?f=%5Cbold%7B7%5Ccdot%20%5C%3A3%5Csqrt%7B2%7Dx-3%5Ccdot%20%5C%3A3%5Csqrt%7B16%7Dx-3%5Ccdot%20%5C%3A3%5Csqrt%7B8%7Dx%7D)
[ Step Two ] Simplify Equations
![\bold{7\cdot \:3\sqrt{2}x: \ 21\sqrt{2}x}](https://tex.z-dn.net/?f=%5Cbold%7B7%5Ccdot%20%5C%3A3%5Csqrt%7B2%7Dx%3A%20%5C%2021%5Csqrt%7B2%7Dx%7D)
![\bold{3\cdot \:3\sqrt{16}x: \ 36x}](https://tex.z-dn.net/?f=%5Cbold%7B3%5Ccdot%20%5C%3A3%5Csqrt%7B16%7Dx%3A%20%5C%2036x%7D)
![\bold{3\cdot \:3\sqrt{8}x: \ 18\sqrt{2}x}](https://tex.z-dn.net/?f=%5Cbold%7B3%5Ccdot%20%5C%3A3%5Csqrt%7B8%7Dx%3A%20%5C%2018%5Csqrt%7B2%7Dx%7D)
[ Step Three ] Rewrite Equation
![\bold{21\sqrt{2}x-36x-18\sqrt{2}x}](https://tex.z-dn.net/?f=%5Cbold%7B21%5Csqrt%7B2%7Dx-36x-18%5Csqrt%7B2%7Dx%7D)
[ Step Four ] Add Similar Elements
![\bold{21\sqrt{2}x-18\sqrt{2}x=3\sqrt{2}x}](https://tex.z-dn.net/?f=%5Cbold%7B21%5Csqrt%7B2%7Dx-18%5Csqrt%7B2%7Dx%3D3%5Csqrt%7B2%7Dx%7D)
[ Step Five ] Rewrite Equation
![\bold{3\sqrt{2}x-36x}](https://tex.z-dn.net/?f=%5Cbold%7B3%5Csqrt%7B2%7Dx-36x%7D)
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Answer:
![\text{C. f(x)} = 3(1.5)^{x-1}](https://tex.z-dn.net/?f=%5Ctext%7BC.%20f%28x%29%7D%20%3D%203%281.5%29%5E%7Bx-1%7D)
Step-by-step explanation:
The numbers don’t increase by a constant amount, so this is not an arithmetic sequence.
It appears to be a <em>geometric sequence</em>.
The <em>general formula</em> for each term in a geometric sequence is
aₙ = a₁rⁿ⁻¹
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Calculate the value of r
You can calculate the r-value by dividing any two consecutive terms in the sequence.
rₙ = aₙ/aₙ₋₁
a₂/a₁ = 4.5/3 = 1.5
a₃/a₂ = 6.75/4.5 = 1.5
a₄/a₃ = 10.125/6.75 = 1.5
a₅/a₄ = 15.1875/10.125 = 1.5
r = 1.5
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Determine the formula for the nth term
a₁ = 3; r = 1.5 Substitute the values
aₙ = 3(1.5)ⁿ⁻¹ Write the equation as a function of x
![\text{f(x)} = 3(1.5)^{x-1}](https://tex.z-dn.net/?f=%5Ctext%7Bf%28x%29%7D%20%3D%203%281.5%29%5E%7Bx-1%7D)
Car 2 will drive faster im not sure but thats my answer
![\bf 1\rule[0.35em]{2em}{0.25pt}\boxed{1.5}\rule[0.35em]{2em}{0.25pt}2\rule[0.35em]{4em}{0.25pt}3\rule[0.35em]{4em}{0.25pt}4\rule[0.35em]{4em}{0.25pt}5\rule[0.35em]{4em}{0.25pt}6\rule[0.35em]{3em}{0.25pt}\boxed{6.7}](https://tex.z-dn.net/?f=%5Cbf%201%5Crule%5B0.35em%5D%7B2em%7D%7B0.25pt%7D%5Cboxed%7B1.5%7D%5Crule%5B0.35em%5D%7B2em%7D%7B0.25pt%7D2%5Crule%5B0.35em%5D%7B4em%7D%7B0.25pt%7D3%5Crule%5B0.35em%5D%7B4em%7D%7B0.25pt%7D4%5Crule%5B0.35em%5D%7B4em%7D%7B0.25pt%7D5%5Crule%5B0.35em%5D%7B4em%7D%7B0.25pt%7D6%5Crule%5B0.35em%5D%7B3em%7D%7B0.25pt%7D%5Cboxed%7B6.7%7D)
so, from 2 to 6, is 4 units.
from 1.5 to 2, is 0.5 units.
from 6 to 6.7, is 0.7 units.
4 + 0.5 + 0.7 => 4 + 1.2 => 5.2.