X = approximately 633
Steps:
lnx + ln3x = 14
ln3x^2 = 14 : Use the log property of addition which is to multiply same log together so you multiply x and 3x because they have log in common
(ln3x^2) = (14) : take base of e on both sides to get rid of the log
e e
3x^2 = e^14 : e cancels out log on the left side and the right side is e^14
x^2 = e^14 / 3 : divide both sides by 3
√x^2 = <span>√(e^14 / 3) : take square root on both sides to get rid of the square 2 on x
</span>
x = √(e^14) / <span>√3 : square root cancels out square 2 leaving x by itself
x = e^7 / </span>√3 : simplify the √(e^14) so 14 (e^14) divide by 2 (square root) = 7<span>
x = </span>633.141449221 : solve
11/200 would be the answer yeah i know fractions :D
Volume = length * width * depth
width = Volume / (length * depth)
width = 7.35 / (4.2 * .5)
width = 3.5 meters
Double Check
Volume = 4.2 *.5 *3.5 =
<span>
<span>
<span>
7.35
</span>
</span>
</span>
cubic meters correct !!
Answer:
f(x)=11+7√x
f'(x)=7/(2x^(1/2))
putting x=1
f'(1) = 7/(2×1^(1/2))
= 7/2 = 3.5
putting x=2
f'(2) = 7/(2×2^(1/2))
= 7/(2×√2)
= 7√2/4
= 2.47 (rounded to the nearest hundredth)
f'(3) = 7/(2×3^(1/2))
= 7/(2×√3)
= 7√3/6
= 2.02 (rounded to the nearest hundredth)
