DeoxNA
  • DeoxNA
In the graph y=sqrt(x), given that the area of the shaded region is 72, find the value of the constant a.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
DeoxNA
  • DeoxNA
|dw:1332649986192:dw| sorry for the drawing, but I hope you get the idea
anonymous
  • anonymous
Which area is shaded?
myininaya
  • myininaya
\[\int\limits_{0}^{a}\sqrt{x} dx=72 \]

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

DeoxNA
  • DeoxNA
|dw:1332650141113:dw| sorry I didn't notice
myininaya
  • myininaya
Oh that other part is the shaded region ?
experimentX
  • experimentX
a*sqrt(a) - the above answer = 72
experimentX
  • experimentX
the above expression
DeoxNA
  • DeoxNA
@experimentX I tried that but I got 36 and the book says the answer must be 4.2
myininaya
  • myininaya
|dw:1332650225304:dw| \[\int\limits_{0}^{a}(f(a)-\sqrt{x}) dx =[f(a) x -\frac{x^{\frac{1}{2}+1}}{\frac{1}{2}+1}]_0^a\] \[=[f(a)(a)-\frac{a^\frac{3}{2}}{\frac{3}{2}}]-[f(a)0-\frac{0^\frac{3}{2}}{\frac{3}{2}}]\] \[=a f(a)-\frac{2}{3} \cdot a^\frac{3}{2} =72 \] hmmm... we have two unknowns a and f(a) ---- and f(a)=sqrt(a)
myininaya
  • myininaya
so really we only have one known lol
myininaya
  • myininaya
which is that a lol since we know that f(a)=sqrt(a)
myininaya
  • myininaya
\[a \sqrt{a}-\frac{2}{3} a^\frac{3}{2}=72 \] Do you think you can solve this?
experimentX
  • experimentX
let's see, a*a^(1/2) - a^(3/2)/(3/2) = 72 http://www.wolframalpha.com/input/?i=a*a%5E%281%2F2%29+-+a%5E%283%2F2%29%2F%283%2F2%29+%3D+72 Got the same value as you did
myininaya
  • myininaya
actually it really is easy because those are like terms :)
myininaya
  • myininaya
\[a^\frac{3}{2}-\frac{2}{3}a^\frac{3}{2}=72\]
myininaya
  • myininaya
law of exponents if friend 1/2+1=3/2
myininaya
  • myininaya
gosh is*
myininaya
  • myininaya
\[\frac{1}{3}a^{\frac{3}{2}}=72\] Ok now the rest is left to you as an exercise have fun
myininaya
  • myininaya
well let me know though if you do get stuck lol
DeoxNA
  • DeoxNA
hmm... that is question 11 in my book, where the answer sheet says it must be 4.5, but answer 12 is 36..... I suspect a typo....¬ _¬
DeoxNA
  • DeoxNA
I'll solve 12, see if it is 4.5 and post back
myininaya
  • myininaya
yay 36 is correct
myininaya
  • myininaya
i don't know which is 11 and which is 12 sorry
myininaya
  • myininaya
but the question you have asked the answer is for surely 36
myininaya
  • myininaya
If you don't understand something I did you should ask
DeoxNA
  • DeoxNA
The answer to 12 is 4.5 afterall, so it is a typo...Anyway thanks for all the help
myininaya
  • myininaya
No questions?
DeoxNA
  • DeoxNA
No, I understand it, I was just confused why I was getting 36 while the answer sheet said it should be 4.5, but it was just a typo
myininaya
  • myininaya
ok cool

Looking for something else?

Not the answer you are looking for? Search for more explanations.