1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
KengaRu [80]
4 years ago
11

Find the values of c such that the area of the region bounded by the parabola

Mathematics
1 answer:
KATRIN_1 [288]4 years ago
5 0

<u>Solution-</u>

The two parabolas are,

y=16x^2-c^2 \ and \ y=c^2-16x^2

By solving the above two equations we calculate where the two parabolas meet,

So \ 16x^2-c^2 = c^2-16x^2 \Rightarrow 32x^2=2c^2 \Rightarrow x=\frac{1}{4}c

Given the symmetry, the area bounded by the two parabolas is twice the area bounded by either parabola with the x-axis.

\therefore Area=2\int_{-c}^{c}y.dx= 2\int_{-c}^{c}(16x^2-c^2).dx\\=2[\frac{16}{3}x^3-c^2x]_{-c}^{ \ c}=2[(\frac{16}{3}c^3-c^3)-(-\frac{16}{3}c^3+c^3)]=2[\frac{32}{3}c^3-2c^3]=2(\frac{26c^3}{3})\\=\frac{52c^3}{3}

So \frac{52c^3}{3}=\frac{250}{3}\Rightarrow c=\sqrt[3]{\frac{250}{52}}=1.68

You might be interested in
Six bags of soil are used to fill 5 flower pots. how much soil does each flower pot use? between what two whole numbers does the
Zarrin [17]
So Basically It's 5×6?
7 0
3 years ago
Read 2 more answers
how many kiloliters are in 34 dekaliters? A. 0.34 kl, B. 3.4 kl, C. 340 kl, D. 3,400 kl
zloy xaker [14]
Answer: A (0.34 kl)

working:
34 dekalitres = 340 litres
340 litres = 0.34 kilolitres

Therefore, 0.34 kl
(deka = 1 x 10)
(kilo = 1 x 10^3)
8 0
3 years ago
Read 2 more answers
Solve 2(x + 1) + 4 = 8. (1 point)
DIA [1.3K]
X=1

Distribute
2x+2+4=8
Add
2x+6=8
Subtract
2x=2
Divide
X=1
8 0
3 years ago
Read 2 more answers
Estimate the result by rounding the numbers to the second decimal before performing the operation. Then also round your answer t
umka2103 [35]

Answer:

40615

Step-by-step explanation:

Note, rounding off decimals involves observing if the said decimal is up to the value of 5. If it is, then it can be rounded up, if not, its rounded off.

Since we need to round the numbers to the second decimal before performing the operation, we will have, 8123÷0.2

Note, 8123 has no decimal so we ignore

But 0.211 has a second decimal which is the first 1 so because it's not up to 5, we round it off to 0.

Hence we have 8123 ÷ 0.2= 40615.0

Since our answer has no decimal, we leave it like that.

8 0
3 years ago
Read 2 more answers
What is the scale factor from uvw to xyz
Elis [28]

Scale factor = XY/UV = YZ/VW = XZ/WV

Scale factor = 21/3 = 28/4 = 14/2

Scale factor = 7

3 0
3 years ago
Other questions:
  • Which step should be used to prove that point P is equidistant from R and Q?
    5·1 answer
  • Ln bisects km into two congruent angles measuring (3x-4) degrees and (4x-27)degrees. find m
    6·1 answer
  • Estimate the quotient 719.711 divied by 8.75
    6·1 answer
  • A pool holds 6500 liters of water. How many kiloliters of water will it hold?
    5·2 answers
  • A 10-acre field produced 750 bushels of corn. At that rate, how much corn can be produced from a 14-acre field?
    15·1 answer
  • Please help meeee out
    10·2 answers
  • I’ll give brainliest if correct, answer fast please only got a few mins
    8·1 answer
  • Which is the exact (not estimated) distance between the coordinates (-1, -1) and (4, 7)?
    11·2 answers
  • AHAHAHAHAHAAHAHAHAHAHAHAHAHAHAHAHAHAHA HELP ME IM GOING CRAZY XDDDDDD
    12·1 answer
  • NEED HELP ASAP PLEASE
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!