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
frosja888 [35]
3 years ago
9

3.

Mathematics
1 answer:
loris [4]3 years ago
7 0

(a) It looks like the ODE is

<em>y'</em> = 4<em>x</em> √(1 - <em>y </em>^2)

which is separable:

d<em>y</em>/d<em>x</em> = 4<em>x</em> √(1 - <em>y</em> ^2)   =>   d<em>y</em>/√(1 - <em>y</em> ^2) = 4<em>x</em> d<em>x</em>

Integrate both sides. On the left, substitute <em>y</em> = sin(<em>t </em>) and d<em>y</em> = cos(<em>t</em> ) d<em>t</em> :

∫ d<em>y</em>/√(1 - <em>y</em> ^2) = ∫ 4<em>x</em> d<em>x</em>

∫ cos(<em>t</em> ) / √(1 - sin^2(<em>t</em> )) d<em>t</em> = ∫ 4<em>x</em> d<em>x</em>

∫ cos(<em>t</em> ) / √(cos^2(<em>t</em> )) d<em>t</em> = ∫ 4<em>x</em> d<em>x</em>

∫ cos(<em>t</em> ) / |cos(<em>t</em> )| d<em>t</em> = ∫ 4<em>x</em> d<em>x</em>

Since we want the substitutiong to be reversible, we implicitly assume that -<em>π</em>/2 ≤ <em>t</em> ≤ <em>π</em>/2, for which cos(<em>t</em> ) > 0, and in turn |cos(<em>t</em> )| = cos(<em>t</em> ). So the left side reduces completely and we get

∫ d<em>t</em> = ∫ 4<em>x</em> d<em>x</em>

<em>t</em> = 2<em>x</em> ^2 + <em>C</em>

arcsin(<em>y</em>) = 2<em>x</em> ^2 + <em>C</em>

<em>y</em> = sin(2<em>x</em> ^2 + <em>C </em>)

(b) There is no solution for the initial value <em>y</em> (0) = 4 because sin is bounded between -1 and 1.

You might be interested in
Cu cît este mai mic împatritul lui63 fata de înnoitul rasturnatului sau?
never [62]
Indeed you need to speech English
4 0
3 years ago
Please help me with this :) i give 30 points .
Tatiana [17]

Answer:

2  B  4/75

3 B 1/7

Step-by-step explanation:

4 red, 3 blue, 2 yellow, 6 orange

total = 15

2.  P(red) = red/total = 4/15

replace it

so we still have 4 red, 3 blue, 2 yellow, 6 orange

total = 15

P(blue) = blue/total = 3/15 = 1/5

P(red, replace, blue) = 4/15 * 1/5 = 4/75

3 P(orange) = orange/total = 6/15 = 2/5

not replacing it

so we  have 4 red, 3 blue, 2 yellow, 5 orange

total = 14

P(orange) = orange/total = 5/14

P(orange, no replace, orange) = 2/5*5/14 = 2/14 = 1/7

6 0
3 years ago
Read 2 more answers
Amanda has a job transporting soft drinks by truck. Her truck is filled with cans that weigh 14 ounces each and bottles that wei
Korvikt [17]

T(x)= 14x + 70(930-x)
4 0
3 years ago
Question 14. Two sides of a triangle have lengths of 7
babymother [125]

Answer:

8 < x < 22

Step-by-step explanation:

If x is the third side , then

difference of 2 sides < x < sum of 2 sides , that is

15 - 7 < x < 15 + 7

8 < x < 22

6 0
3 years ago
Sandra wants to buy a new MP3 player that is on sale for $95. She has saved $73. How much morre money does she need?
iVinArrow [24]
95 - 73= 22; She needs $22.

Hope this helps :)

4 0
3 years ago
Read 2 more answers
Other questions:
  • Meyer used 6 loads of gravel to cover 2/5 of his driveway. how many loads of gravel will he need to cover the entire driveway?
    5·2 answers
  • Write -7.5 as a common fraction.
    8·1 answer
  • A pyramid has a volume of 8 cm cubed, what is the volume of a rectangular prism with the same dimensions?
    6·1 answer
  • The last digit of the heights of 39 statistics students were obtained as part of an experiment conducted for a class. Use the fr
    12·1 answer
  • a reciple calls for 6 cup of water and 4 cups of flour if the reciple is increased to use 6 cups of flour how much water shoud b
    7·1 answer
  • Can someone please help first answer gets brainlist
    13·1 answer
  • Which set of population data is the least dispersed from its mean?
    11·2 answers
  • How to solve quadratic inequalities.
    10·1 answer
  • The Empire State Building is 1,454 feet tall (if you include the lightning rod). If a piece of gum is dropped from the top, how
    12·1 answer
  • How would i solve this the shaded region is the whole inside circle.​
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!