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
oee [108]
3 years ago
7

Show that y=cos(t)y=cos(t) is a solution to (dydt)2=1−y2(dydt)2=1−y2. Enter your answers below in terms of the independent varia

ble tt in the order in which the terms were given. Be sure you can justify your answer.
Mathematics
1 answer:
GrogVix [38]3 years ago
7 0

Answer:

(\frac{dy}{dt})^2=sin^2t

Step-by-step explanation:

y=cost

DE :(\frac{dy}{dt})^2=1-y^2

If y is a solution of given DE then it satisfied the DE.

Differentiate w.r.t t

\frac{dy}{dt}=-sint

Using the formula

\frac{d(cosx)}{dx}=-sinx

LHS:(\frac{dy}{dt})^2=(-sint)^2=sin^2t

RHS

1-y^2=1-cos^2t=sin^2t

By using the formula

sin^2t=1-cos^2t

LHS=RHs

Hence, y is a solution of given DE

(\frac{dy}{dt})^2=sin^2t

You might be interested in
Byron is conducting an experiment to determine whether a new medication is effective in reducing coughing. He finds 1,200 volunt
hammer [34]

Answer:

The medication is effective, but may take some time to work its way to the immune system

Step-by-step explanation:

3 0
3 years ago
Why is volume of a cone is written in cubic units
frutty [35]

Answer:

The formula for the volume of a cone is 1/3 Bh. This means 1/3 the Area of the base times the height. You can calculate the area by multiply length and width. Area is two-dimensional. Multiplying height by it adds another dimension. When writing area, we say units squared. When writing volume, we say units cubed, because it is three dimensional.

Step-by-step explanation:

6 0
3 years ago
What is the solution to the inequality?<br> <br> 10x + 18 &lt; -2
padilas [110]
Let's solve your inequality step-by-step.

<span><span><span>10x</span>+18</span><<span>−2

</span></span>Step 1: Subtract 18 from both sides.

<span><span><span><span>10x</span>+18</span>−18</span><<span><span>−2</span>−18

</span></span><span><span>10x</span><<span>−20

</span></span>Step 2: Divide both sides by 10.

<span><span><span>10x/</span>10</span><<span><span>−20/</span>10

</span></span><span>x<<span>−2

</span></span>Answer:

<span>x<<span>−<span>2</span></span></span>
4 0
3 years ago
A line that includes the points (
barxatty [35]

Answer:

-7

Step-by-step explanation:

Refer to the photo.

the slope=(0-g)/(5-4)

i.e. 7=(-g)/1

g=-7

3 0
3 years ago
if you’re good with set theory in math 30 please help with questions 31 and 32!! real answers only !!
GREYUIT [131]

Answer:  31) d     32) c

<u>Step-by-step explanation:</u>

31)

A = {1, 3, 5, 15}

B = {2, 3, 5, 7}

A ∪ B = {1, 2, 3, 5, 7, 15}

C = {2, 4, 6, 8}

(A ∪ B) ∩ C = {1, 2, 3, 5, 7, 15} ∩ {2, 4, 6, 8} = {2}

<em>2 is the only number in both sets</em>

32)

The pattern is: reflection, add symbol, ..., reflection, add symbol.

The last image shown is: add symbol

So the next image will be: reflection (flipped to the left)

7 0
3 years ago
Other questions:
  • For the inequalities, how would I put them on the number line ?
    14·1 answer
  • I need the answer pls pls pls answer pls
    6·1 answer
  • What is the measure of the angle?
    11·1 answer
  • What is 28,000 have in common with 27,000
    7·2 answers
  • Which graph represents the function f(x) = 2 (2)X?
    9·2 answers
  • a teacher is shouting she shuts the door she shuts the windows but forgets to shut something what is it? i know but do you know
    13·1 answer
  • Write a rule for each pattern. then find next three numbers in the pattern.<br> 1,-2,4,-5,7,-8...
    6·1 answer
  • In how many year the interest will became equal to the principal is rs.1200 is deposited at the rate of 25% in a bank ​
    7·1 answer
  • For questions 3 - 5, use the FOIL method to find the product of the binomials.
    11·1 answer
  • What is ∑n=17(10n+90) equal to?<br><br> Enter your answer in the box.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!