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DIA [1.3K]
3 years ago
7

Solve the differential equation y prime equals the product of 2 times x and the square root of the quantity 1 minus y squared .

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

Answer:

1. y = sin(x²+C)

2. see below

Step-by-step explanation:

1. \frac{dy}{dx} = 2x\sqrt{1-y^2}

separation of variables

\frac{dy}{\sqrt{1-y^2} } = 2xdx

integration both sides\int\frac{dy}{\sqrt{1-y^2} } = \int2xdx

you should get :

sin^{-1} (y) = x^2+C remember constant of integration!!

2. y = sin(x²+C)

3 = sin(0+C)

y(0) = 3 does not have a solution because our sin graph is not shifted vertically or multiplied by a factor whose absolute value is greater than 1, so our range is [-1,1] and 3 is not part of this range

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Factor the following equation to find its zeros. y = x² - 36
alukav5142 [94]

Answer:

x = 6, x = - 6

Step-by-step explanation:

Given

y = x² - 36

To find the zeros let y = 0, that is

x² - 36 = 0 ← x² - 36 is a difference of squares and factors in general as

a² - b² = (a - b)(a + b), thus

x² - 36 = 0

x² - 6² = 0

(x - 6)(x + 6) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 6 = 0 ⇒ x = - 6

3 0
3 years ago
Help me out please an thank you
MakcuM [25]
The answer is 46.
Since the sum of the interior angles of a triangle is always 180,
We can find out angle C by subtracting the other two angles
180-102-32=46
3 0
3 years ago
Math inspection:who is right?
Pavel [41]

Answer:

I don't know

Step-by-step explanation:

6 0
3 years ago
a particular truck in a transportation fleet was driven 194,070 miles last year versus 329,919 miles this year . by what percent
Ann [662]

We take as the 100% the 194070 miles from last year. Then, we apply a rule of three:

\begin{gathered} 194070\rightarrow100\text{ \%} \\ 329919\rightarrow x\text{ \%} \\ \Rightarrow x=\frac{329919\cdot100}{194070}=\frac{32991900}{194070}=170 \\ x=170\text{ \%} \end{gathered}

Since 329,919 is the 170% of last year's miles, then the increase was of 70%

8 0
1 year ago
Find the percent of decrease from 20 field goals to 14 field<br> goals.<br> % decrease
Galina-37 [17]

Answer:

30%

Step-by-step explanation:

So, 20/20 turns to 14/20. How much was taken away? 6/20. What times 20 is 100? 5. So, 5 x 6 is 30. So, there is a 30% decrease

8 0
3 years ago
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