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klio [65]
3 years ago
10

Determine whether the given relation is an implicit solution to the given differential equation. assume that y is a function of

x.
Mathematics
1 answer:
Xelga [282]3 years ago
6 0
Differentiate:x^2 + y^2 = 4 
You get this:2x + 2yy' = 0 
bring the x variable on the other side:2yy' = -2x 
Now divide 2y to leave y' by itself:y' = -2x/2y 
Answer: y' = -x/y 
The given relation is not a implicit solution to the given differential equation.
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2x+3y=15<br> x+y=6<br> work out the values of x and y
Anna [14]

Answer:

x=3

y=3

Step-by-step explanation:

x = 6-y

-plug in (6-y) into first equation

2(6-y)+3y = 15

12-2y+3y=15

-2y+3y = 3

y=3

x=6-3

x=3

double check:

(2*3) + (3*3) = 6 + 9 = 15

3 + 3 = 6

6 0
4 years ago
Read 2 more answers
Which histogram represents a data set with a mean of 4.5 and a standard deviation of 1.7?
AVprozaik [17]

Answer:

that would be the third one

Step-by-step explanation:

5 0
3 years ago
Short Response To earn a varsity letter on the baseball team, you must play in 60% of the games. Derek played in 11 out of 18 ba
Alla [95]

Answer:

Yes, he earned a Varsity letter because he played in 61% of the games.

Step-by-step explanation:

To know the percent of games he played out of the total, we can do it by dividing the games he played by the total of games and multiply this by 100% to get the percent of games he played:

\frac{11}{18}*100%

We solve:

0.611111*100% = 61.11%

So we know that he earned a letter because he played in 61.11% of the games, more than he needed.

7 0
3 years ago
Find an equation of a line that is tangent to the graph of f and parallel to the given line. Please see picture
ivanzaharov [21]

Answer:

y = 3x - 2 (smaller y-intercept)

y = 3x + 2 (larger y-intercept)

Step-by-step explanation:

First let's write the generic equation of a line:

y = ax + b

This line needs to be parallel to the line 3x - y + 5 = 0, so it needs to have the same slope of this line.

The line 3x - y + 5 = 0 has a slope of 3, so our line has a = 3:

y = 3x + b

Now we need to find the values of b that make this line tangent to the function f(x) = x^3

Let's first find the derivative of f(x) in relation to x:

df(x)/dx = 3x^2

This derivative is the slope of the tangent line to the function for any value of x. We need a slope of 3, so:

3x^2 = 3

x^2 = 1

x = ±1

Now, to find the y-values, we have:

f(1) = 1^3 = 1

f(-1) = (-1)^3 = -1

So, using the points (1,1) and (-1,-1) in our parallel line, we have:

first line using (1,1) : 1 = 3*1 + b

b = -2

second line using (-1,-1) : -1 = -3*1 + b

b = 2

The value of b is the y-intercept of the line, so the line with smaller y-intercept is y = 3x - 2, and the line with larger y-intercept is y = 3x + 2

8 0
3 years ago
∠ A and ∠B are vertical angles. Find each angle if, m∠ A=7x+2 and m∠ B=4x+11. Solve for x
tino4ka555 [31]

Answer:

x=3

Step-by-step explanation:

Vertical angles are equal so

<A = <B

7x+2 = 4x+11

Subtract 4x from each side

7x+2-4x = 4x+11-4x

3x+2 =11

Subtract 2 from each side

3x+2-2 = 11-2

3x = 9

Divide by 3

3x/3 = 9/3

x=3

7 0
3 years ago
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