The value of y is 5
<h3>How to determine the value </h3>
From the given line, it can be concluded that:
The segment RT is divided into RS and ST
But we have the following parameters
The length of the sides are:
Since RT is RS added to ST:
We have;
RT = RS + ST
substitute the values
43 = 4y + 4 + 3y + 4
collect like terms
43 = 4y + 3y + 4 + 4
Add like terms
43 = 7y + 8
43 = 7y + 8
Make '7y' subject of formula
7y = 43 - 8
7y = 35
Make 'y' the subject of formula
y = 35/ 7
y = 5
Thus, the value of y is 5
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Answer: (3, -2)
Step-by-step explanation:
The solution to the system is where the graphs intersect.
Hey there! I'm happy o help!
To get from 60 to -20, you multiply by -1/3. This is our constant of proportionality. Let's see which points below follow this.
-10(-1/3)=3 1/3≠30
30(-1/3)=-10≠-15
-30(-1/3)=10
80(-1/3)=-26 2/3≠-30
Therefore, the correct answer is (-30,10).
Have a wonderful day! :D
Answer:
true
Step-by-step explanation:
add
x*y' + y = 8x
y' + y/x = 8 .... divide everything by x
dy/dx + y/x = 8
dy/dx + (1/x)*y = 8
We have something in the form
y' + P(x)*y = Q(x)
which is a first order ODE
The integrating factor is 
Multiply both sides by the integrating factor (x) and we get the following:
dy/dx + (1/x)*y = 8
x*dy/dx + x*(1/x)*y = x*8
x*dy/dx + y = 8x
y + x*dy/dx = 8x
Note the left hand side is the result of using the product rule on xy. We technically didn't need the integrating factor since we already had the original equation in this format, but I wanted to use it anyway (since other ODE problems may not be as simple).
Since (xy)' turns into y + x*dy/dx, and vice versa, this means
y + x*dy/dx = 8x turns into (xy)' = 8x
Integrating both sides with respect to x leads to
xy = 4x^2 + C
y = (4x^2 + C)/x
y = (4x^2)/x + C/x
y = 4x + Cx^(-1)
where C is a constant. In this case, C = -5 leads to a solution
y = 4x - 5x^(-1)
you can check this answer by deriving both sides with respect to x
dy/dx = 4 + 5x^(-2)
Then plugging this along with y = 4x - 5x^(-1) into the ODE given, and you should find it satisfies that equation.