We write the equation in terms of dy/dx,
<span>y'(x)=sqrt (2y(x)+18)</span>
dy/dx = sqrt(2y + 18)
dy/dx = sqrt(2) ( sqrt(y + 9))
Separating the variables in the equation, we will have:
<span>1/sqrt(y + 9) dy= sqrt(2) dx </span>
Integrating both sides, we will obtain
<span>2sqrt(y+9) = x(sqrt(2)) + c </span>
<span>where c is a constant and can be determined by using the boundary condition given </span>
<span>y(5)=9 : x = 5, y = 9
</span><span>sqrt(9+9) = 5/sqrt(2) + C </span>
<span>C = sqrt(18) - 5/sqrt(2) = sqrt(2) / 2</span>
Substituting to the original equation,
sqrt(y+9) = x/sqrt(2) + sqrt(2) / 2
<span>sqrt(y+9) = (2x + 2) / 2sqrt(2)
</span>
Squaring both sides, we will obtain,
<span>y + 9 = ((2x+2)^2) / 8</span>
y = ((2x+2)^2) / 8 - 9
To simplify 4/(2+7i), we multiply it by a fraction equal to one that removes the i value in the denominator. The best value to do this is the complex conjugate divided by itself, so we have 4(2-7i)/((2+7i)(2-7i)). Simplifying, we have (8-28i)/(4-(-49))=(8-28i)/53, which is a completely simplified fraction since 8 and 53 are relatively prime (or coprime), and there are no radicals in the denominator.
Answer and workin your attached below. Hope it helps
Answer:
30 degrees
Step-by-step explanation:
Angle B is an inscribed angle -- its vertex is on the circle and it intersects the circle in two points, <em>A</em> and <em>C</em>.
The measure of an inscribed angle is always one half the measure of the intercepted arc. The intercepted arc has measure 60 degrees, so the measure of angle B is 30 degrees.
Angles C and D are supplementary, or they add up to 180.
b = 180 - 75 - (180 - 127)
Hope this helps!
