Answer:
r = 1
Step-by-step explanation:
Solve for r
by simplifying both sides of the equation, then isolating the variable.
15x²+16x+4 =0 (ax² +bx +c=0)
Δ = b²-4ac =256 - 4×15×4 =16
x1 = (-b+√Δ) / 2a = (-16+√16) / 30 =( -16+4) / 30 = -12/30 = - 2/5
x2 = (-b -√Δ) / 2a = (-16 -√16) / 30 = (-16 -4) /30 = -20/30 = -2/3
Answer: As the dough rises, the distance between the raisins increases, indicating that the galaxies are moving apart.
Step-by-step explanation:
The tangent line to <em>y</em> = <em>f(x)</em> at a point (<em>a</em>, <em>f(a)</em> ) has slope d<em>y</em>/d<em>x</em> at <em>x</em> = <em>a</em>. So first compute the derivative:
<em>y</em> = <em>x</em>² - 9<em>x</em> → d<em>y</em>/d<em>x</em> = 2<em>x</em> - 9
When <em>x</em> = 4, the function takes on a value of
<em>y</em> = 4² - 9•4 = -20
and the derivative is
d<em>y</em>/d<em>x</em> (4) = 2•4 - 9 = -1
Then use the point-slope formula to get the equation of the tangent line:
<em>y</em> - (-20) = -1 (<em>x</em> - 4)
<em>y</em> + 20 = -<em>x</em> + 4
<em>y</em> = -<em>x</em> - 24
The normal line is perpendicular to the tangent, so its slope is -1/(-1) = 1. It passes through the same point, so its equation is
<em>y</em> - (-20) = 1 (<em>x</em> - 4)
<em>y</em> + 20 = <em>x</em> - 4
<em>y</em> = <em>x</em> - 24
