Understand that a function<span> is a rule that assigns to each input exactly one output. The graph of a </span>function<span> is the set of ordered pairs consisting of an input and the corresponding output.</span>
Answer:
-1/2
Step-by-step explanation:
The slope of the given line is the coefficient of x, which is 2.
The slope of the perpendicular line is the negative reciprocal of that:
-1/2
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We can calculate dy/dx using implicit differentiation:
xy + y² = 6
Differentiate both sides. Remember to use the Product Rule for the "xy" term:
(1)y + x(dy/dx) + 2y(dy/dx) = 0
Move y to the opposite side:
x(dy/dx) + 2y(dy/dx) = -y
Factor out dy/dx:
dy/dx(x + 2y) = -y
Divide both sides by x + 2y:
dy/dx = -y/x + 2y
We need both x and y to find dy/dx, so plug in the given value of x into the original equation:
-1(y) + y² = 6
-y + y² = 6
y² - y - 6 = 0
(y - 3)(y + 2) = 0
Thus, y = -2 and 3.
We can calculate dy/dx at each point:
At y = -2: dy/dx = -(-2) / -1+ 2(-2) = -2/5.
At y = 3: dy/dx = -(3) / -1 + 2(3) = -3/5.
Answer:
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Step-by-step explanation:
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256. Since each side is congruent, the length equals 8. 8 times 8 equals 64. Divide it by 2 to find the area of the triangle. 64 divided by 2 equals 32. Since there are 8 congruent triangles, 32 x 8 equals 256.