PLEASE HELP!!!!!!
2 answers:
Answer: The correct options are
(C) x = -6
(D) x = 6.
Step-by-step explanation: We are given to select the values of x that are the solutions to the following equation :
The solution of the given equation (i) is as follows :
Thus, the solutions to the given equation are x = -6 and x = 6.
Option (C) and (D) are correct options.
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Answer: The person's speed is 8 miles per hour.
Step-by-step explanation:
To solve we want to convert the and
proportionally for the number of miles per hour. We know that multiplying a fraction by its reciprocal will equal 1. So let's do that for the value of the hour.
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Since we multiplied that to the number of hours we must also do that for the number of miles.
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Hi there!
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.