10. Answer is 9 . (51 - 6) / ( 3.5+5.5)
11. 5x-18 - 4x = -36
x -18 = -36
x = -18
Answer is -18
B and C because both bases are squares
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.
The difference in elevation between the bottom of the canyon and the bird's nest is 947 1/2 feet
<h3>What is the difference in elevation between the bottom of the canyon and the bird's nest?</h3>
The given parameters are:
Nest = 71 4/5 feet above the seal level
Bottom of canyon = 875 7/10 below sea level
Below sea level means negative
So, we have:
Nest = 71 4/5 feet
Bottom of canyon = -875 7/10
The difference in elevation between the bottom of the canyon and the bird's nest is calculated as
Difference = |Nest - Bottom of canyon|
This gives
Difference = |71 4/5 - (-875 7/10)|
Evaluate the difference
Difference = |947 1/2|
Remove the absolute bracket
Difference = 947 1/2
Hence, the difference in elevation between the bottom of the canyon and the bird's nest is 947 1/2 feet
Read more about depth at:
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Given:
The point is (6,2).
To find:
The image of given point after rotation of 270 degrees.
Solution:
Let the given point be P(6,2).
Rotation of 270 degrees means the figure is rotated 270 degrees counterclockwise about the origin. So, the rule of rotation is

Using this rule, we get

Therefore, the image of given point is (2,-6).