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!
![\large\boxed{\text{At (-1, -2), }\frac{dy}{dx} = -\frac{2}{5}}}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%5Ctext%7BAt%20%28-1%2C%20-2%29%2C%20%7D%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20-%5Cfrac%7B2%7D%7B5%7D%7D%7D)
![\large\boxed{\text{At (-1, 3), }\frac{dy}{dx} = -\frac{3}{5}}}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%5Ctext%7BAt%20%28-1%2C%203%29%2C%20%7D%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20-%5Cfrac%7B3%7D%7B5%7D%7D%7D)
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:
brainly.com/question/17147411
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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
![(x,y)\to (y,-x)](https://tex.z-dn.net/?f=%28x%2Cy%29%5Cto%20%28y%2C-x%29)
Using this rule, we get
![P(6,2)\to P'(2,-6)](https://tex.z-dn.net/?f=P%286%2C2%29%5Cto%20P%27%282%2C-6%29)
Therefore, the image of given point is (2,-6).