Answer:
Step-by-step explanation:
We can use the distance formula derived from the Pythagorean theorem
D = 
the two points given are
(0, 3) and (-2, -3)

Answer:
Step-by-step explanation:
Please find the attachment.
We have been given that a container is shaped like a triangle prism. Each base of container is an equilateral triangle with each side 6 cm. The height of container is 15 cm.
To find the lateral surface area of our given container we will use lateral surface area formula of triangular prism.
, where, a, b and c represent base sides of prism and h represents height of the prism.
Upon substituting our given values in above formula we will get,



Therefore, lateral surface area of our given container is 270 square cm.
First set up the equation (sum of the angles is 180)
2x + 2(x-1) + (5x +2) = 180
distribute:
2x + 2x -2 + 5x +2 = 180
combine like terms:
9x = 180
solve for x:
x = 20
SO:
2x° = 2(20) = 40 degrees
2(x-1)° = 2(20) - 2 = 40 - 2 = 38 degrees
5x + 2°= 5(20) + 2 = 100 + 2=102 degrees
check: 40 + 38 + 102 = 180
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dy
Find —— for an implicit function:
dx
x²y – 3x = y³ – 3
First, differentiate implicitly both sides with respect to x. Keep in mind that y is not just a variable, but it is also a function of x, so you have to use the chain rule there:

Applying the product rule for the first term at the left-hand side:
![\mathsf{\left[\dfrac{d}{dx}(x^2)\cdot y+x^2\cdot \dfrac{d}{dx}(y)\right]-3\cdot 1=3y^2\cdot \dfrac{dy}{dx}-0}\\\\\\ \mathsf{\left[2x\cdot y+x^2\cdot \dfrac{dy}{dx}\right]-3=3y^2\cdot \dfrac{dy}{dx}}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cleft%5B%5Cdfrac%7Bd%7D%7Bdx%7D%28x%5E2%29%5Ccdot%20y%2Bx%5E2%5Ccdot%20%5Cdfrac%7Bd%7D%7Bdx%7D%28y%29%5Cright%5D-3%5Ccdot%201%3D3y%5E2%5Ccdot%20%5Cdfrac%7Bdy%7D%7Bdx%7D-0%7D%5C%5C%5C%5C%5C%5C%0A%5Cmathsf%7B%5Cleft%5B2x%5Ccdot%20y%2Bx%5E2%5Ccdot%20%5Cdfrac%7Bdy%7D%7Bdx%7D%5Cright%5D-3%3D3y%5E2%5Ccdot%20%5Cdfrac%7Bdy%7D%7Bdx%7D%7D)
dy
Now, isolate —— in the equation above:
dx


Compute the derivative value at the point (– 1, 2):
x = – 1 and y = 2

I hope this helps. =)
Tags: <em>implicit function derivative implicit differentiation chain product rule differential integral calculus</em>