Taking
and differentiating both sides with respect to
yields
![\dfrac{\mathrm d}{\mathrm dx}\bigg[3x^2+y^2\bigg]=\dfrac{\mathrm d}{\mathrm dx}\bigg[7\bigg]\implies 6x+2y\dfrac{\mathrm dy}{\mathrm dx}=0](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5B3x%5E2%2By%5E2%5Cbigg%5D%3D%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5B7%5Cbigg%5D%5Cimplies%206x%2B2y%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%3D0)
Solving for the first derivative, we have
Differentiating again gives
![\dfrac{\mathrm d}{\mathrm dx}\bigg[6x+2y\dfrac{\mathrm dy}{\mathrm dx}\bigg]=\dfrac{\mathrm d}{\mathrm dx}\bigg[0\bigg]\implies 6+2\left(\dfrac{\mathrm dy}{\mathrm dx}\right)^2+2y\dfrac{\mathrm d^2y}{\mathrm dx^2}=0](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5B6x%2B2y%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5D%3D%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5B0%5Cbigg%5D%5Cimplies%206%2B2%5Cleft%28%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%5Cright%29%5E2%2B2y%5Cdfrac%7B%5Cmathrm%20d%5E2y%7D%7B%5Cmathrm%20dx%5E2%7D%3D0)
Solving for the second derivative, we have
Now, when
and
, we have
I think the perimeter is at least 6m
- About 127.3(square root of 16,200, or 90√2) Look at this problem like a right triangle. Each leg is 90 feet, so the hypotenuse is the square root of 90^2 + 90^2
- About 52.3(square root of 2735.64) Another right triangle problem! Once again, with Pythagorean theorem (a^2 + b^2 = c^2) You can deduce that 60^2 = 29.4^2 + the width of the TV^2.
- About 11.6(Square root of 134.75)Another right triangle problem, you can deduce that 9.5^2 + The pool length^2 = 15^2
Hope it helps <3
(If it does, please give brainliest, only need one more for rank up :) )
I have taken that test (although I don't see you're statements)
I believe the statements to choose from are:
A.) The slope of the line is −10.
B.) The slope of the line is 3.
C.) One point on the line is (3, 6).
D.) One point on the line is (3,−6)
<u>The answers are:</u>
A.) The slope of the line is -10
D.) One point on the line is (3,-6)
<u>Explanation: </u>
The given equation of line is (1). The point slope form of a line is (2) Where m is the slope of line and (x₁,y₁) are points. On comparing (1) and (2) we get The slope of given line is -10 and the line passing through the points (3,-6).
