Answer:
10.7
Step-by-step explanation:
√114 = 10.7 <----to the nearest tenth
Answer:
Step-by-step explanation:
Maximum rate of change of a function f(x,y) is expressed as the gradient of such function at the given point. Gradient of a function is expressed as;
∇f(x,y) = ![\dfrac{\delta f}{\delta x}i + \dfrac{\delta f}{\delta y}j](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cdelta%20f%7D%7B%5Cdelta%20x%7Di%20%2B%20%20%5Cdfrac%7B%5Cdelta%20f%7D%7B%5Cdelta%20y%7Dj)
Given f(x,y)=ln(x²+y²) at the point (-2, 2)
![\dfrac{\delta f}{\delta x} = 2x * \frac{1}{x^2+y^2} \\\dfrac{\delta f}{\delta x} = \frac{2x}{x^2+y^2} \\\\\\\dfrac{\delta f}{\delta y} = 2y * \frac{1}{x^2+y^2} \\\dfrac{\delta f}{\delta y} = \frac{2y}{x^2+y^2} \\](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cdelta%20f%7D%7B%5Cdelta%20x%7D%20%3D%202x%20%2A%20%5Cfrac%7B1%7D%7Bx%5E2%2By%5E2%7D%20%5C%5C%5Cdfrac%7B%5Cdelta%20f%7D%7B%5Cdelta%20x%7D%20%3D%20%5Cfrac%7B2x%7D%7Bx%5E2%2By%5E2%7D%20%5C%5C%5C%5C%5C%5C%5Cdfrac%7B%5Cdelta%20f%7D%7B%5Cdelta%20y%7D%20%3D%202y%20%2A%20%5Cfrac%7B1%7D%7Bx%5E2%2By%5E2%7D%20%5C%5C%5Cdfrac%7B%5Cdelta%20f%7D%7B%5Cdelta%20y%7D%20%3D%20%5Cfrac%7B2y%7D%7Bx%5E2%2By%5E2%7D%20%5C%5C)
![\nabla f(x, y) = \frac{2x}{x^2+y^2}i+\frac{2y}{x^2+y^2}j\\ \\\nabla f(x, y) \ at \ the \ point \ (-2,2) \ will \ give;\\\nabla f(x, y) = \frac{2(-2)}{(-2)^2+2^2}i+\frac{2(2)}{(-2)^2+2^2}j\\ \nabla f(x, y) = \frac{-4}{8}i+\frac{4}{8}j\\\nabla f(x, y) = \frac{-1}{2}i+\frac{1}{2}j\\](https://tex.z-dn.net/?f=%5Cnabla%20f%28x%2C%20y%29%20%3D%20%5Cfrac%7B2x%7D%7Bx%5E2%2By%5E2%7Di%2B%5Cfrac%7B2y%7D%7Bx%5E2%2By%5E2%7Dj%5C%5C%20%20%5C%5C%5Cnabla%20f%28x%2C%20y%29%20%5C%20at%20%5C%20the%20%5C%20point%20%5C%20%28-2%2C2%29%20%5C%20will%20%5C%20give%3B%5C%5C%5Cnabla%20f%28x%2C%20y%29%20%3D%20%5Cfrac%7B2%28-2%29%7D%7B%28-2%29%5E2%2B2%5E2%7Di%2B%5Cfrac%7B2%282%29%7D%7B%28-2%29%5E2%2B2%5E2%7Dj%5C%5C%20%5Cnabla%20f%28x%2C%20y%29%20%3D%20%5Cfrac%7B-4%7D%7B8%7Di%2B%5Cfrac%7B4%7D%7B8%7Dj%5C%5C%5Cnabla%20f%28x%2C%20y%29%20%3D%20%5Cfrac%7B-1%7D%7B2%7Di%2B%5Cfrac%7B1%7D%7B2%7Dj%5C%5C)
<em>Hence the maximum rate of range of the function at the point (-2,2) is </em>
<em></em>
To get the direction, we willl use the formula;
![tan \theta = \frac{y}{x}\\ \theta = tan^{-1}\frac{y}{x}](https://tex.z-dn.net/?f=tan%20%5Ctheta%20%3D%20%5Cfrac%7By%7D%7Bx%7D%5C%5C%20%5Ctheta%20%3D%20tan%5E%7B-1%7D%5Cfrac%7By%7D%7Bx%7D)
From the vector gotten, x = -1/2 and y = 1/2
![\theta = tan^{-1}\frac{(1/2)}{-1/2}\\ \theta = tan^{-1}-1\\ \theta = -45^0](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20tan%5E%7B-1%7D%5Cfrac%7B%281%2F2%29%7D%7B-1%2F2%7D%5C%5C%20%5Ctheta%20%3D%20tan%5E%7B-1%7D-1%5C%5C%20%5Ctheta%20%3D%20-45%5E0)
<em>Since tan theta is negative in the second quadrant, the direction in which it occurs will be 180-45 = 135°</em>
Answer:
3:1:5
Step-by-step explanation:
Divide the values by £1.40
The answer is A) one who provides assurance of something. A guarantor is someone or something that guarantees something, hence the name guarantor. In this case, the federal govt. is guaranteeing economic security. Hope this helps:)
The probability a sample is within 2 standard deviations of the mean is about 95.45%