Mathematics, 14.07.2019 06:20 bignutz29

F(x, y) = x2 i + y2 j c is the arc of the parabola y = 2x2 from (1, 2) to (2, 8) (a) find a function f such that f = ∇f.

Answers: 1

Show answers

Answers

Answer from: lilly9240

$\mathbf F(x,y)=x^2\,\mathbf i+y^2\,\mathbf j$

If a scalar function f(x,y)

exists for which $\nabla f(x,y)=\mathbf F(x,y)$ , then we'd have

$\dfrac{\partial f}{\partial x}=x^2\implies f(x,y)=\dfrac{x^3}3+g(y)$
$\implies\dfrac{\partial f}{\partial y}=y^2=g'(y)\implies g(y)=\dfrac{y^3}3+C$

so the scalar function would be given by

$f(x,y)=\dfrac{x^3+y^3}3+C$

where

is an arbitrary constant.

Presumably, this question is being asked in the context of the line integral of $\mathbf F(x,y)$ along the given contour

. Since $\mathbf F(x,y)$ is conservative - and consequently a scalar potential function f(x,y)

exists - we can simply use the gradient theorem to evaluate the line integral. We would get

$\displaystyle\int_C\mathbf F\cdot\mathrm d\mathbf r=f(2,8)-f(1,2)=\dfrac{511}3$

(and we get the same answer by parameterizing

and computing the integral as we usually would)

Answer from: Quest

"it's not the heat, it's the humidity". that's a partly valid phrase you may have heard in the summer, but it's actually both. the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature. this has important considerations for the human body's comfort. when the body gets too hot, it begins to perspire or sweat to cool itself off. if the perspiration is not able to evaporate, the body cannot regulate its temperature. evaporation is a cooling process. when perspiration is evaporated off the body, it effectively reduces the body's temperature. when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases. in other words, the human body feels warmer in humid conditions. the opposite is true when the relative humidity decreases because the rate of perspiration increases. the body actually feels cooler in arid conditions. there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation:

75% of the temperatures are below what value? how do you know? 75% of the temperatures are above w

Answer from: Quest

shift 4 units up, and 1 unit left.

it will translate f(x) = 3^x to g(x) = 3^(x+1) + 4

Another question on Mathematics

Mathematics, 20.06.2019 18:04

George is 187 cm tall. his son, ralph, is 142 cm tall. who casts the longer shadow. george when the sun is 65° above the horizon, or ralph when the sun is 56° above the horizon? how much longer? (nearest centimeter)

Answers: 2

Answer

Mathematics, 21.06.2019 16:00

What is the length of the unknown leg in the right triangle ?

Answers: 2

Answer

Mathematics, 21.06.2019 16:20

The lengths of nails produced in a factory are normally distributed with a mean of 4.91 centimeters and a standard deviation of 0.05 centimeters. find the two lengths that separate the top 4% and the bottom 4%. these lengths could serve as limits used to identify which nails should be rejected. round your answer to the nearest hundredth, if necessary.

Answers: 3

Answer

Mathematics, 21.06.2019 17:30

How do you find principle and simple interest

Answers: 1

Answer

You know the right answer?

F(x, y) = x2 i + y2 j c is the arc of the parabola y = 2x2 from (1, 2) to (2, 8) (a) find a function...

Questions