In 1 through 6 estimate sum or difference

Mathematics

1 answer:

evablogger [386]3 years ago

6 0

I could help if there was a pic or something

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Consider f and c below. f(x, y) = x2y3i + x3y2j,

kirza4 [7]

If there is a scalar function $f(x,y)$ such that $\mathbf f(x,y)=\nabla f(x,y)$ , then it would satisfy

$\dfrac{\partial f}{\partial x}=x^2y^3$
$\dfrac{\partial f}{\partial y}=x^3y^2$

From the first PDE, we have

$f(x,y)=\dfrac13x^3y^3+g(y)$

Take the derivative with respect to $y$ to get

$\dfrac{\partial f}{\partial y}=x^3y^2+\dfrac{\mathrm dg}{\mathrm dy}=x^3y^2$
$\implies\dfrac{\mathrm dg}{\mathrm dy}=0\implies g(y)=C$

So,

$f(x,y)=\dfrac13x^3y^3+C$

By the fundamental theorem of calculus,

$\displaystyle\int_{\mathcal C}\mathbf f(x,y)\cdot\mathrm d\mathbf r=\int_{\mathcal C}\nabla f(x,y)\cdot\mathrm d\mathbf r=f(\mathbf r(1))-f(\mathbf r(0))$
$=f(-1,3)-f(0,0)=-9$

4 0

4 years ago

You are selling concessions at a local swim meet. Hot dogs are being sold for $1.00 and soda is being sold for $0.50. At the end

Fantom [35]

Answer:

Step-by-step explanation:

Let's set up an equation in standard form.

x + 0.5y = 150

0.5y = -x + 150

y = -2x + 300

The y-intercept is 300. This means that when 0 hot dogs were sold, 300 sodas were sold.

8 0

3 years ago

The orthocenter of an obtuse triangle always lies __________.

aev [14]

The intersection of three altitudes of a triangle is called the orthocenter, while altitude is the line drawn from one of the vertex of a triangle and extends it in such a way that it cuts perpendicularly the opposite side of the same triangle.

For obtuse triangle, the orthocenter always lies outside of the triangle. So option “C” is correct.

An image of obtuse triangle along with orthocenter is attached herewith.