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likoan [24]
3 years ago
14

if you have a rectangle with a length of 0.5 x + 10 feet and a width of 6 feet how could you find the area written in its simple

st form
Mathematics
1 answer:
Greeley [361]3 years ago
3 0
<h2>Greetings!</h2>

Answer:

x + 20 = area

Step-by-step explanation:

You need to recall the equation for a rectangle:

Width x Length = Area

So simply plug the values into this:

(0.5x+10) * 6

(0.5x * 6) + (10 * 6)

= 3x + 60

Simplified down by dividing by three:

\frac{3x}{3} + \frac{60}{3} = area

<h3>x + 20 = area</h3>
<h2>Hope this helps!</h2>
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\bf F(G(x,y))\cdot(\displaystyle\frac{\partial G}{\partial x}\times\displaystyle\frac{\partial G}{\partial y})=(xy,3y-x^2y-y^3,3x-x^3-xy^2)\cdot(2x,2y,1)=\\\\=2x^2y+6y^2-2x^2y^2-2y^4+3x-x^3-xy^2

we just have then to compute a double integral of a polynomial on the unit square 0≤ x≤1 and  0≤ y≤1

\bf \displaystyle\int_{0}^{1}\displaystyle\int_{0}^{1}(2x^2y+6y^2-2x^2y^2-2y^4+3x-x^3-xy^2)dxdy=\\\\=2\displaystyle\int_{0}^{1}x^2dx\displaystyle\int_{0}^{1}ydy+6\displaystyle\int_{0}^{1}dx\displaystyle\int_{0}^{1}y^2dy-2\displaystyle\int_{0}^{1}x^2dx\displaystyle\int_{0}^{1}y^2dy-2\displaystyle\int_{0}^{1}dx\displaystyle\int_{0}^{1}y^4dy+\\\\+3\displaystyle\int_{0}^{1}xdx\displaystyle\int_{0}^{1}dy-\displaystyle\int_{0}^{1}x^3dx\displaystyle\int_{0}^{1}dy-\displaystyle\int_{0}^{1}xdx\displaystyle\int_{0}^{1}y^2dy

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