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3 years ago

1. Find the area. 7in 5in 3in

Mathematics

1 answer:

ololo11 [35]3 years ago

6 0

First we need to find the length of the missing triangle side which we can do with Pythagorean theorem
A2+B2=C2
5^2+3^2= x^2
25+9=x^2
34=x^2
You square booth sides and end up with a decimal of 5.831 rounded for the missing side.
Area for a rectangle is length times width so we multiply 7x5.831=40.817
Area of a triangle is the height times the base divided by 2 so 5.831x3= 17.493
Then you add those to together for the total area of the shape 40.817+17.493=58.31
58.31 is your approximate answer.

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Dimensions of a Box A large plywood box has a volume of . Its length is ft greater than its height, and its width is ft less tha

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Few things are missing, they are volume of the box is 180 feet cube. Length is 9 feet greater than its height, and weight is 4 feet less than its height.

Step-by-step explanation:

Given, the volume of the box, V = 180 feet cube

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And width is, b = ( x-4) feet

so volume of the box is

V = l x b x h

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Factorizing we get

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Therefore,

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3 years ago

8. Terry, a plumber, worked 9 months out of the year. What percent of the year

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3 years ago

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For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential f

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The key idea is that, if a vector field is conservative, then it has curl 0. Equivalently, if the curl is not 0, then the field is not conservative. But if we find that the curl is 0, that on its own doesn't mean the field is conservative.

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We want to find $f$ such that $\nabla f=\vec F$ . This means

$\dfrac{\partial f}{\partial x}=-6x+5y\implies f(x,y)=-3x^2+5xy+g(y)$

$\dfrac{\partial f}{\partial y}=5x+10y=5x+\dfrac{\mathrm dg}{\mathrm dy}\implies\dfrac{\mathrm dg}{\mathrm dy}=10y\implies g(y)=5y^2+C$

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so $\vec F$ is conservative.

$\mathrm{curl}\vec F=\left(\dfrac{\partial(-2y)}{\partial z}-\dfrac{\partial(1)}{\partial y}\right)\vec\imath+\left(\dfrac{\partial(-3x)}{\partial z}-\dfrac{\partial(1)}{\partial z}\right)\vec\jmath+\left(\dfrac{\partial(-2y)}{\partial x}-\dfrac{\partial(-3x)}{\partial y}\right)\vec k=\vec0$

Then

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$\implies\boxed{f(x,y,z)=-\dfrac32x^2-y^2+z+C}$

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$\implies\boxed{f(x,y,z)=-x^3+\dfrac53y^3+\dfrac53z^3+C}$

so $\vec F$ is conservative.

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4 years ago