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2 years ago

In a Venn diagram, the rectangle represents the entire group. True False

Mathematics

2 answers:

prohojiy [21]2 years ago

8 0

True because the rectangle represents the universe and closed figures.

lora16 [44]2 years ago

3 0

A Venn Diagram is 2 or 3 circles combined

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2. Find the fraction which is exactly halfway between 1/7 and 4/7

Ksivusya [100]

Answer:

That would be the fraction exactly between 2/7 and 3/7

which would be 2.5 / 7 or 5 / 14

Step-by-step explanation:

4 0

3 years ago

Evaluate the integral Integral ∫ from (1,2,3 ) to (5, 7,-2 ) y dx + x dy + 4 dz by finding parametric equations for the line seg

n200080 [17]

$\vec F(x,y,z)=y\,\vec\imath+x\,\vec\jmath+3\,\vec k$

is conservative if there is a scalar function $f(x,y,z)$ such that $\nabla f=\vec F$ . This would require

$\dfrac{\partial f}{\partial x}=y$

$\dfrac{\partial f}{\partial y}=x$

$\dfrac{\partial f}{\partial z}=3$

(or perhaps the last partial derivative should be 4 to match up with the integral?)

From these equations we find

$f(x,y,z)=xy+g(y,z)$

$\dfrac{\partial f}{\partial y}=x=x+\dfrac{\partial g}{\partial y}\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)$

$f(x,y,z)=xy+h(z)$

$\dfrac{\partial f}{\partial z}=3=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=3z+C$

$f(x,y,z)=xy+3z+C$

so $\vec F$ is indeed conservative, and the gradient theorem (a.k.a. fundamental theorem of calculus for line integrals) applies. The value of the line integral depends only the endpoints:

$\displaystyle\int_{(1,2,3)}^{(5,7,-2)}y\,\mathrm dx+x\,\mathrm dy+3\,\mathrm dz=\int_{(1,2,3)}^{(5,7,-2)}\nabla f(x,y,z)\cdot\mathrm d\vec r$

$=f(5,7,-2)-f(1,2,3)=\boxed{18}$

8 0

3 years ago

Line segment EF has a length of 5 units. it is translated 5 units to the right on a coordinate plane to obtain line segment E'F.

Phantasy [73]

<span>In Geometry, a translation is a function where an object is moved a certain distance. This means that the location of the line is changed, but it is not changed in any other way. This means, that if the line was originally 5 units, it will still be 5 units long.</span>

4 0

3 years ago

Given S'T'U'V' is a dilation of STUV, find the scale factor of dilation.

Lyrx [107]

Step-by-step explanation:

Scale factor of STUV to S'T'U'V

= Length of T'U' / Length of TU

= 6/12 = 0.5.

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2 years ago

Consumption of alcoholic beverages by young women of drinking age has been increasing in the United Kingdom, the United States,

horrorfan [7]

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3 years ago

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