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3 years ago

Identify the square root of 2 as either rational or irrational, and approximate to the tenths place

Mathematics

1 answer:

Pie3 years ago

6 0

Answer: Irrational

Step-by-step explanation:

It is irrational because you cannot multiply a number by the same number to get the square root of 2.

I think the approximation is 1.4 or 1.42

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This table represents the altitude change in meters, m, as a hiker hikes down a mountain in h hours. When graphed, all of the po

Reika [66]

Answer:

Step-by-step explanation:

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3 years ago

Evaluate the integral Integral from (5 comma 2 comma 4 )to (7 comma 9 comma negative 3 )y dx plus x dy plus 3 dz by finding para

padilas [110]

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\int_{(5,2,4)}^{(7,9,-3)}y\,\mathrm dx+x\,\mathrm dy+3\,\mathrm dz$

Parameterize the line segment (call it $C$ ) by

$\vec r(t)=(1-t)(5\,\vec\imath+2\,\vec\jmath+4\,\vec k)+t(7\,\vec\imath+9\,\vec\jmath-3\,\vec k)$

$\vec r(t)=(2t+5)\,\vec\imath+(7t+2)\,\vec\jmath+(4-7t)\,\vec k$

with $0\le t\le1$ . Then

$\vec r'(t)=2\,\vec\imath+7\,\vec\jmath-7\,\vec k$

and the line integral is

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\int_0^1((7t+2)\,\vec\imath+(2t+5)\,\vec\jmath+3\,\vec k)\cdot\vec r'(t)\,\mathrm dt$

$=\displaystyle\int_0^1((2t+5)+2(7t+2)-21)\,\mathrm dt$

$=\displaystyle\int_0^1(28t+18)\,\mathrm dt=\boxed{32}$

Alternatively, if we can show that $\vec F$ is conservative, then we can apply the fundamental theorem of calculus. We need to find $f$ such that $\nabla f=\vec F$ , which requires

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

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

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

Integrating both sides of the first equation with respect to $x$ gives

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

Differentiating both sides wrt $y$ gives

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

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

Differentiating wrt $z$ gives

$\dfrac{\partial f}{\partial z}=3=\dfrac{\mathrm dh}{\mathrm dz}$

$\implies h(z)=3z+C$

So we have

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

and $\vec F$ is conservative. By the FTC, we find

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=f(7,9,-3)-f(5,2,4)=\boxed{32}$

5 0

3 years ago

How do i factor 10x-10y?

rusak2 [61]

I hope this helps you

10.x-10.y

10 (x-y)

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4 years ago

Find the surface area and round to the nearest hundredths place when necessary.

pashok25 [27]

Answer:

First lets find the area of the bottom circle:

7.2 is your radius so:

7.2^2 = 51.84 the reason why you square your radius is because thats apart of the formula when finding the are of a circle.

lets continue:

51.84 x 3.14(pi) = 162.7776

Now we need to find the area of the round surface but first we need to find the circumference of one circle and multiply it by the height.

2 x 3.14 x 7.2 = 45.216

Now lets multiply it by the height:

45.216 x 17 = 768.672

Now lets add both areas:

768.672 + 162.7776 = 931.4496 dont forget to round to the nearest hundredths place! 931.4496 rounded up = 931.45 square meters is your answer.

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3 years ago

A small bar of gold measures 4 mm by 72 mm by 2 mm. One cubic millimeter of gold weighs about 0.0005 ounces. Find the volume in

Zinaida [17]

Answer:

A small bar of gold measures 40 mm by 25 mm by 2 mm. One cubic millimeter of gold weighs about 0.0005 ounce. Find the volume in cubic millimeters and the weight in ounces of this small bar of gold.

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3 years ago