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BartSMP [9]
3 years ago
12

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:

d

Step-by-step explanation:

6 0
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)
6 0
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.

6 0
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.

3 0
3 years ago
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