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4 years ago

Pls help im stuck on this

Mathematics

1 answer:

Law Incorporation [45]4 years ago

7 0

<h3>Answer: Choice C</h3>

The -2/5 means we go to the left 2/5 of a full unit. So we take 2 small little steps (going over 2 little tickmarks), then we move 4 small steps to the right due to the +4/5 portion. Ultimately, we end up at 2/5 as the answer

So -2/5 + 4/5 = 2/5

This can be thought of as -2+4 = 2, then you just stick 5 in the denominator for each term.

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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

I really need help!!

Arte-miy333 [17]

TJ was 3 eight years ago

3 0

3 years ago

Read 2 more answers

In ΔEFG, the measure of ∠G=90°, the measure of ∠E=40°, and EF = 75 feet. Find the length of GE to the nearest tenth of a foot

juin [17]

Answer:

19.4 feet

Step-by-step explanation:

Since the triangle has a right angle( as one of the angles in it is equal to 90°), we may find the length of the unknown side using the trigonometric notations SOH CAH TOA where

SOA stands for

Sin Ф = opposite side/hypotenuses side

Cosine Ф = adjacent side/hypotenuses side

Tangent Ф = opposite side/adjacent side

Given that the measure of ∠G=90° and ∠E=40°

EF is the hypotenuse side

FG is the opposite side and

GE is the adjacent side. As such if EF = 75 feet

Cos 75 = GE/75

GE = 75 Cos 75°

= 19.41 feet

≈ 19.4 feet in the nearest tenth of a foot

5 0

3 years ago

Read 2 more answers

Hello I need the answer fast pls The tennis courts are 3 blocks west and 2 blocks south of Miguel’s house. The bike path is 5 bl

TiliK225 [7]

Answer:

Step-by-step explanation:

If its correct please give brainliest

8 0

4 years ago

A wireless phone plan cost Eric $35 for a month of service during which he sent 450 text messages. If he was charged an fixed fe

Lelechka [254]

Answer:

$.05 per message

Step-by-step explanation:

450m + 12.5 = 35

450m = 35-12.5

450m = 22.5 divide both sides by 450

m=22.5/450

m=.05

3 0

3 years ago