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Stolb23 [73]
4 years ago
8

Jessica has some money already saved to buy a laptop that cost $1300. She calculates she will reach her goal of saving enough mo

ney to buy the laptop in 5 months if she saves $120 a month.
If Jessica was to save $150 a month instead of $120, how many fewer month/s would she be able to save the money for the laptop?
Mathematics
1 answer:
Korvikt [17]4 years ago
4 0

Answer:

one less month

Step-by-step explanation:

120 * 5 =600, she needs 600 to get to her goal

150 * 4 =600

hope this helps!

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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
Larisa earns $7 per hour.she worked 40 hours at the regular rate, 3 hours at time and half, and 6 hours at double time.
VARVARA [1.3K]

Answer:

$6.07/hr. if I understand the question properly.  See below.

Step-by-step explanation:

I don't see the question, but will assume we want to find Larisa's base pay.  The $7/hr given is the average for the work sequence noted in the problem.  If this is incorrect, ignore the answer.

==================================

Let x be Larisa's base salary.  We are told, I think, that in one stretch of time Larisa earned an average of $7/hour.  That was composed of:

<u>Hours</u>  <u>Rate($/hr)</u>

  40           x

    3        1.5x

<u>     6    </u>     2x

  49

Her total income over this period would be:

40x +3(1.5x) + 6(2x)  [The hours worked times the pay rate for each period]

Her average income per hour would be:

(40x +3(1.5x) + 6(2x))/49

which we are told is $7/hr.

(40x +3(1.5x) + 6(2x))/49 = 7

40x + 4.5x + 12x = 343

56.5x = 343

x = $6.07/hr

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2 years ago
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Answer:

https://forms.gle/VqfekaGgk8cfJhPW9

Step-by-step explanation:

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A cable that weighs 8 lb/ft is used to lift 650 lb of coal up a mine shaft 450 ft deep. Find the work done. Show how to approxim
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Answer:

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Step-by-step explanation:

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Answer:

C. 3/5

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