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icang [17]
3 years ago
15

Jacinta, an internet website designer, works a 38 hour week and earns $3115.35 every fortnight. Calculate her earnings:

Mathematics
2 answers:
sveticcg [70]3 years ago
6 0

Step-by-step explanation:

total working duration = 2 weeks

Working duration in hours = 38× 2= 76 hours

a) per year

24*3115.35 = $74768

b) 3115.35/2

$1557.675

c)

3115.35/76

$40.99

Lubov Fominskaja [6]3 years ago
4 0

Answer:

  • a) $80999.10
  • b) $1557.68
  • c) $40.99

Step-by-step explanation:

<u>Given</u>

  • Jacinta earns $3115.35 every 2 weeks, working 38 hours a week

<u>Earnings calculated as:</u>

a) per year

Number of weeks in a year = 52

  • $3115.35*52/2 = $80999.10

b) per week

  • 1/2*$3115.35 = $1557.68

c) per hour

  • $3115.35/(38*2) = $40.99
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Answer:97/125

Step-by-step explanation:

“As illustrated in the Venn diagram,

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This implies that,

n(U)=125

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This implies that,

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This implies that,

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This implies that,

n(a)=59-(6+11+19)=59-36=23

b=[Those who use the pool only]

This implies that,

n(b)=70-(6+19+24)=70-49=21

c=[Those who use the track only]

This implies that,

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Find the solution of the problem (1 3. (2 cos x - y sin x)dx + (cos x + sin y)dy=0.
lakkis [162]

Answer:

2*sin(x)+y*cos(x)-cos(y)=C_1

Step-by-step explanation:

Let:

P(x,y)=2*cos(x)-y*sin(x)

Q(x,y)=cos(x)+sin(y)

This is an exact differential equation because:

\frac{\partial P(x,y)}{\partial y} =-sin(x)

\frac{\partial Q(x,y)}{\partial x}=-sin(x)

With this in mind let's define f(x,y) such that:

\frac{\partial f(x,y)}{\partial x}=P(x,y)

and

\frac{\partial f(x,y)}{\partial y}=Q(x,y)

So, the solution will be given by f(x,y)=C1, C1=arbitrary constant

Now, integrate \frac{\partial f(x,y)}{\partial x} with respect to x in order to find f(x,y)

f(x,y)=\int\  2*cos(x)-y*sin(x)\, dx =2*sin(x)+y*cos(x)+g(y)

where g(y) is an arbitrary function of y

Let's differentiate f(x,y) with respect to y in order to find g(y):

\frac{\partial f(x,y)}{\partial y}=\frac{\partial }{\partial y} (2*sin(x)+y*cos(x)+g(y))=cos(x)+\frac{dg(y)}{dy}

Now, let's replace the previous result into \frac{\partial f(x,y)}{\partial y}=Q(x,y) :

cos(x)+\frac{dg(y)}{dy}=cos(x)+sin(y)

Solving for \frac{dg(y)}{dy}

\frac{dg(y)}{dy}=sin(y)

Integrating both sides with respect to y:

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Replacing this result into f(x,y)

f(x,y)=2*sin(x)+y*cos(x)-cos(y)

Finally the solution is f(x,y)=C1 :

2*sin(x)+y*cos(x)-cos(y)=C_1

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