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3 years ago

Evaluate the double intergal between the two cirlces

1 answer:

5 0

3down votefavoriteFind the area between the circles x2+y2=4x2+y2=4 and x2+y2=6xx2+y2=6x using polar coordinates.I have found that the equation of the first circle, call it C1C1, is r=2r=2 on the other hand, for C2C2, I get that its equation is r=6cosθr=6cosθ. Then, to find the bounds of integration, I have found that their angle of intersection should be θ=arccos(1/3)θ=arccos⁡(1/3) and θ=−arccos(1/3)θ=−arccos⁡(1/3). Then, to set up the double integral:A=∫arccos(1/3)−arccos(1/3)∫26cosθrdrdθA=∫−arccos⁡(1/3)arccos⁡(1/3)∫6cos⁡θ2rdrdθHowever, when evaluating this integral with the calculator, I get a negative value. What would be the problem in this case? Thanks in advance for your help.

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Laura takes very good care of her vehicles. She owns a blue van and a red truck. Although she bought them both new, she has owne

MrRissso [65]

The age of the van owned = 12 years

The age of the truck owned = 29 years

Step-by-step explanation:

Here, the given question is INCOMPLETE.

Laura takes very good care of her vehicles. She owns a blue van and a red truck. Although she bought them both new, she has owned the truck for 17 years longer than she has owned the van. If the sum of the ages of the vehicles is 41 years, how old is the van and how old is the truck?

Let us assume the number of years Laura has owned the van = S years

So, according to the question:

The number of years she has owned truck = S + 17 years

Now, Sum of the age of ( Truck + Van) = 41 years

⇒ (S + 17 years) + (S years) = 41 years

or, 2 S + 17 = 41

or, 2 S = 4 1 -1 7 = 24

or, S = 24/2 = 12 years

or, S = 12 years

Hence the age of the van owned = 12 years

The age of the truck owned = S + 17 = 12 + 17 = 29 years

6 0

3 years ago

Need help with number 10

Paraphin [41]

Answer:

Step-by-step explanation:

the answer is d, tan = (cateto opuesto / cateto adyascente)

8 0

2 years ago

Read 2 more answers

The function in Exercise represents the rate of flow of money in dollars per year. Assume a 10-year period at 8% compounded cont

Kryger [21]

Answer:

a) $P= $56,972.5$

b) $A=$1,26,792.3$

Step-by-step explanation:

Given Data:

Interest rate= $r= 0.08$ per year

No. of years= $t=10$

Rate of continuous money flow is given by the function

$f(t)=2000$

a) to find the present value of money

$P=\int\limits^n_0 {f(t)e^{-rt} } \, dt$

Put f(t)=2000 and n=10 years and r=0.08

$P=\int\limits^n_0 {2000e^{-0.08t} } \, dt$

Now integrate

$P= {2000(\frac{e^{-0.08t}}{-0.08} )$

$P= -\frac{2000}{0.08} (e^{-0.08*10}-e^{-0.08*0})$

$P= -\frac{2000}{0.08} (e^{-0.8}-e^{0})$

$P= -\frac{2000}{0.08} (0.4493-2.7282)$

$P= -\frac{2000}{0.08} (-2.2789)$

$P= -25000(-2.2789)$

$P= $56972.5$

(b) to find the accumulated amount of money at t=10

$A=P(e^{rt} )$

Where P is the present worth already calculated in part a

$A=56972.5(e^{0.08*10} )$

$A=56972.5(e^{0.8} )$

$A=56972.5(2.2255 )$

$A=$1,26,792.3$

5 0

3 years ago

A triangle has sides which are consecutive odd integers and an

wolverine [178]

Answer:

Perimeter = 15

Step-by-step explanation:

We are told that the length of each of the 3 sides of the triangle are consecutive odd integers.

Thus means that we can write the 3 terms as;

(x - 2), x, (x + 2)

Thus, perimeter is;

P = (x - 2) + x + (x + 2)

P = 3x

If an angle is 120°, it means that the corresponding side that is directly opposite the angle is the largest side of the triangle.

Thus, this side is (x + 2)

Using cosine rule, we have;

(x + 2)² = x² + (x - 2)² - 2(x(x - 2))cos 120

Expanding, we have;

x² + 4x + 4 = x² + x² - 4x + 4 - (2x² + 4x)(-½)

This reduces to;

4x = x² - 4x + x² - 2x

2x² = 10x

2x = 10

x = 10/2

x = 5

Thus, other sides are;

(x - 2) = 5 - 2 = 3

And (x + 2) = 5 + 2 = 7

So,perimeter is;

P = 3x = 3 × 5 = 15

8 0

2 years ago

Plz help me I am freaking out

DanielleElmas [232]

Answer:

Wanchen has the weaker flavor, no need to freak out.

Step-by-step explanation:

2/3 water for 1/6 lime juice so more water and less lime juice compared to 1/4 water for 1/5 cup of lime juice

8 0

3 years ago