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2 years ago

Simplify 2x + 2y - x + 4 - 1 + 3x + 2y + 7

Mathematics

2 answers:

xxTIMURxx [149]2 years ago

8 0

4x + 4y + 10..........

Degger [83]2 years ago

4 0

Add all the like terms together
4x+4y+10

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Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = yzi + 4xzj + ex

natima [27]

Answer:

The result of the integral is 81π

Step-by-step explanation:

We can use Stoke's Theorem to evaluate the given integral, thus we can write first the theorem:

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S curl \vec F \cdot d\vec S$

Finding the curl of F.

Given $F(x,y,z) = < yz, 4xz, e^{xy} >$ we have:

$curl \vec F =\left|\begin{array}{ccc} \hat i &\hat j&\hat k\\ \cfrac{\partial}{\partial x}& \cfrac{\partial}{\partial y}&\cfrac{\partial}{\partial z}\\yz&4xz&e^{xy}\end{array}\right|$

Working with the determinant we get

$curl \vec F = \left( \cfrac{\partial}{\partial y}e^{xy}-\cfrac{\partial}{\partial z}4xz\right) \hat i -\left(\cfrac{\partial}{\partial x}e^{xy}-\cfrac{\partial}{\partial z}yz \right) \hat j + \left(\cfrac{\partial}{\partial x} 4xz-\cfrac{\partial}{\partial y}yz \right) \hat k$

Working with the partial derivatives

$curl \vec F = \left(xe^{xy}-4x\right) \hat i -\left(ye^{xy}-y\right) \hat j + \left(4z-z\right) \hat k\\curl \vec F = \left(xe^{xy}-4x\right) \hat i -\left(ye^{xy}-y\right) \hat j + \left(3z\right) \hat k$

Integrating using Stokes' Theorem

Now that we have the curl we can proceed integrating

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S curl \vec F \cdot d\vec S$

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S curl \vec F \cdot \hat n dS$

where the normal to the circle is just $\hat n= \hat k$ since the normal is perpendicular to it, so we get

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S \left(\left(xe^{xy}-4x\right) \hat i -\left(ye^{xy}-y\right) \hat j + \left(3z\right) \hat k\right) \cdot \hat k dS$

Only the z-component will not be 0 after that dot product we get

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S 3z dS$

Since the circle is at z = 3 we can just write

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S 3(3) dS\\\displaystyle \int\limits_C \vec F \cdot d\vec r = 9\int \int_S dS$

Thus the integral represents the area of a circle, the given circle $x^2+y^2 = 9$ has a radius r = 3, so its area is $A = \pi r^2 = 9\pi$ , so we get

$\displaystyle \int\limits_C \vec F \cdot d\vec r = 9(9\pi)\\\displaystyle \int\limits_C \vec F \cdot d\vec r = 81 \pi$

Thus the result of the integral is 81π

5 0

3 years ago

An article claims that 12% of trees are infested by a bark beetle. A random sample of 1,000 trees were tested for traces of the

galben [10]

Answer:

0.68

Step-by-step explanation:

The formula for z test is given above as:

z = p' - p/√(pq/n)

p' = sample proportion

= Number of infested samples(trees)/ Number of samples

p' = 127/1000 = 0.127

p = 12% = 0.12

q= 1 - 0.12 = 0.88

n = number of samples = 1000

z = 0.127 - 0.12/√(0.88 × 0.12/1000)

z = 0.007/√0.0001056

z = 0.007 /0.0102761861

z = 0.6811865737

Therefore, the z test statistic is approximately ≈ 0.68

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3 years ago

Who want crown things

ivolga24 [154]

Answer:

meeee plzzzzzzz even thow i have no idea whta that ios

Step-by-step explanation:

3 0

2 years ago

A study examines the relationship between being a registered nurse (yes/no) and passing a cultural competency exam (yes/no) amon

Leni [432]

Answer:

The appropriate test to determine if there is an association between being a registered nurse and passing a cultural competency exam among a group of 987 randomly selected hospital employees is a:

Chi-square Test.

Step-by-step explanation:

The Chi-Square Test uses either a diagram (like a scatter plot) or a hypothesis test to show the existence of an association between two variables or statistically demonstrate that a relationship exists between the two variables. Using the computed t-score, the significant association between two categorical variables can be measured and established.

5 0

3 years ago

What is 160 bananas; 20% decrease??

inessss [21]

Answer:

128

Step-by-step explanation:

160 x .20 = 32

160 - 32 = 128

6 0

3 years ago