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3 years ago

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Let F (x; y) = xy2i + x2y j. Evaluate ∫F.ds (from c to [infinity]) where C is the upper half of the circle of radius 1 centered

at the origin orientated counterclockwise.

1 answer:

77julia77 [94]3 years ago

4 0

Answer:

The integral $\int F \bullets ds$ is 0.

Step-by-step explanation:

A parameterization of curve C can be:

X (t) = cost 0 <= t <= pi

Y (t) = sint 0 <= t <= pi

r (t) = costi + sintj

r '(t) = -sinti + costj

$Fds = [-costsin^3t + sintcos^3t] dt$

The integral $\int F \bullets ds$ is given by:

$\int _0^{\pi }\left[-costsin^3t + sintcos^3t dt\right]dt$

$= \int _0^{\pi }-sin ^3tcostdt + \int _0^{\pi }sintcos^3tdt = 0$

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1. Is the square root of 2 between 1.3 and 1.4? How do you know?

VikaD [51]

Answer:

Step-by-step explanation:

1st . 1.3^2= 1.69

1.4^2= 1.96

It's not bettween 1.3 & 1.4

2. 1.4^2=1.96

1.5^2= 2.25

it's betteen 1.4 & 1.5

3 . 1.4 & 1.5 so it's eqaul 1.4

3 0

3 years ago

Read 2 more answers

Will mark brainliest! Questions are in the picture!

alexdok [17]

Answer:

52.9 inches .

Step-by-step explanation:

Given that the triangular indentation has an area of 100 in.² and the base and height of this traingle are represented by expressions 3x and x+3 respectively . We need to find out the <u>perimeter </u>to the nearest tenth.

As we know that the area of triangle is ,

$\rm\longrightarrow Area_{\triangle}=\dfrac{1}{2}(base)(height)$

Substituting the respective values,

$\rm\longrightarrow 100\ =\dfrac{1}{2}(x+3)(3x)\\\\\rm\longrightarrow 2(100) = 3x(x+3)\\\\\rm\longrightarrow200 = 3x^2+9x\\\\\rm\longrightarrow 3x^2+9x-200=0$

On using the <u>Quadratic</u><u> formula</u> , we have;

$\rm\longrightarrow x =\dfrac{-9\pm\sqrt{9^2-4(3)(-200)}}{2(3)} \\\\\rm\longrightarrow x =\dfrac{-9\pm \sqrt{81+1200}}{6}\\\\\rm\longrightarrow x =\dfrac{-9\pm \sqrt{1281}}{6}$

On simplifying above , we will get ,

$\rm\longrightarrow x = 6.802,-9.802$

Since sides can't be negative, therefore,

$\rm\longrightarrow\underline{\underline{ x =6.802}}$

Therefore ,

$\rm\longrightarrow Base = 3x =3(6.802)in = 20.406\ in\\$
$\rm\longrightarrow Height = x +3=6.802+3=9.802\ in$

Next let's find out the <u>hypotenuse </u>using Pythagoras theorem, as ;

$\rm\longrightarrow h=\sqrt{ b^2+p^2}\\$

$\rm\longrightarrow h =\sqrt{ (20.406)^2+(9.802)^2}\\$

$\rm\longrightarrow h =\sqrt{416.40+96.07}\\$

$\rm\longrightarrow h = 22.63\ in$

Now we may find perimeter as ,

$\rm\longrightarrow P = p + b + h \\$

$\rm\longrightarrow P = (22.63 + 9.802 + 20.406)in.$

$\\\rm\longrightarrow P = 52.89 \ in.\\$

$\rm\longrightarrow \underline{\underline{ Perimeter = 52.9\ in .}}$

8 0

2 years ago

g A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is cha

leva [86]

Answer:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

$z=\frac{0.410-0.35}{\sqrt{0.385(1-0.385)(\frac{1}{1000}+\frac{1}{700})}}=2.502$

$p_v =2*P(Z>2.502)= 0.0123$

Comparing the p value with the significance level assumed $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportion analyzed is significantly different between the two groups at 5% of significance.

Step-by-step explanation:

Data given and notation

$X_{1}=410$ represent the number of people indicating that their financial security was more than fair for the recent year

$X_{2}=245$ represent the number of people indicating that their financial security was more than fair for the year before

$n_{1}=1000$ sample 1 selected

$n_{2}=700$ sample 2 selected

$p_{1}=\frac{410}{1000}=0.410$ represent the proportion estimated of indicating that their financial security was more than fair this year

$p_{2}=\frac{245}{700}=0.35$ represent the proportion estimated of indicating that their financial security was more than fair the year before

$\hat p$ represent the pooled estimate of p

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

$\alpha$ significance level given

Concepts and formulas to use

We need to conduct a hypothesis in order to check if is there is a difference between the two proportions, the system of hypothesis would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{410+245}{1000+700}=0.385$

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.410-0.35}{\sqrt{0.385(1-0.385)(\frac{1}{1000}+\frac{1}{700})}}=2.502$

Statistical decision

Since is a two sided test the p value would be:

$p_v =2*P(Z>2.502)= 0.0123$

Comparing the p value with the significance level assumed $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportion analyzed is significantly different between the two groups at 5% of significance.

7 0

3 years ago

Blizzard [7]

Answer: h = 5

Step-by-step explanation:

Easy. 5 + 9 = 14

7 0

2 years ago

8+ _=11<br> what is the answer

crimeas [40]

Answer:

The answer is 3

Step-by-step explanation:

B/c 8+2=10 just add one more and 2+1=3

5 0

3 years ago