2x+2y = 5 3x + 3y = 7 How many solutions does the system of equations above have?

If c is the curve given by \mathbf{r} \left( t \right = \left( 1 5 \sin t \right \mathbf{i} \left( 1 3 \sin^{2} t \right \mathbf

jonny [76]

With the curve $C$ parameterized by

$C:\mathbf r(t)=\underbrace{15\sin t}_{x(t)}\,\mathbf i+\underbrace{13\sin^2t}_{y(t)}\,\mathbf j+\underbrace{12\sin^3t}_{z(t)}\,\mathbf k$

with $0\le t\le\dfrac\pi2$ , and given the vector field

$\mathbf f(x,y,z)=x\,\mathbf i+y\,\mathbf j+z\,\mathbf k$

the work done by $\mathbf f$ on a particle moving on along $C$ is given by the line integral

$\displaystyle\int_C\mathbf f\cdot\mathrm d\mathbf r=\int\limits_{t=0}^{t=\pi/2}\mathbf f(x(t),y(t),z(t))\cdot\frac{\mathrm d\mathbf r(t)}{\mathrm dt}\,\mathrm dt$

where

$\mathrm d\mathbf r=(15\cos t\,\mathbf i+26\sin t\cos t\,\mathbf j+36\sin^2t\cos t\,\mathbf k)\,\mathrm dt$

The integral is then

$\displaystyle\int_0^{\pi/2}(15\sin t\,\mathbf i+13\sin^2t\,\mathbf j+12\sin^3t\,\mathbf k)\cdot(15\cos t\,\mathbf i+13\sin2t\,\mathbf j+18\sin t\sin2t\,\mathbf k)\,\mathrm dt$
$=\displaystyle\int_0^{\pi/2}(432\sin^5t\cos t+338\sin^3t\cos t+225\sin t\cos t$
$=269$

6 0

3 years ago

(08.01 MC)Below are the data collected from two random samples of 500 American adults on the number of hours they spend doing le

Mazyrski [523]

Answer:

Dan is correct

Step-by-step explanation:

From the question, we have:

$Hours:1\ 2\ 3\ 4\ 5$

Required

The average

The average hour is calculated using:

$\bar x = \frac{\sum x}{n}$

So, we have:

$\bar x = \frac{1+2+3+4+5}{5}$

$\bar x = \frac{15}{5}$

$\bar x = 3$

Dan calculated the mean as 3; while Bret calculated the mean as 4.

Hence, we can conclude that Dan s correct

4 0

2 years ago

Dans un repère du plan, on donne les points (−2 ; 3), (6 ; 2) (−1 ; 0).

kondor19780726 [428]

Answer:

faut-il faire les ponits avec le pallergrom de (−2 ; 3), (6 ; 2) (−1 ; 0) ?

Step-by-step explanation:

3 0

2 years ago

An art dealer is trying to determine whether the age of a painting plays a significant role in its price at auction. She collect

klasskru [66]

Answer:

-0.20

Step-by-step explanation:

Given the data:

Age at auction (x) ____price sold (y)

391

51

32

84

47

104

88

43

470

51

Y:

76.9

95.4

86.3

49.3

80

57

47.8

80

70

86.9

General formula for a simple linear regression :

y = ab + c

Where ;

y = predicted variable ; a = slope / gradient

b = predictor / independent variable ; c = intercept

From the result obtained from the calculator :

y = -0.01246X + 74.65552

Correlation Coefficient is used to measure the strength of relationship between linear variables.

The regression Coefficient obtained is - 0.20

This shows that there is a weak negative correlation between the age at auction and the price at which painting is sold. This is because the negative sign means that value of y decreases as x increases or vice versa, however, due to a correlation vale which is closer to 0 than 1 or - 1, we can conclude that the negative relationship between the variables is weak.

5 0

2 years ago

Mya's bedroom is in the shape of a rectangular prism 15 feet long, 12 feet wide, and 10 feet high. It has no windows. Mya wants

azamat

Answer:

1800

Step-by-step explanation:

15x12x10= 120x 15= 1800

6 0

2 years ago