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3 years ago

HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Mathematics

1 answer:

adelina 88 [10]3 years ago

3 0

The answer is 2.041*10 to the 6th power

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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

2 years ago

Evaluate the expression when x= -7. x²+4x-3

I am Lyosha [343]

The answer is 18
-7^2+4(-7)-3
49+(-28)-3
21-3
18

3 0

2 years ago

Read 2 more answers

When a decimal is written in word form, what indicates whether the number can be written as a mixed number or as a fraction less

vekshin1

9514 1404 393

Answer:

"and"

Step-by-step explanation:

Properly written, the word "and" separates the integer portion from the fractional portion of the number. If there is no "and", then there is no integer portion, so the number is a fraction less than 1.

<u>Examples</u>:

one <em>and</em> three tenths = 1 3/10

thirty-one thousandths = 31/1000

8 0

2 years ago

16/ ? = -8 can anyone help plz

erma4kov [3.2K]

I believe the answer is 8

3 0

2 years ago

Read 2 more answers

Simplify the linear expression

vekshin1

Answer:

$\huge\boxed{-\frac{7}{8}a - \frac{1}{6}}$

Step-by-step explanation:

This question utilizes combining like terms and common denominators. First you have to convert both terms including "a" to have a denominator of 8. You would do this by multiplying both the numerator, and the denominator by the same value. This value in the case of $-\frac{1}{4} a$ would be 2, and in the case of $\frac{2}{3}$ the value would be 2. This would result in the equation: $-\frac{5}{8}a+\frac{4}{6}-\frac{2}{8}a-\frac{5}{6}$ . Then simply combine like terms to get your final answer.

5 0

1 year ago