Take away 1/5 of 50% =

Find the line integral of f(x, y) = y e^X^2 along the curve r(t) = 3t i - 4t J, -2 lessthanorequalto t lessthanorequalto -1. The

Semenov [28]

$\vec r(t)=3t\,\vec\imath-4t\,\vec\jmath$

$\implies\left\|\dfrac{\mathrm d\vec r(t)}{\mathrm dt}\right\|=\|3\,\vec\imath-4\,\vec\jmath\|=\sqrt{3^2+(-4)^2}=5$

The line integral of $f(x,y)$ along the curve $C$ parameterized by $\vec r(t)$ is

$\displaystyle\int_Cf(x,y)\,\mathrm ds=\int_{-2}^{-1}f(3t,-4t)\left\|\dfrac{\mathrm d\vec r(t)}{\mathrm dt}\right\|\,\mathrm dt=-20\int_{-2}^{-1}te^{9t^2}\,\mathrm dt$

Substitute $u=9t^2$ so that $\mathrm du=18t\,\mathrm dt$ . Then

$\displaystyle\int_Cf(x,y)\,\mathrm dS=-\frac{20}{18}\int_{36}^9e^u\,\mathrm du=\frac{10}9\int_9^{36}e^u\,\mathrm du=\boxed{\frac{10}9(e^{36}-e^9)}$

8 0

4 years ago

Find the difference: 5.68 -<br> - 2.15 - (-1.34) = *

Lerok [7]

Answer:

THE ANSWER FOR THIS QUESTION IS 9.17

3 0

3 years ago

Read 2 more answers

Which function has an inverse that is a function?

Wittaler [7]

Answer is option C.

m(x) = -7x

This is a bijective function.

Here for everyvalue of theres is only one and one unique value of y.

And hence its inverse will also be a function.

7 0

3 years ago

Please ,help hurry up,will give u brainliest.

Nataliya [291]

Answer:

Take a look at the picture!

5 0

2 years ago

A bridge hand is made up of 13 cards from a deck of 52. find the probability that a hand chosen at random contains at least 3 ki

Vlad [161]

1.
In total there are C(52, 13) ways that we can pick a hand, that is $\frac{52!}{13!39!}$

2.
P(a hand contains at least 3 kings)
=P(a hand contains exactly 3 kings)+P(a hand contains 4 kings)

3.
first let's find P(a hand contains exactly 3 kings):

P(a hand contains exactly 3 kings)
=n(a hand contains exactly 3 kings)/C(52, 13)

n(a hand contains exactly 3 kings)=C(4, 3)*C(48, 10)

where C(4,3) is the total number of ways we can pick 3 out of 4 kings,

C(48, 10) is the number of picking 10 letters to complete a hand, out of the 52-4=48 non-king cards.

so P(a hand contains exactly 3 kings)=[C(4, 3)*C(48, 10)]/C(52, 13)

4. with the same reasoning as in step 3:

P(a hand contains 4 kings)=n(a hand contains 4 kings)/C(52, 13)

= [C(4, 4)*C(48, 9]/C(52, 13)

5.

P(a hand contains at least 3 kings)
=P(a hand contains exactly 3 kings)+P(a hand contains 4 kings)

=[C(4, 3)*C(48, 10)]/C(52, 13)+ [C(4, 4)*C(48, 9)]/C(52, 13)

= $\frac{C(4, 3)*C(48, 10)+C(4, 4)*C(48, 9)}{C(52, 13)}$

= $\frac{4* \frac{48!}{10!38!} + \frac{48!}{9!39!}}{ \frac{52!}{13!39!} }$

simplify by 38! in the denominators and 48! in the numerators :

$\frac{4* \frac{1}{10!} + \frac{1}{9!39}}{ \frac{52*51*50*49}{13!39} } 

$

now simplify by 9! in all denominators:

$\frac{ \frac{4}{10}+ \frac{1}{39} }{ \frac{52*51*50*49}{13*12*11*10*39}}$

$\frac{ 0.426 }{ 9.7} =0.044$

4 0

4 years ago