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Anuta_ua [19.1K]
3 years ago
6

Evaluate the line integral c y3 ds, c.x = t3, y = t, 0 ≤ t ≤ 3

Mathematics
1 answer:
Temka [501]3 years ago
7 0
\displaystyle\int_{\mathcal C}y^3\,\mathrm dS=\int_{t=0}^{t=3}t^3\sqrt{1^2+(3t^2)^2}\,\mathrm dt=\int_0^3t^3\sqrt{1+9t^4}\,\mathrm dt

Take u=1+9t^4 so that \mathrm du=36t^3\,\mathrm dt. Then

\displaystyle\int_{\mathcal C}y^3\,\mathrm dS=\frac1{36}\int_{u=1}^{u=730}\sqrt u\,\mathrm du=\frac{730^{3/2}-1}{54}
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HELP! LOTS OF POINTS
seropon [69]
Use the equation=
x^2+5^2=9^2
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x^2+25-25=81-25
x^2=56
\sqrt{x} = \sqrt{56}
x=7.48331477355
5 0
3 years ago
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Lee has $220 to spend on shirts at $22 each and pants $38 each. what inequality represents the possible number of shirts and pan
Viefleur [7K]

The inequality that models the given situation is:

y*$22 + x*$38 ≤ $220

And some solutions are (1, 1), (1, 2), (2, 2).

<h3>Which inequality models the given situation?</h3>

To find the inequality, we first need to define the variables that we will use, the variables are:

  • x = number of pants bought.
  • y = number of shirts bought.

Knowing the price of each individual item, the total cost will be given by:

C = y*$22 + x*$38

And Lee has $220 to spend, so the maximum amount that he can spend is $220, then we have the inequality:

y*$22 + x*$38 ≤ $220

Now, to find solutions you just need to find some values of x and y that make the inequality true, for example, one solution is x = 1 and y = 1.

1*$22 + 1*$38 ≤ $220

$60 ≤ $220

This is true, so (1, 1) is a solution.

Another solutions are (2, 2), (1, 2), (0, 3), etc.

If you want to learn more about inequalities you can read:

brainly.com/question/24372553

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6 0
2 years ago
Solve.
zvonat [6]

Answer:

x

Step-by-step explanation:

<u><em>The correct question is</em></u>

Solve. −3/5x+1/5>7/20 Drag and drop a number or symbol into each box to show the solution

we have

-\frac{3}{5}x+\frac{1}{5} >\frac{7}{20}

Solve for x

Multiply by 20 both sides

-12x+4 >7

subtract 4 both sides

-12x >7-4

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divide by -12 both sides

Remember that when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol

x

simplify

x

6 0
3 years ago
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ahrayia [7]

Answer:

2.5 cm

Step-by-step explanation:

5 Cm is the diameter and the radius is half the diameter so 5/2=2.5 or 1/2

4 0
3 years ago
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Jupiter's orbit is about 3×10^9 miles and Earth's orbit is about 6×10^8 miles. How many times longer is Jupiter's orbit than Ear
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Answer:

5

Step-by-step explanation:

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