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Marina86 [1]
3 years ago
11

The line integral of (2x+9z) ds where the curve is given by the parametric equations x=t, y=t^2, z=t^3 for t between 0 and 1. Pl

ease don't respond if you can't explain how to get out of an impossible square root. Thanks
Mathematics
1 answer:
Naya [18.7K]3 years ago
7 0
Let r = (t,t^2,t^3)

Then r' = (1, 2t, 3t^2)

General Line integral is:
\int_a^b f(r) |r'| dt

The limits are 0 to 1
f(r) = 2x + 9z = 2t +9t^3
|r'| is magnitude of derivative vector \sqrt{(x')^2 + (y')^2 + (z')^2}

\int_0^1 (2t+9t^3) \sqrt{1+4t^2 +9t^4} dt

Fortunately, this simplifies nicely with a 'u' substitution.

Let u = 1+4t^2 +9t^4

du = 8t + 36t^3  dt

\int_0^1 \frac{2t+9t^3}{8t+36t^3} \sqrt{u}  du \\  \\ \int_0^1 \frac{2t+9t^3}{4(2t+9t^3)} \sqrt{u}  du \\  \\  \frac{1}{4} \int_0^1 \sqrt{u}  du

After integrating using power rule, replace 'u' with function for 't' and evaluate limits:
=\frac{1}{4} |_0^1 (\frac{2}{3}) (1+4t^2 +9t^4)^{3/2} \\  \\ =\frac{1}{6} (14^{3/2} - 1)
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Jerome has 1/4 of thw group's video games at his house. Mario has 2/5 of the group's video games at his house. What fraction of
OLga [1]

Answer:

\frac{13}{20} of the group's video games is either at Jeromes house or Marios  house.

Step-by-step explanation:

Given the statement: Jerome has 1/4 of the group's video games at his house.

Also,Mario has 2/5 of the group's video games at his house.

⇒ Jerome has group's video games at his house(J) = \frac{1}{4}

and

Mario has group's video games at his house(M) = \frac{2}{5}

To find the fraction of the group's video games is either at Jerome house or Mario house.

Between two they have = J+M = \frac{1}{4} + \frac{2}{5} = \frac{5+8}{20} =\frac{13}{20} of the group's video games.




4 0
3 years ago
On Monday, Aisha spent 5/6 of an hour practicing the violin. On Tuesday, she practiced for 2/3 of an hour. Which equation shows
Rudiy27

Answer:

1/6

Step-by-step explanation:

5/6 - 4/6 = 1/6

4 0
3 years ago
GIVING BRAINLEST TO WHOEVER ANSWERS CORRECT
Nina [5.8K]

Answer:

everything is black :/

Step-by-step explanations:

5 0
3 years ago
In un trapezio rettangolo la base minore, il lato obliquo e l'altezza misurano rispettivamente 60 cm. 95 cm è 76 cm. Calcola il
KengaRu [80]

Answer:

2p=348 cm\: S=6726 cm^{2}

Step-by-step explanation:

Ciao, come stai?

1) Per prima cosa, dobbiamo trovare la misura della base più grande. Scomponendo la figura possiamo visualizzare un triangolo e un quadrato. Ci sono somiglianze con gli angoli. Quindi è un triangolo rettangolo. Applichiamo il teorema di Pitagora:

a^2=b^2+c^2\\95^2=b^2+76^2\\57=b

2) Perimetro:

2p=60+57+76+60+95\\2p=348 cm

3) L' area

\frac{(B+b)h}{2} =\frac{(117+60)76}{2} =6726 \:cm^{2}

8 0
3 years ago
An experiment consists of rolling two fair number cubes. What is the probability that the sum of the two numbers will be >3
liraira [26]

Answer:   \bold{\dfrac{5}{12}}

<u>Step-by-step explanation:</u>

greater than 3 means the sum is either 4, 5, or 6.

There are 15 permutations that meet the criteria:

(1, 3), (1, 4), (1, 5), (1,6)

(2, 2), (2, 3), (2, 4), (2, 5), (2,6)

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3,6)

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4,6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5,6)

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6,6)

There are 6²= 36 total permutations for 2 dice.

Probability=\dfrac{\#\ of\ permutations> 3}{total\ \#\ of\ permutations}\\\\.\qquad \qquad =\dfrac{15}{36}\\\\.\qquad \qquad =\dfrac{5}{12}\\\\

3 0
3 years ago
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