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Verizon [17]
4 years ago
11

If 29 of a song plays in 13 minute, what fraction of the song plays in 1 minute? Write a number sentence involving division that

explains your answer.
Mathematics
1 answer:
lisov135 [29]4 years ago
4 0

Answer:

\frac{29}{13} of a song plays in 1 minute

Step-by-step explanation:

29 of a song plays in 13 minute

The songs played in 13 minutes = 29

The songs played in 1 minute = \frac{29}{13}

So, \frac{29}{13} of a song plays in 1 minute

29 by 13 fraction of a songs are played in 1 minute

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3 years ago
Consider F and C below. F(x, y, z) = y2 sin(z) i + 2xy sin(z) j + xy2 cos(z) k C: r(t) = t2 i + sin(t) j + t k, 0 ≤ t ≤ π (a) Fi
Liono4ka [1.6K]

Answer:

a) f (x,y,z)= xy^2\sin(z)

b) \int_C F \cdot dr =0

Step-by-step explanation:

Recall that given a function f(x,y,z) then \nabla f = (\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z}). To find f, we will assume it exists and then we will find its form by integration.

First assume that F = \nabla f. This implies that

\frac{\partial f}{\partial x} = y^2\sin(z) if we integrate with respect to x we get that

f(x,y,z) = xy^2\sin(z) + g(y,z) for some function g(y,z). If we take the derivative of this equation with respect to y, we get

\frac{\partial f}{\partial y} = 2xy\sin(z) + \frac{\partial g}{\partial y}

This must be equal to the second component of F. Then

2xy\sin(z) + \frac{\partial g}{\partial y}=2xy\sin(z)

This implies that \frac{\partial g}{\partial y}=0, which means that g depends on z only. So f(x,y,z) = xy^2\sin(z) + g(z)

Taking the derivative with respect to z and making it equal to the third component of F, we get

xy^2\cos(z)+\frac{dg}{dz} = xy^2\cos(z)

which implies that \frac{dg}{dz}=0 which means that g(z) = K, where K is a constant. So

f (x,y,z)= xy^2\sin(z)

b) To evaluate \int_C F \cdot dr we can evaluate it by using f. We can calculate the value of f at the initial and final point of C and the subtract them as follows.

\int_C F \cdot dr = f(r(\pi))-f(r(0))

Recall that r(\pi) = (\pi^2, 0, \pi) so f(r(\pi)) = \pi^2\cdot 0 \cdot \sin(\pi) = 0

Also r(0) = (0, 0, 0) so f(r(0)) = 0^2\cdot 0 \cdot \sin(0) = 0

So \int_C F \cdot dr =0

5 0
3 years ago
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max2010maxim [7]

Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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3 years ago
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