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andreev551 [17]
4 years ago
9

Determine whether or not f is a conservative vector field. if it is, find a function f such that f = ∇f. (if the vector field is

not conservative, enter dne.) f(x, y) = (yex + sin(y))i + (ex + x cos(y))j
Mathematics
1 answer:
sineoko [7]4 years ago
7 0
\mathbf f(x,y)=(ye^x+\sin y)\,\mathbf i+(e^x+x\cos y)\,\mathbf j is continuous, so \mathbf f(x,y) is indeed conservative. So we know there is some scalar function f(x,y) such that \nabla f(x,y)=\mathbf f(x,y).

\dfrac{\partial f}{\partial x}=ye^x+\sin y
\displaystyle\int\frac{\partial f}{\partial x}\,\mathrm dx=\int(ye^x+\sin y)\,\mathrm dx
f(x,y)=ye^x+x\sin y+g(y)

\dfrac{\partial f}{\partial y}=\dfrac{\partial(ye^x+x\sin y+g(y))}{\partial y}
e^x+x\cos y=e^x+x\cos y+g'(y)
0=g'(y)
\implies g(y)=C

So we have

f(x,y)=ye^x+x\sin y+C
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Bianca has a stamp collection of 5 cent stamps and 7 cent stamps. She has 3 less 7 cent stamps as 5 cent stamps. If the collecti
amm1812

Answer:

She has 9 5 cent stamps and 6 7 cent stamps.

Step-by-step explanation:

Let the number of five cent stamps be represented by F and the number of seven cent stamps be represented by S.

The difference between the number of five cent and seven cent stamps is 3

F-S=3

The sum of the collection from each type of stamp is 87 cents

5F+7S=87

Let us solve the equations simultaneously.

F-S=3

5F+7S=87

Using substitution method,

F= 3+S

5(3+S)+7S=87

15+5S+7S=87

12S=87-15

12S=72

S=6

F=3+S

=3+6=9

Therefore the number of five cent stamps is 9 and seven cent stamps is 6.

7 0
3 years ago
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The amount (a) after d days will be
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.. a(4) = 5000*(1/2)^(4*4) = 5000/2^16 ≈ 0.076 . . . grams

George will have about 0.076 grams after 4 days.
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3 years ago
A piggy bank contains $5.45 in dimes and quarters. If the bank contains 29 coins, how many quarters are in the bank?
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Jason inherited a piece of land from his great-uncle. Owners in the area claim that there is a 45% chance that the land has oil.
oksian1 [2.3K]

Answer:

0.36 = 36% probability that the land has oil and the test predicts it

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

P(B|A) = \frac{P(A \cap B)}{P(A)}

In which

P(B|A) is the probability of event B happening, given that A happened.

P(A \cap B) is the probability of both A and B happening.

P(A) is the probability of A happening.

45% chance that the land has oil.

This means that P(A) = 0.45

He buys a kit that claims to have an 80% accuracy rate of indicating oil in the soil.

This means that P(B|A) = 0.8

What is the probability that the land has oil and the test predicts it?

This is P(A \cap B). So

P(B|A) = \frac{P(A \cap B)}{P(A)}

P(B \cap A) = P(B|A)*P(A) = 0.8*0.45 = 0.36

0.36 = 36% probability that the land has oil and the test predicts it

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What is the value of the expression 6/7 divided by 3/4
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