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makkiz [27]
2 years ago
12

Class

Mathematics
1 answer:
Brums [2.3K]2 years ago
6 0

Answer:

Amy has $75 to buy 6 new books.If each book costs $5, which equation represents the amount of money ( m) Amy will have left? A. 75-11= m B. 75+15= m C. 75-30= m D.75+30= m

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Can you solve what is 5 x 1 2/3
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Which best defines a pioneer species?
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What is the value of variable for -4(y - 2) = 12<br> Explain please
Scrat [10]

Answer:

-4(y - 2) = 12

Standard form:

−4y − 4 = 0

Factorization:

−4(y + 1) = 0

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4

= −1

Step-by-step explanation:

7 0
3 years ago
Evaluate the integral Integral ∫ from (1,2,3 ) to (5, 7,-2 ) y dx + x dy + 4 dz by finding parametric equations for the line seg
n200080 [17]

\vec F(x,y,z)=y\,\vec\imath+x\,\vec\jmath+3\,\vec k

is conservative if there is a scalar function f(x,y,z) such that \nabla f=\vec F. This would require

\dfrac{\partial f}{\partial x}=y

\dfrac{\partial f}{\partial y}=x

\dfrac{\partial f}{\partial z}=3

(or perhaps the last partial derivative should be 4 to match up with the integral?)

From these equations we find

f(x,y,z)=xy+g(y,z)

\dfrac{\partial f}{\partial y}=x=x+\dfrac{\partial g}{\partial y}\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)

f(x,y,z)=xy+h(z)

\dfrac{\partial f}{\partial z}=3=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=3z+C

f(x,y,z)=xy+3z+C

so \vec F is indeed conservative, and the gradient theorem (a.k.a. fundamental theorem of calculus for line integrals) applies. The value of the line integral depends only the endpoints:

\displaystyle\int_{(1,2,3)}^{(5,7,-2)}y\,\mathrm dx+x\,\mathrm dy+3\,\mathrm dz=\int_{(1,2,3)}^{(5,7,-2)}\nabla f(x,y,z)\cdot\mathrm d\vec r

=f(5,7,-2)-f(1,2,3)=\boxed{18}

8 0
3 years ago
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