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Nataly_w [17]
2 years ago
8

(Please help)There are 16 cups in a gallon. The equation g = 1/16c gives the number of gallons in terms of the number of cups. W

rite another equation for this situation, giving the
number of cups in terms of the number of gallons:
C=
Mathematics
2 answers:
mezya [45]2 years ago
7 0

Answer:

c = 16g

Step-by-step explanation:

g = 1/16 c

Multiply both sides by 16.

16g = c

c = 16g

Olegator [25]2 years ago
4 0

Answer:

c = 16g

Step-by-step explanation:

g=1/16c

This is an algebric equation that requires you to multiply both sides by 16.

g × 16 = 1/16c × 16

16g = c

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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}

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Where, m and c are constants in which;
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Comparing this standard way way of writing the equation of a straight line with the current scenario, this equation can be rewritten as;
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