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2 years ago

Can some one help me plz I really need help

Mathematics

1 answer:

Sonbull [250]2 years ago

6 0

1. 2x + 50 = 100
subtract 50 on both sides and then divide by 2.

x = 25

180 - 100 = 80

m
2. 7x - 4 = 87
add 4 on both sides and divide by 7.

x = 13

180 - 87 = 93

m
3. 5x - 2 = 38
add both sides by 2 and divide by 5.

x = 8

180 - 38 = 142

m
4. 14 + 6x = 134
subtract both sides by 14 and divide by 6.

x = 20

180 - 134 = 46

m
5. x = 53

m
6. x = 14

m

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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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2 years ago

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Read 2 more answers

According to the Rational Root Theorem, which number is a potential root of f(x) = 9x8 + 9x6 – 12x + 7?

bogdanovich [222]

Answer:

Seven-thirds

Step-by-step explanation:

The give equation is $f(x)=9x^8+9x^6-12x+7$ .

The leading coefficient is 9

The constant term is 7

According to the rational root theorem, the ratio of factors the constant terms to that of the coefficient of the leading term are all possible rational roots of the given polynomial.

Base on this theorem, $\frac{7}{3}$ or seven thirds is a potential root because the numeration is a factor of 7 and the denominator is a factor of 9.