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3 years ago

7x + 6(-3 + 4x) = 199what does x equal?

Mathematics

1 answer:

tresset_1 [31]3 years ago

8 0

Simplify. Note the equal sign. What you do to one side, you do to the other. Follow PEMDAS.

Isolate the x.

First, distribute 6 to all terms within the parenthesis

6(-3) = -18

6(4x) = 24x

7x - 18 + 24x = 199

Simplify. Combine like terms

31x - 18 = 199

Isolate the x. Add 18 to both sides

31x - 18 (+18) = 199 (+18)

31x = 199 + 18

31x = 217

Isolate the x. Divide 31 from both sides

31x/31 = 217/31

x = 217/31

x = 7

7 is your answer for x

hope this helps

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Answer:

The parametrization of the curve on the surface is

$c(t) = [x(t) , y(t), z(t)] \equiv [\frac{\sqrt{97} }{2} cost - 4 , \frac{\sqrt{97} }{2} sint + \frac{5}{2} , 5\frac{\sqrt{97} }{2} sint -8 \frac{\sqrt{97} }{2} cost +\frac{93}{2} ]$

Where

$x = \frac{\sqrt{97} }{2} cost - 4$

$y = \frac{\sqrt{97} }{2} sint + \frac{5}{2}$

$z = 5\frac{\sqrt{97} }{2} sint -8 \frac{\sqrt{97} }{2} cost +\frac{93}{2}$

Step-by-step explanation:

From the question we are told that

The equation for the paraboloid is $z = x^2 + y^2$

The equation of the plane is $8x - 5y + z -2 = 0$

Form the equation of the plane we have that

$z = 5y -8x +2$

$x^2 + y^2 = 5y -8x +2$

=> $x^2 + 8x + y^2 -5y = 2$

Using completing the square method to evaluate the quadratic equation we have

$(x + 4)^2 + (y - \frac{5}{2} )^2 = 2 +(\frac{5}{2} )^2 + 4^2$

$(x + 4)^2 + (y - \frac{5}{2} )^2 = \frac{97}{4}$

$(x + 4)^2 + (y - \frac{5}{2} )^2 = ( \frac{\sqrt{97} }{2} )^2$

representing the above equation in parametric form

$(x + 4) = \frac{\sqrt{97} }{2} cost$ , $(y -\frac{5}{2} ) = \frac{\sqrt{97} }{2} sin t$

$x = \frac{\sqrt{97} }{2} cost - 4$

$y = \frac{\sqrt{97} }{2} sint + \frac{5}{2}$

So from $z = 5y -8x +2$

$z = 5[\frac{\sqrt{97} }{2} sint + \frac{5}{2}] -8[ \frac{\sqrt{97} }{2} cost - 4] +2$

$z = 5\frac{\sqrt{97} }{2} sint + \frac{25}{2} -8 \frac{\sqrt{97} }{2} cost + 32 +2$

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Generally the parametrization of the curve on the surface is mathematically represented as

$c(t) = [x(t) , y(t), z(t)] \equiv [\frac{\sqrt{97} }{2} cost - 4 , \frac{\sqrt{97} }{2} sint + \frac{5}{2} , 5\frac{\sqrt{97} }{2} sint -8 \frac{\sqrt{97} }{2} cost +\frac{93}{2} ]$

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