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4 years ago

Let x represent the number of small candle. let y represent the number the number of large candles.

Mathematics

1 answer:

Maru [420]4 years ago

8 0

Answer:

The inequality that models the situation is $2.25x+4.75y \leq 80$

Step-by-step explanation:

Let

x ----> represent the number of small candles

y ----> represent the number of large candles

we know that

The inequality that represent this situation is equal to

$2.25x+4.75y \leq 80$

using a graphing tool

The solution is the shaded triangular area, because the number of candles cannot be a negative number

see the attached figure

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Using the slope-intercept method to graph this equation, in what order should these points on the line be drawn 6(2x-4y)=3(2x+4)

Tanzania [10]

<span>6(2x-4y)=3(2x+4)
(2x-4y)=3/6(2x+4)
2x-4y=1/2(2x+4)
2(x-2y)=1/2x2(x+2)
x-2y=1/2(x+2)
x-2y=1/2x+1
x-1/2x=1+2y
x/2-1=2y
y-y1=m(x-x1) that is slope point intercept form
now plugin some points and get according y values so u can graph</span><span />

4 0

3 years ago

Consider the paraboloid z=x2+y2. The plane 8x−5y+z−2=0 cuts the paraboloid, its intersection being a curve. Find "the natural" p

Jet001 [13]

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 $z = 5y -8x +2$

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

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

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

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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4 years ago

PLEASE HELP! 10 POINTS! WILL GIVE BRAINLIEST!

emmasim [6.3K]

Answer: B. 24%

Step-by-step explanation:

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3 years ago

13g = –(9 – 12g) – 5

Elena L [17]

Answer:

g = - 14

Step-by-step explanation:

13g = - (9 - 12g) - 5

13g = - 9 + 12g - 5

13g = 12g - 14

g = - 14

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Svetllana [295]

The correct answer is the one you have selected

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3 years ago

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