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3 years ago

15DANCE TICKETS WERE SOLD IN ONE HALF HOUR. IF THIS RATE CONTINUES HOW LONG WOULD YOU EXPECT IT TO TAKE TO SELL 270 tickets.

Mathematics

1 answer:

Oliga [24]3 years ago

5 0

Answer:

9 hours

Step-by-step explanation:

Using the initial ratio of 15 tickets in half an hour, you can set up a proportion (equivalent ratios) to find the amount of time it would take to sell 270 tickets:

$\frac{tickets}{time}=\frac{15}{0.5}=\frac{270}{x}$

Where 'x' is the amount of time to seel 270 tickets.

Cross-multiply: 0.5(270) = 15x or 135 = 15x

Divide: 15x/15 = 135/15 or x = 9 hours

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An ice cream factory makes 120 quarts of ice cream in 2 hours. How many quarts could be made in 36 hours?

AlekseyPX

Answer:

2,160

Step-by-step explanation:

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3 years ago

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The equations that must be solved for maximum or minimum values of a differentiable function w=f(x,y,z) subject to two constrai

sammy [17]

The Lagrangian is

$L(x,y,z,\lambda,\mu)=x^2+y^2+z^2+\lambda(4x^2+4y^2-z^2)+\mu(2x+4z-2)$

with partial derivatives (set equal to 0)

$L_x=2x+8\lambda x+2\mu=0\implies x(1+4\lambda)+\mu=0$

$L_y=2y+8\lambda y=0\implies y(1+4\lambda)=0$

$L_z=2z-2\lambda z+4\mu=0\implies z(1-\lambda)+2\mu=0$

$L_\lambda=4x^2+4y^2-z^2=0$

$L_\mu=2x+4z-2=0\implies x+2z=1$

Case 1: If $y=0$ , then

$4x^2-z^2=0\implies4x^2=z^2\implies2|x|=|z|$

Then

$x+2z=1\implies x=1-2z\implies2|1-2z|=|z|\implies z=\dfrac25\text{ or }z=\dfrac23$

$\implies x=\dfrac15\text{ or }x=-\dfrac13$

So we have two critical points, $\left(\dfrac15,0,\dfrac25\right)$ and $\left(-\dfrac13,0,\dfrac23\right)$

Case 2: If $\lambda=-\dfrac14$ , then in the first equation we get

$x(1+4\lambda)+\mu=\mu=0$

and from the third equation,

$z(1-\lambda)+2\mu=\dfrac54z=0\implies z=0$

Then

$x+2z=1\implies x=1$

$4x^2+4y^2-z^2=0\implies1+y^2=0$

but there are no real solutions for $y$ , so this case yields no additional critical points.

So at the two critical points we've found, we get extreme values of

$f\left(\dfrac15,0,\dfrac25\right)=\dfrac15$ (min)

and

$f\left(-\dfrac13,0,\dfrac23\right)=\dfrac59$ (max)

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3 years ago

Find a formula for the inverse of the function. f(x) = e^6x − 9

STatiana [176]

Answer:

$f^{-1}(x)=\frac{1}{6}\ln(x+9)$

Step-by-step explanation:

So we have the function:

$f(x)=e^{6x}-9$

To solve for the inverse of a function, change f(x) and x, change the f(x) to f⁻¹(x), and solve for it. Therefore:

$x=e^{6f^{-1}(x)}-9$

Add 9 to both sides:

$x+9=e^{6f^{-1}(x)}$

Take the natural log of both sides:

$\ln(x+9)=\ln(e^{6f^{-1}(x)})$

The right side cancels:

$\ln(x+9)=6f^{-1}(x)$

Divide both sides by 6:

$f^{-1}(x)=\frac{1}{6}\ln(x+9)$

And we're done!

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3 years ago

12(5+2y)=4y-(6-9y) how to solve and check solution

stepladder [879]

Answer:

Step-by-step explanation:

12(5+2y)=4y-(6-9y)

Distribute

12*5 +12*2y = 4y - 6 +9y

60 +24y = 4y - 6 +9y

Combine like terms

60+24y =13y -6

Subtract 13 y from each side

60 +24y-13y=13y-13y -6

60+11y = -6

Subtract 60 from each side

60+11y-60 =-6 -60

11y = -66

Divide by 11

11y/11 = -66/11

y =-6

Check

12(5+2(-6))=4(-6)-(6-9(-6) )

12 (5-12) = -24 - (6+54)

12(-7) = -24 -60

-84 = -84

True so the solution is correct

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