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3 years ago

Solve the combined inequality

Mathematics

2 answers:

natta225 [31]3 years ago

6 0

Answer:

6.72<x<10.08

Step-by-step explanation:

multiply 1.12 and 6 for the low end

multiply 1.12 and 9 for the high end

Inessa05 [86]3 years ago

3 0

Answer:

6.72<=X<=10.08

Step-by-step explanation:

6*1.12<=X<=9*1.12

We put 6*1.12 because that is the least she would pay, putting it into the lower end.

We put 9*1.12 because that is the most she would pay, putting it into the higher end.

6.72<=X<=10.08

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P(x)-x15x-48x + 450, x è 3 is an approximation to the total profit (in thousands of dollars) from the sale of x hundred thousand

aleksklad [387]

Answer: C. 8 hundred thousand

Step-by-step explanation:

Assuming the given profit function is:

$P(x) =- x^3+15x^2-48x+450$

Then we differentiate:

$P'(x)=-3x^2+30x-48$

And we set the derivative equal to 0 and solve the resulting equation in order to get the critical points:

$-3x^2+30x-48=0$

Divide by -3 the equation:

$x^2-10x+16=0$

Factor:

$(x-8)(x-2)=0$

Set each factor equal to zero and solve:

$x-8=0\to x=8$

$x-2=0\to x=2$

Then we check which is the maximum by using the first derivative test.

Into the derivative, let’s plug x=0 which is a value in the interval before the critical point x=2:

$P'(0)=-3(0)^2+30(0)-48=-48$

The derivative is negative, so the profit function is decreasing before x=2

Into the derivative, let’s plug x=3 which is a value in the interval after the critical point x=2 and before the critical point x=8:

$P'(3)=-3(3)^2+30(3)-48=15$

The derivative is positive, so the profit function is increasing between x=2 and x=8

Notice then at x=2 we have a local minimum since the function changed from decreasing to increasing there.

Into the derivative, let’s now plug x=10 which is a value in the interval after the critical point x=8:

$P'(10)=-3(10)^2+30(10)-48=-48$

The derivative is negative, so the profit function is decreasing after x=8.

Therefore, at x=8 we have a local maximum because the function changed from increasing to decreasing there.

So, the solution is x=8, meaning 8 hundred thousand tires must be sold to maximize profit. That is option C.

7 0

3 years ago

Help!?!? Find the area of the shaded region. Round your answer to the nearest hundredth.

Lerok [7]

Check the picture below.

so if y = 2, then 2y = 4, thus

$\textit{area of a segment of a circle}\\\\A=\cfrac{r^2}{2}\left(\cfrac{\pi \theta }{180}~~ - ~~sin(\theta ) \right)~~\begin{cases}r=radius\\\theta =\stackrel{degrees}{angle}\\[-0.5em]\hrulefill\\r=4\\\theta =60\end{cases}\\\\\\A=\cfrac{4^2}{2}\left(\cfrac{\pi (60) }{180}~~ - ~~sin(60^o ) \right)\implies A=8\left( \cfrac{\pi }{3}~~ - ~~\cfrac{\sqrt{3}}{2} \right)\\\\\\A=\cfrac{8\pi }{3}~~ - ~~4\sqrt{3}\implies A\approx 1.45$

7 0

2 years ago

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VladimirAG [237]

Answer:

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3 0

3 years ago

"10 subtracted from a number is 15."

inessss [21]

Answer:

Step-by-step explanation:

25 - 10 = 15.

5 0

3 years ago

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Alexa claims that 16 ÷ 4, 32/8, and 8 halves are all equivalent expressions. Is Alexa correct? Explain how you know.

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