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kenny6666 [7]
3 years ago
9

Hunter and Brian are creating a poster for a project and they need to combine two different size boards to create their project.

If the total area cannot exceed 7x to the second power -6x+2 square inches and one board Is 2x to the second power -9x+8 square inches, then what must be the maximum area of the second board?
Mathematics
2 answers:
Jet001 [13]3 years ago
8 0

Answer:

5x² + 3x - 6

Step-by-step explanation:

Data:

  • Total area: 7x² - 6x + 2
  • Area of one board: 2x² - 9x + 8
  • Area of the other board: f(x)

The addition of the area of the two boards cannot exceed the total area. Then:

f(x) + 2x² - 9x + 8 ≤ 7x² - 6x + 2

f(x) ≤ 7x² - 6x + 2 - 2x² + 9x - 8

f(x) ≤ (7x² - 2x²) + (-6x + 9x) + (2 - 8)

f(x) ≤ 5x² + 3x - 6 in square inches

shepuryov [24]3 years ago
7 0

Answer:

<em>The maximum area of the second board must be (5x^2+3x-6) square inches.</em>

Step-by-step explanation:

The total area of two different size boards cannot exceed (7x^2-6x+2) square inches.

The area of one board is  (2x^2-9x+8) square inches.

Suppose, the area of the second board is  y square inches.

That means......

y+(2x^2-9x+8)\leq 7x^2-6x+2\\ \\ y\leq (7x^2-6x+2)-(2x^2-9x+8)\\ \\y \leq 7x^2-6x+2-2x^2+9x-8\\ \\ y\leq 5x^2+3x-6

So, the maximum area of the second board must be (5x^2+3x-6) square inches.

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DaniilM [7]

Answer:

$27.17

Step-by-step explanation:

Regular price of necklace = $44

If a discount of 35% is applied, then the new price of the necklace will be 65% of the regular price, as 100% - 35% = 65%

⇒ 65% of $44

= 0.65 × $44

= $28.60

If a second discount of 5% is then applied, the final price of the necklace will be 95% of the sale price, as 100% - 5% = 95%

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Therefore:

The sale price with a 35% discount is $28.60

The sale price with an additional 5% discount is $27.17

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The function f(x) = g(x), where f(x) = 2x – 5 and g(x) = x2 – 6.
den301095 [7]

Answer:

x=2.4

Step-by-step explanation:

<u>Solving Equations Using Successive Approximations</u>

We need to find the solution to the equation

f(x)=g(x)

where

f(x)=2x-5

g(x)=x^2-6

The approximation has been already started and reached a state for x=2.5 where

f(2.5)=0

g(2.5)=2.5^2-6=0.25

The difference between the results is 0.25, we need further steps to reach a good solution (to the nearest tenth)

Let's test for x=2.4

f(2.4)=-0.2

g(2.4)=2.4^2-6=-0.24

The new difference is -0.2+0.24=0.04

It's accurate enough, thus the solution is

\boxed{x=2.4}

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Answer:

W=2452.5 J

Step-by-step explanation:

The work is define as the integral of the force times distance. So we have:

W=\int^{a}_{b}Fxdx

Now, we can write the force in terms of density.

F=m*g=\rho Vg

V is the volume (V=2*1*1=2 m³)

So the work will be:

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The limit of integration is between 0 and 0.5 because we want to pump half of the water out of the aquarium.

W=19620(\frac{x^{2}}{2})|^{0.5}_{0}=19620(\frac{0.5^{2}}{2})

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I hope it helps you!

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