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Elza [17]
3 years ago
11

Two cuboid-shaped metal bars are the same size. They are 12.4 cm long, 5.6 cm wide and 2.5 cm thick.

Mathematics
1 answer:
nordsb [41]3 years ago
8 0

Answer:

191 grams

Step-by-step explanation:

12.4×5.6×2.5=173.6

7.9×173.6=1371.44

9.0×173.6=1562.4

1562.4-1371.44=191

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Consider the system of quadratic equations \begin{align*} y &=3x^2 - 5x, \\ y &= 2x^2 - x - c, \end{align*}where $c$ is
shtirl [24]

Hello, we need to solve this system, c being a real number.

\begin{cases}y &= 3x^2-5x\\y &= 2x^2-x-c\end{cases}

y=y, right? So, it comes.

3x^2-5x=2x^2-x-c\\\\3x^2-2x^2-5x+x+c=0\\\\\boxed{x^2-4x+c=0}

We can compute the discriminant.

\Delta=b^2-4ac=4^2-4c=4(4-c)

If the discriminant is 0, there is 1 solution.

It means for 4(4-c)=0  4-c=0  \boxed{c=4}

And the solution is

x_2=x_1=\dfrac{4}{2}=2

If the discriminant is > 0, there are 2 real solutions.

It means 4(4-c) > 0 <=> 4-c > 0 <=> \boxed{c

And the solution are

x_1=\dfrac{4-\sqrt{4(4-c)}}{2}=\dfrac{4-2\sqrt{4-c}}{2}=2-\sqrt{4-c}\\\\x_2=2+\sqrt{4-c}

If the discriminant is < 0, there are no real solutions.

It means 4(4-c) < 0 <=> 4-c < 0 <=> \boxed{c>4}

There are no real solutions and the complex solutions are

x_1=\dfrac{4-\sqrt{4(4-c)}}{2}=\dfrac{4-2\sqrt{i^2(c-4)}}{2}=2-\sqrt{c-4}\cdot i\\\\x_2=2+\sqrt{c-4}\cdot i

Thank you.

8 0
4 years ago
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4 0
4 years ago
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abruzzese [7]

Answer:

$5.25

Step-by-step explanation:

8.75/5=1.75

1.75 x 3=5.25

3 0
3 years ago
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irina1246 [14]

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Step-by-step explanation:

x² + 6x + 1 = 0

a = 1 , b = 6 , c = 1

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