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2 years ago

F(x) = -x² + 7x - 12 One factor of this is (x - 4). Find the other factor.

Mathematics

1 answer:

saveliy_v [14]2 years ago

4 0

Answer:

(3-x) is the other factor.

Step-by-step explanation:

The given function is :

$F(x)=-x^{2}+7x-12$

One of the factor is (x-4)

We need to find the other factor.

It can be solved as follows :

$F(x)=-x^{2}+4x+3x-12\\\\=(-x+3)(x-4)$

So, the other factor is (3-x).

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3 years ago

A tank has the shape of a surface generated by revolving the parabolic segment y = x2 for 0 ≤ x ≤ 3 about the y-axis (measuremen

Darina [25.2K]

Answer:

$100\pi\int\limits^9_0 {(\sqrt y)^2(14-y)} \, dy$ ft-lbs.

Step-by-step explanation:

Given:

The shape of the tank is obtained by revolving $y=x^2$ about y axis in the interval $0\leq x\leq 3$ .

Density of the fluid in the tank, $D=100\ lbs/ft^3$

Let the initial height of the fluid be 'y' feet from the bottom.

The bottom of the tank is, $y(0)=0^2=0$

Now, the height has to be raised to a height 5 feet above the top of the tank.

The height of top of the tank is obtained by plugging in $x=3$ in the parabolic equation . This gives,

$H=3^2=9\ ft$

So, the height of top of tank is, $y(3)=H=9\ ft$

Now, 5 ft above 'H' means $H+5=9+5=14$

Therefore, the increase in height of the top surface of the fluid in the tank is given as:

$\Delta y=(14-y)$ ft

Now, area of cross section of the tank is given as:

$A(y)=\pi r^2\\r\to radius\ of\ the\ cross\ section$

Radius is the distance of a point on the parabola from the y axis. This is nothing but the x-coordinate of the point.

We have, $y=x^2$

So, $x=\sqrt y$

Therefore, radius, $r=\sqrt y$

Now, area of cross section is, $A(y)=\pi (\sqrt y)^2$

Work done in pumping the contents to 5 feet above is given as:

$W=D\int\limits^{y(3)}_{y(0)} {A(y)(\Delta y)} \, dy$

Plug in all the values. This gives,

$W=100\int\limits^9_0 {\pi (\sqrt y)^2(14-y)} \, dy\\\\W=100\pi\int\limits^9_0 { (\sqrt y)^2(14-y)} \, dy\textrm{ ft-lbs}$

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2 years ago

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nikitadnepr [17]

Answer:

63-2c

Step-by-step explanation:

You write 63 and substitute decreased with a subtraction sign. Twice means to multiple by 2. so for twice of Carlo's height you would write 2c.

I hope this helps!!!!!

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3 years ago

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jenyasd209 [6]

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2 years ago