What is the quadratic equation whose roots are -3, -1 and has a leading coefficient of 2 with X to represent the variable?

Mathematics

1 answer:

dexar [7]2 years ago

3 0

$f(x)=2(x+3)(x+1)\\
f(x)=2(x^2+x+3x+3)\\
f(x)=2(x^2+4x+3)\\
f(x)=2x^2+8x+6$

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Hi! I need help with the attached question in calc. Thank you:)

Elena L [17]

Answer:

3π square units.

Step-by-step explanation:

We can use the disk method.

Since we are revolving around AB, we have a vertical axis of revolution.

So, our representative rectangle will be horizontal.

R₁ is bounded by y = 9x.

So, x = y/9.

Our radius since our axis is AB will be 1 - x or 1 - y/9.

And we are integrating from y = 0 to y = 9.

By the disk method (for a vertical axis of revolution):

$\displaystyle V=\pi \int_a^b [R(y)]^2\, dy$

So:

$\displaystyle V=\pi\int_0^9\Big(1-\frac{y}{9}\Big)^2\, dy$

Simplify:

$\displaystyle V=\pi\int_0^9(1-\frac{2y}{9}+\frac{y^2}{81})\, dy$

Integrate:

$\displaystyle V=\pi\Big[y-\frac{1}{9}y^2+\frac{1}{243}y^3\Big|_0^9\Big]$

Evaluate (I ignored the 0):

$\displaystyle V=\pi[9-\frac{1}{9}(9)^2+\frac{1}{243}(9^3)]=3\pi$

The volume of the solid is 3π square units.

Note:

You can do this without calculus. Notice that R₁ revolved around AB is simply a right cone with radius 1 and height 9. Then by the volume for a cone formula:

$\displaystyle V=\frac{1}{3}\pi(1)^2(9)=3\pi$

We acquire the exact same answer.

8 0

2 years ago

Solve by factoring, help

zubka84 [21]

Answer:

$x = - 4 \\ x = - 7$

Step-by-step explanation:

$x {}^{2} + 28 = - 11x \\ x {}^{2} + 11x + 28 = 0 \\ x {}^{2} + 7x + 4x + 28 = 0 \\ x(x + 7) + 4(x + 7) = 0 \\ (x + 4)(x + 7) = 0 \\ \\ x = - 4 \: \: \: \: \: \: \\ \: x = - 7$