$6x^2-4x+1=6\left(x-\dfrac13\right)^2+\dfrac13\ge0$

which means the parabola lies above the x-axis over its entire domain. This means the area is given by

$\displaystyle\int_{-1}^2(6x^2-4x+1)\,\mathrm dx=2x^3-x^2+x\bigg|_{x=-1}^{x=2}=10-(-5)=15$

4 0

3 years ago

∠ A and ∠B are vertical angles. Find each angle if, m∠ A=7x+2 and m∠ B=4x+11. Solve for x

tino4ka555 [31]

Answer:

x=3

Step-by-step explanation:

Vertical angles are equal so

<A = <B

7x+2 = 4x+11

Subtract 4x from each side

7x+2-4x = 4x+11-4x

3x+2 =11

Subtract 2 from each side

3x+2-2 = 11-2

3x = 9

Divide by 3

3x/3 = 9/3

x=3

7 0

3 years ago

The circumference of a circle is 5 Pi cm. What is the area of the circle?

Ber [7]

Answer:

6.25 pi cm^2

Step-by-step explanation:

The formula for circumference is

C = 2*pi*r

We know the circumference is 5 pi

5 pi = 2 * pi *r

Divide each side by pi

5 pi/pi = 2 * pi *r/pi

5 = 2r

Divide by 2

5/2 = 2r/2

2.5 = r

We need to find the area of the circle

The area is given by

A = pi * r^2

= pi * (2/5)^2

= pi *6.25

= 6.25 pi cm^2

4 0

3 years ago

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