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antoniya [11.8K]
2 years ago
14

O

Mathematics
1 answer:
erastovalidia [21]2 years ago
6 0

Answer:

D .

Sorry if i'm wrong.

x(2 {x}^{2}  + 4x - 1 )\\  = 2  {x}^{3}  + 4 {x}^{2}  - x

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What is the area of a sector with a central angle of (2pi/3) radians and a diameter of 12 in?
Stels [109]

Answer:

The area of the sector is 37.68\ in^{2}

Step-by-step explanation:

step 1

Find the area of the circle

The area of the circle is equal to

A=\pi r^{2}

we have

r=12/2=6\ in ----> the radius is half the diameter

substitute

A=(3.14)(6)^{2}

A=113.04\ in^{2}

step 2

Find the area of a sector with a central angle of (2pi/3)

Remember that

The area of 113.04\ in^{2} subtends a central angle of 2\pi \ radians

so

by proportion

Let

x----> the area of the sector

\frac{2\pi}{113.04}=\frac{(2\pi/3)}{x}\\ \\x=113.04*(2\pi/3)/(2\pi)\\ \\x=37.68\ in^{2}

8 0
3 years ago
Tamara wants to calculate the height of a tree outside her home. Using her clinometer, she measures the angle from 35 feet away
serg [7]

Answer:

71.32 feet

Step-by-step explanation:

We set up a trigonometric function to get height of tree

Distance ,x = 35 feet away from tree base

Angle = 62⁰ at eye level

Y = tan(angle) * x

= Y = tan(62⁰) x 35

Y = 1.881 x 35

Y = 65.82 feet

We add Tamara's height to the total height of the tree

= 65.82feet + 5.5 feet

= 71.32 feet is the height of the tree

3 0
3 years ago
Match solutions and differential equations. Note: Each equation may have more than one solution. Select all that apply. (a) 7y''
Nonamiya [84]

Answer:

a-e^x,e^{-x}

b-x^{-2}

c-x^3

Step-by-step explanation:

a.7 y''-7 y =0

Auxillary equation

D^2-1=0

(D-1)(D+1)=0

D=1,-1

Then , the solution of given differential equation

y=e^x,y=e^{-x}

2.7x^2y''+14xy'-14 y=0

Y=y=x^3

y=3x^2

y''=6x

Substitute in the given differential equation

42x^3+42x^3-14x^3\neq 0

Hence, x^3 is not a solution of given differential equation

e^x,e^{-x} are also not a solution of given differential equation.

y=x^{-2}

y'=-2x^{-3}

y''=6x^{-4}

Substitute the values in the differential equation

7x^2(6x^{-4})+14x(-2x^{-3})-14 x^{-2}

=42x^{-2}-28x^{-2}-14x^{-2}=0

Hence, x^{-2} is a solution of given differential equation.

c.7x^2y''-42y=0

y=x^3

y'=3x^2

y''=6x

Substitute the values in the differential equation

42x^3-42x^3=0

Hence, x^3 is a solution of given differential equation.

a-e^x,e^{-x}

b-x^{-2}

c-x^3

6 0
3 years ago
Read 2 more answers
Y
Luba_88 [7]

Answer:

a

Step-by-step explanation:

y\leq\frac{1}{2}x+2 \\\\1\leq \frac{1}{2}(0)+2\\\\1\leq 0+2\\\\1\leq 2

This statement is true

Hope this helps!

3 0
3 years ago
I need help please!!!
MAVERICK [17]

Answer:

1). 10. 2). 9. 3). 2(square root)14. 4). (square root)6. 5). right triangle. 6). not a right triangle. 7). 13. 8). 3(square root)34. 9). acute. 10). acute. 11). right. 12). obtuse

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
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