True or false: As long as its argument is restricted to [0,2pi] the polar form of a complex number is not unique.

Some say its true, some say its false. I'm sure one of the answers I looked at is correct, but some teachers probably purposefully left a one star

Answer:490pi

Step-by-step explanation:just trust me

The volume of the given figure is required.

The required volume is 490π cm³

r = Radius of semicircle = 7 cm

h = Height of prism = 20 cm

The volume of a cylinder is

[tex]\pi r^2h[/tex]

The volume of the given shape will be half of a cylinder, so

[tex]V=\dfrac{1}{2}\pi r^2h\\\Rightarrow V=\dfrac{1}{2}\pi\times 7^2\times 20\\\Rightarrow V=490\pi\ \text{cm}^3[/tex]

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Answer:

i think this

Step-by-step explanation:

Let Va = the velocity of the airplane

Let Vw = the velocity of the wind

When flying with the wind:

(Va+Vw)*(4 hours) = 4000

4Va + 4Vw = 4000

4Vw = 4000 - 4Va

Vw = 1000 - Va

When flying against the wind:

(Va-Vw)*(7 hours) = 4200 km

7Va - 7Vw = 4200

Substitute 1000-Va for Vw and solve for Va:

7Va - 7(1000-Va) = 4200

7Va -7000 + 7Va = 4200

14Va = 11200

Va = 800 km/hr

Rate of wind:

Vw = 1000 - Va = 1000 - 800 = 200 km/hour

Answer:

This is your answer

Answer:

43.4

Step-by-step explanation:

You will need to use the phythagoream therom, which is a² + b² = c².  Plug the values in for the variables to get 7² + b² = 44², (c would equal the hypothenuse because the hypothenuse is the longest side of the triangle.)  Square the values to get 49 + b² = 1936.  Subtract 49 from both sides to get b² = 1887, then take the square root of both sides to get b = 43.4 (rounded to the nearest tenth.)  

I am really sorry if I'm wrong, but have a good day/night!  :)

Answer:

Use the Pythagoras' theorem

-the square of the hypotenuse equals to the sum of the squares on the other two side:

a^2 = b^2 + x^2

-given the hypotenuse and another side and asked to find the missing side:

Therefore you play with the equation to make the missing side the subject of formula as I did above.

Answer:

129.8 mmHg

42 years

Step-by-step explanation:

Given the relation :

P = 0.006 y² − 0.02 y + 121

Systolic blood pressure, P

Age, y

A.)

Find P when age y = 40

P = 0.006(40)² − 0.02(40) + 121

P = 9.6 - 0.8 + 121

P = 129.8 mmHg

B)

P = 130.74 mmHg

y =?

130.74 = 0.006y² − 0.02y + 121

130.74 - 121 = 0.006y² − 0.02y

9.74 = 0.006y² − 0.02y

0.006y² − 0.02y - 9.74 = 0

Using a quadratic equation solver :

The roots are 41.99 and - 38.66

Age cannot be negative ;

Hence age = 41.99 = 42 years

Answer:

D) 76 sq in

Step-by-step explanation:

It’s 4 triangles. A=1/2bh

1/2(8)(5)=20 (two of these)

1/2(8)(6)=24

1/2(4)(6)=12

20+20+24+12=76

Answer:

Look at explanation

Step-by-step explanation:

Ok,

I got...

radius of convergence = 1

interval of convergence = 3 ≤ x ≤ 5

Answer:

1. -25

2. 2.1

Step-by-step explanation:

-1/2(x + 5) = 10

divide both sides by 2.

-1(x + 5) = 20

-(x + 5) = 20

-x = 20 + 5

x = -25

k/3.5 + 7.4 = 8

2k/7 +37/5 = 8

10k = 280 - 259

10k = 21

k = 21/10 (2.1)

Answer:

1.x=15

2.k=2.1

Step-by-step explanation:

1.-1/2(x+5)=-10

 -x+5/2=-10 multiply both sides by 2

  -x-5=-10

  -x=-20+5

 -x=-15 multiply both sides by -1

  x=15

2.k/3.5+7.4=8

 k/3.5=8-7.4

  k/3.5=0.6

 multiply both sides by 3.5

  k=2.1

Answer:

the second option is the right one

Step-by-step explanation:

you have to multiply the powers for 3^5

Answer:

Option B will be your answer

Step-by-step explanation:

hope it helps you

have a great day!!

Answer:

80

Step-by-step explanation:

80+20=100

Answer:

17/7=2.42(approximately) should be on each side of the goal

Answer:

I have study up to 8 class hahahahahah

Answer:

owo - well uh

Answer:

I think 990 because if u subtract 1,000-10 it is 990 so its equal

Answer:

Value of equation = 144

Step-by-step explanation:

Given:

5g + 7g + g(5 + 7)

when g = 6

Find:

Value of equation

Computation:

5g + 7g + g(5 + 7)

5g + 7g + g(12)

5(6) + 7(6) + (6)(12)

30 + 42 + 72

Value of equation = 144

Answer:

Step-by-step explanation:

Simple interest is

I=Prt

I=11500(0.10)(60/360)

I=$191.67

The coordinates of the fourth corner is, (- 6, 2)

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

Three of the corners are,

⇒ (0, 5), (5, - 4), (- 1, - 7)

Let the coordinates of the fourth corner is, (x, y)

We know that;

Mid point of diagonal of rectangle intersect at one point, so we get;

⇒ (x + 5) / 2 , (y + (-4))/2 = ( (0 - 1)/ 2, (5 - 7)/2 )

⇒ (x + 5) / 2 = (0 - 1) / 2

⇒ x + 5 / 2 = - 1/2

⇒ x + 5 = - 1

⇒ x = - 6

⇒ ( y - 4 )/ 2 = (5 - 7) / 2

⇒ y - 4 = - 2

⇒ y = - 2 + 4

⇒ y = 2

Thus, The coordinates of the fourth corner is, (- 6, 2)

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Answer:

[tex]\Huge\boxed{240ft^2}[/tex]

Step-by-step explanation:

Hello There!

The figure shown is a trapezoid with the following dimensions

base 1 = 12ft

base 2 = 20 ft

height = 15 ft

Given these dimensions we need to find the area

We can do this by using the area of a trapezoid formula

[tex]A=\frac{a+b}{2} h[/tex]

where a and b = bases and h = height

Knowing the dimensions all we have to do is plug in the values

[tex]A=\frac{12+20}{2} 15\\12+20=32\\\frac{32}{2} =16\\16*15=240\\A=240ft^2[/tex]

So we can conclude that the area of the floor that needs to be replaced with tile is 240 ft²

Answer:

the answer is d

Step-by-step explanation:

I'm smurt

Answer:

[tex] - 8x[/tex]

the answer is -8x.

Answer:

-8x is your answer

Step-by-step explanation:

-12x + 5x - x

-7x-x

-8x

Answer:

Use Trigonometric formulae to simplify expressions

Step-by-step explanation:

Re-order to group the x and y,

Sin(y) / Sin(a+y) = x

to differentiate apply d/dx to both sides

[tex]\frac{d}{dx}[/tex]Sin(y) / Sin(a+y) = [tex]\frac{d}{dx}[/tex]x

use division rule on left side which will give

[tex]\frac{dy}{dx}[/tex]Cos(y)Sin(a+y) - [tex]\frac{dy}{dx}[/tex]Cos(a+y)Sin(y) / Sin²(a+y) = 1

Group them so dy/dx is on the left hand side:

[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / Cos(y)Sin(a+y) - Cos(a+y)Sin(y)

Apply trigonometric sum formula to expand Sin(a+y) and Cos(a+y),

[tex]\frac{dy}{dx}[/tex] =  Sin²(a+y) / Cos(y)[Sin(a)Cos(y) + Cos(a)Sin(y)] - Sin(y)[Cos(a)Cos(y) - Sin(a)Sin(y)]

Simplify it

[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / (Cos²(y) + Sin²(y))(Sin(a))

[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / (1)(Sin(a))

Answer:

4x = 24

Divide by 4 to isolate the x

x = 6

Answer:

B

Step-by-step explanation:

Because its didn't say European

Answer:

Q.1 a²+10a+24

splitting the middle.

a²+6a+4a+24

=a(a+6)+4(a+6)

(a+6)(a+4)

Q.2 x²+9x+18

splitting the middle

x²+6x+3x+18

x(x+6)+3(x+6)

(x+6)(x+3)

Answer:

See diagram below.

====================================================

Explanation:

Start at the lower left corner of the entire figure. Move 20 ft directly to the right until reach the end of the driveway at the bottom. Now move 10 ft up so you reach the other side of the driveway (the 26 ft side). In the process of moving 10 ft up, mark a new line segment. I've done so in red in the diagram below.

I've also drawn a green box. The red line and green box form a shape of a flag on a flagpole. The pole being 10 ft tall and the green box (flag) is a 6 by 3 rectangle. The 6 is from 26-20 = 6 and the 3 is from 10-7 = 3. Note how I'm subtracting the opposite side values to help figure out the dimensions of this green box.

The 10 ft by 20 ft portion of the driveway is 10*20 = 200 square feet. The green box adds on another 18 sq ft because 6*3 = 18. In all, we have 200+18 = 218 square feet for the driveway.

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If you want to know the area of the garden, then we first compute the overall area of everything shown. That's 32*14 = 448 square feet. Subtract off the driveway's area to get 448-218 = 230. Therefore, the garden's area is 230 square feet.