What is the distance from the origin to point A graphed on the complex plane below?

In an airplane 35% of the passengers are children they’re 140 children on the airplane how many passengers are on the airplane

Angelina_Jolie [31]

Answer:

there are 49 passengers

Step-by-step explanation: 35%=0.35

0.35*140= 49

3 0

2 years ago

4. Using the geometric sum formulas, evaluate each of the following sums and express your answer in Cartesian form.

nikitadnepr [17]

Answer:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=1$

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=0$

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})=\frac{1}{2}$

Step-by-step explanation:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=\frac{1}{2}(\sum_{n=0}^9 (e^{\frac{i\pi n}{2}}+ e^{\frac{i\pi n}{2}}))$

$=\frac{1}{2}(\frac{1-e^{\frac{10i\pi}{2}}}{1-e^{\frac{i\pi}{2}}}+\frac{1-e^{-\frac{10i\pi}{2}}}{1-e^{-\frac{i\pi}{2}}})$

$=\frac{1}{2}(\frac{1+1}{1-i}+\frac{1+1}{1+i})=1$

2nd

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=\frac{1-e^{\frac{i2\pi N}{N}}}{1-e^{\frac{i2\pi}{N}}}$

$=\frac{1-1}{1-e^{\frac{i2\pi}{N}}}=0$

3th

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})==\frac{1}{2}(\sum_{n=0}^\infty ((\frac{e^{\frac{i\pi n}{2}}}{2})^n+ (\frac{e^{-\frac{i\pi n}{2}}}{2})^n))$

$=\frac{1}{2}(\frac{1-0}{1-i}+\frac{1-0}{1+i})=\frac{1}{2}$

What we use?

We use that

$e^{i\pi n}=cos(\pi n)+i sin(\pi n)$

and

$\sum_{n=0}^k r^k=\frac{1-r^{k+1}}{1-r}$

6 0

3 years ago

Complete the slope equation of the line through 2,3 and 7, 4 <br><br> Y-4=

In-s [12.5K]

Answer:

The slope equation of the line AB is $(y -4) = \frac{1}{5} (x-7)$

Step-by-step explanation:

Here, the given points are A (2, 3) and B (7,4).

Now, slope of any line is given as :

$m = \frac{y_2 - y_1}{x_2 - x_1}$

or, $m = \frac{4 -3}{7-2} = \frac{1}{5}$

Hence, the slope of the line AB is (1/5)

Now , A POINT SLOPE FORM of an equation is

(y - y0) = m (x - x0) ; (x0, y0) is any arbitrary point on line.

Hence, the equation of line AB with slope (1/5 ) and point (7,4) is given as:

$(y -4 ) = \frac{1}{5} ( x - 7)$

or, 5y - 20 = x -7

⇒ x - 57 + 13 = 0 ( SIMPLIFIED FORM of equation)

Hence, the slope equation of the line AB is $(y -4) = \frac{1}{5} (x-7)$

3 0

2 years ago

the smiths are planning to complete a 1890 mile trip in 3 days. if they drive 596 miles the first day and 612 miles the second d

Bingel [31]

They must travel 682 miles because 596+612=1,208 and 1,890-1,208=682

6 0

3 years ago

The diagram shows the cross-section of a wall of a cinema. It has to be painted. Work out the area that needs to be painted.

mestny [16]

Answer:

Area = 370 m²

Cost to paint = £105

Step-by-step explanation:

Area of the wall of a cinema hall = Area of a trapezoid (1)+ Area of a rectangle (2) + Area of a trapezoid (3)

Area of a trapezoid = $\frac{1}{2}(b_1+b_2)h$

where $b_1$ and $b_2$ are the parallel sides and h is the distance between these sides.

Area of trapezoid (1) = $\frac{1}{2}(11+12)\times 6$

= 69 m²

Area of the rectangle (2) = Length × Width

= 12 × 15

= 180 m²

Area of the trapezoid (3) = $\frac{1}{2}(12+10)\times 11$

= 121 m²

Now area of the wall = 69 + 180 + 121

= 370 m²

One tin covers the area = 25 m²

Number of tins required to paint the wall = $\frac{\text{Total area}}{\text{Area covered by one tin}}$

= $\frac{370}{25}$

= 14.8

Therefore, number of tins to be purchased = 15

Cost to paint the complete wall = 15 × £7

= £105

8 0

2 years ago