All categories

3 years ago

(x-yi)(3+5i) is the conjugate of 6+24i

Mathematics

1 answer:

Nataly_w [17]3 years ago

5 0

Answer:

x=-3

y=3

(-3-3i)(3+5i)

Step-by-step explanation:

$(x-yi)(3+5i)\\=3x+5xi-3yi+5y\\=(3x+5y)+(5x-3y)i\\$

and we have that must equal

6-24i

3x+5y=6

5x-3y=-24 and if we work it we found out that the solutions are

x=-3 and

y=3

You might be interested in

5). Jonathan bought a new jacket. The jacket originally cost $79.95 but is on sale for 20% off. How much

Harlamova29_29 [7]

Answer:c
Explanation: well 79.95-20%=63.96

5 0

2 years ago

¿Cuántas diagonales tiene un cuadrado de 64 centímetros de perímetro? Ayudenme pliss esq no entendí la pregunta :(

Ulleksa [173]

Answer:

English: the diagonal length and probably be 22.2

Spanish: la longitud diagonal y probablemente sea 22,2

5 0

3 years ago

Q2.What is the ratio of volumes of the two cylinders formed by rolling a sheet of dimensions lxb in two different ways? Q3.What

Kobotan [32]

Answer:

2. b : l

3. 20cm

4. 49 $cm^{2}$

5. $(2\pi+1):2\pi$

Step-by-step explanation:

<u>Solution 2:</u>

Let cylinder is rolled along 'l':

Height of cylinder , h = length of rectangle = l

Perimeter of base = b

Let 'r' be the radius of cylinder's base:

$2\pi r = b\\\Rightarrow r = \dfrac{b}{2\pi}$

Volume of a cylinder is given as:

$V = \pi r^{2} h$

Putting the values:

$V_1 = \pi (\dfrac{b}{2\pi})^2 l\\\Rightarrow V_1 = (\dfrac{b^2}{4\pi}) l$

Let cylinder is rolled along 'b':

Height of cylinder , h = length of rectangle = b

Perimeter of base = l

Let 'r' be the radius of cylinder's base:

$2\pi r = l\\\Rightarrow r = \dfrac{l}{2\pi}$

Volume of a cylinder is given as:

$V = \pi r^{2} h$

Putting the values:

$V_2 = \pi (\dfrac{l}{2\pi})^2 b\\\Rightarrow V_2 = (\dfrac{l^2}{4\pi}) b$

Taking ratio:

$V_1:V_2 = \dfrac{(\dfrac{b^2}{4\pi}) l}{(\dfrac{l^2}{4\pi}) b} = b:l$

Solution 3:

Rectangle is rolled along its length to make a cylinder, so height will be equal to its length.

$\therefore$ height of cylinder = 20 cm

Solution 4:

Side of square = 7 cm

Height of cylinder =Side of square = 7 cm

7 cm will be the circumference of the circle.

i.e. $2\pi r$ = 7 cm

Curved surface area of a cylinder:

$CSA = 2\pi rh$

Putting the above values:

CSA = 7 $\times$ 7 = 49 $cm^{2}$

Solution 5:

As calculated in above step:

CSA = $2\pi rh =$ 7 $\times$ 7 = 49 $cm^{2}$

Total surface area = $2\pi r^{2} + 2\pi r h$

Calculating value of r:

$2\pi r$ = 7 cm

$\Rightarrow 2 \pi r = 7\\\Rightarrow r = \dfrac{7}{2\pi}$

Total surface area =

$2\pi (\dfrac{7}{2\pi})^{2} + 49\\\Rightarrow \dfrac{49}{2\pi}+49\\\Rightarrow 49(\dfrac{1}{2\pi}+1) cm^2$

Ratio of TSA: CSA is

$49(\dfrac{1}{2\pi}+1) cm^2 : 49 cm^2\\\Rightarrow (\dfrac{1}{2\pi}+1):1\\\Rightarrow (2\pi+1): 2\pi$

5 0

3 years ago

F Jay makes $15 an hour, how long will it take him to earn $90?

Allushta [10]

OK my friend if you times 15 by each of the amount of hours you will find out which one it is but in this case it will be 15 times 6 hours will equal out to be $90

4 0

3 years ago

Read 2 more answers

Math Need Help

crimeas [40]

Hi there! The answer is 5/6 hours (which is 50 minutes)

To find the total time Ann spent on her papers, we must add the fractions.
$\frac{1}{3} + \frac{1}{2} = \frac{2}{6} + \frac{3}{6} = \frac{5}{6}$

In the first step, we had to make the denominators the same. We need to use the LCM of the numbers 2 and 3. LCM(2,3) = 6.

In the second step we added the fractions. Remember that we only need to add the numerators (the denominator remains the same).

~ Hope this helps you!

8 0

3 years ago

Read 2 more answers